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{"sheet":"bdt","index":0,"n_rows":453,"n_cols":41,"rows_kept":453}
[{"$nulls":6},"Black, Derman & Toy"]
[]
["Given:",null,"cc Spot","ln",{"$nulls":11},"90-day forward","90-day forward"]
["Node","Maturity","Yield","Volatility","df",{"$nulls":9},"df","df","Libor"]
[1,0.25,0.0217,{"$nulls":11},{"$f":"EXP(-C5*B5)","v":0.9945896887383608},{"$f":"O5","v":0.9945896887383608},{"$f":"4*(1/P5-1)","v":0.021758967835277865}]
[2,0.5,0.023177,0.1877,{"$f":"EXP(-B6*C6)","v":0.9884783880394524},"We take the market parameters as sacrosanct--we'll build a tree to match them.",{"$nulls":8},{"$f":"E6","v":0.9884783880394524},{"$f":"O6/O5","v":0.9938554554022567},{"$f":"4*(1/P6-1)","v":0.024730133801021736}]
[3,0.75,0.02442,0.1866,null,"  Volatilities are for the annualized discount rates to this node.",{"$nulls":8},{"$f":"EXP(-B7*C7)","v":0.9818517003554561},{"$f":"O7/O6","v":0.9932960722619948},0.026996694843416158]
[4,1,0.02555,0.2777,{"$f":"EXP(-B8*C8)","v":0.9747736390653005},"It's important to know what these volatilities mean. ",{"$nulls":8},{"$f":"E8","v":0.9747736390653005},0.9927911096068854,0.029044943385800437]
[5,1.25,0.026586,0.3019,null,"In this version, we use the term structure of future short rate volatilities.",{"$nulls":8},{"$f":"EXP(-B9*C9)","v":0.9673136330226542},0.9923469349768222,0.030848344478864753]
[6,1.5,0.027546,0.2976,{"$f":"EXP(-B10*C10)","v":0.9595229932867391},"  These come from caplet prices.  (In fact, dealers often quote caplet prices in terms of their implied",{"$nulls":8},{"$f":"EXP(-B10*C10)","v":0.9595229932867391},0.9919461077876356,0.03247713620380921]
[7,1.75,0.0276,0.33,null,"        volatilities from Black's Model.)",{"$nulls":8},{"$f":"EXP(-B11*C11)","v":0.9528478898281131},0.9930433105768929,0.02802169592810877]
[8,2,0.0276,0.44,{"$f":"EXP(-B12*C12)","v":0.9462958698523343},{"$nulls":9},{"$f":"EXP(-B12*C12)","v":0.9462958698523343},0.9931237503428163,0.027695439384306297]
[9,2.25,0.0274,0.49,{"$nulls":10},{"$f":"EXP(-B13*C13)","v":0.9402119033760095},0.9935707565993348,0.025883384179584468]
[10,2.5,0.0271,0.55,{"$f":"EXP(-B14*C14)","v":0.9344940678936807},{"$nulls":9},{"$f":"EXP(-B14*C14)","v":0.9344940678936807},0.993918567227454,0.024474571551712287]
[11,2.75,0.0268,0.62,null,null,"Compute swap rate:",null,"50 * c *",{"$f":"SUM(E6:E16)","v":5.727142978106113}," + 100 *",{"$f":"E16","v":0.9235780199686064}," = 100",null,0.9289503371438451,0.9940676661946811,0.023870945639054675]
[12,3,0.0265,0.7,{"$f":"EXP(-B16*C16)","v":0.9235780199686064},{"$nulls":7},{"$f":"100-100*E16","v":7.642198003139356},null,0.9235780199686064,0.9942167875284308,0.023267410263493993]
[{"$nulls":11},"c =",{"$f":"M16/(50*J15)","v":0.026687645244248902}]
[]
[null,"Assume: The short rate (I.e., the yield on a one-year T-Bill) follows a binomial process."]
[null,null,"In the spirit of the binomial model, the difference between the nodes in a time period is determined by the standard deviation: "]
[null,null,"Use continuous compounding/discounting in the tree."]
[]
[null,"So, the price of a 3-mo zero is:",null,null,{"$f":"100*EXP(-B5*C5)","v":99.45896887383608}]
[{"$nulls":11},"ru"]
[null,"Implying the tree:  (What are the 2 possible short rates in 1 quarter?)",{"$nulls":4},"That is, our tree will look like this:",null,null,{"$f":"C5","v":0.0217},null,"    where ru and rd are consistent with the 180-day spot rate and the vol on the caplet struck in 90 days."]
[{"$nulls":11},"rd","Of course this also means that they're consistent with the 90-day forward rate for the tenor starting in 90 days."]
[null,null,"Price of the 6-mo zero:",null,{"$f":"100*EXP(-B6*C6)","v":98.84783880394524}]
[]
[null,null,"What we know:"]
[{"$nulls":3},"From sigma(2), the ratio (of the logs) of the rates.",{"$nulls":3},"So if we find one of the rates, we can construct all of the others."]
[{"$nulls":7},"We'll find the lowest rate at each term in the tree and use sigma to fill in all the higher rates at that time."]
[{"$nulls":3},"Let's use solver to solve for rd:",{"$nulls":6},"Targets","Criterion:",{"$f":"ABS(K33-I33)","v":7.347011887759436e-12}]
[{"$nulls":4},"ru",{"$f":"F34*EXP(2*D6*SQRT(B5))","v":0.027045721928589866},null,"Model price:",{"$f":"B41","v":98.84783880395258},null,{"$f":"E27","v":98.84783880394524},null,"  Minimize the criterion cell by changing the lowest rate on the tree"]
[{"$nulls":4},"rd",0.022417207111214896,null,"   (from tree)"]
[]
[null,"Price Tree for 6 - Month Zero",{"$nulls":3},"This solves for the second time period of the short-rate tree, using information in today's yield curve."]
[{"$nulls":3},100,null,"The 6-mo spot rate is 2.318%, and in 3 months there is a 50% probability that the 3-month rate will be 2.696% and 50% probability that it will be 2.235%."]
[]
[null,null,{"$f":"100/(1+B5*F33)","v":99.32839794240931},null,null,"This allows us to solve for the price of the note one year from now in the up-state"]
[]
[null,{"$f":"0.5*(C39+C43)*EXP(-C5*B5)","v":98.84783880395258},null,100]
[]
[null,null,{"$f":"100/(1+B5*F34)","v":99.4426931380568},null,null,"This allows us to solve for the price of the note one year from now in the down-state"]
[]
[{"$nulls":3},100,null,"Note: All of these trees are in the \"Risk-Neutral World.\"  There is not enough information to separately identify the"]
[{"$nulls":6},"nodes and the probabilities, so we set the up and down probabilities equal to 50%."]
[]
[null,"To solve for the 3rd time in the tree, we also need to use the restriction that the tree recombines.  (This is consistent with the assumption that the volatility at this point does not depend on which node we're in.)"]
[]
[null,null,"Price of the 9-mo zero:",null,{"$f":"100*EXP(-B7*C7)","v":98.18517003554561},{"$nulls":5},"Target","Criterion"]
[{"$nulls":7},"p:",{"$f":"EXP(2*D7*SQRT(B5))","v":1.2051451305732288}]
[{"$nulls":7},"Pricing Eqn:",{"$f":"B65","v":98.18517003553889},null,{"$f":"E50","v":98.18517003554561},{"$f":"ABS(I52-K52)","v":6.721734280290548e-12},"  Minimize the criterion cell by changing Cell F53"]
[{"$nulls":4},"rd",0.022211100764787006]
[]
[{"$nulls":7},"Short rate tree (out 2 quarters)"]
[null,"Price Tree for 9-month Zero"]
[]
[{"$nulls":4},100]
[{"$nulls":9},{"$f":"J64*I51","v":0.032258842714404025}]
[{"$nulls":3},{"$f":"100/(1+$B$5*J59)","v":99.19998085508102}]
[{"$nulls":8},{"$f":"F33","v":0.027045721928589866}]
[null,null,{"$f":"0.5*(D60+D65)/(1+$B$5*I61)","v":98.60093624470265}]
[{"$nulls":4},100]
[{"$nulls":7},{"$f":"C5","v":0.0217},null,{"$f":"J70*I51","v":0.02676759993135438}]
[null,{"$f":"0.5*(C62+C68)*EXP(-B5*H64)","v":98.18517003553889},null,{"$f":"100/(1+$B$5*J64)","v":99.33525838611071}]
[]
[{"$nulls":8},{"$f":"F34","v":0.022417207111214896}]
[null,null,{"$f":"0.5*(D65+D71)/(1+$B$5*I67)","v":98.83760780472738},null,100]
[]
[{"$nulls":9},{"$f":"F53","v":0.022211100764787006}]
[{"$nulls":3},{"$f":"100/(1+$B$5*J70)","v":99.44778878561188}]
[]
[{"$nulls":4},100]
[]
[]
[]
[]
[null,null,"Price of the 4-Qtr Bill:",null,{"$f":"100*EXP(-B8*C8)","v":97.47736390653004},{"$nulls":6},"Criterion"]
[{"$nulls":7},"p:",{"$f":"EXP(2*D8*SQRT(B5))","v":1.3200901107658698},null,null,{"$f":"ABS(E78-B97)","v":8.839151632855646e-12}]
[]
[{"$nulls":4},"rd",0.018618205805139867]
[]
[{"$nulls":7},"Short rate tree (out 3 quarters)"]
[null,"Price Tree for 1 - Year Zero"]
[]
[]
[]
[{"$nulls":5},100]
[{"$nulls":10},{"$f":"K93*I79","v":0.0428300478454573}]
[{"$nulls":4},{"$f":"F88/(1+$B$5*K89)","v":98.94059242316449}]
[{"$nulls":9},{"$f":"J59","v":0.032258842714404025}]
[{"$nulls":3},{"$f":"0.5*(E90+E94)/(1+$B$5*J91)","v":98.27543646992955},null,100]
[{"$nulls":8},{"$f":"I61","v":0.027045721928589866},null,{"$f":"K99*I79","v":0.032444791076124954}]
[null,null,{"$f":"(0.5*(D92+D97))/(1+B5*I93)","v":97.7926601623195},null,{"$f":"F92/(1+$B$5*K93)","v":99.19540644058102}]
[]
[{"$nulls":7},{"$f":"H64","v":0.0217},null,{"$f":"J64","v":0.02676759993135438}]
[null,{"$f":"(0.5*(C94+C100))*EXP(-B5*H96)","v":97.47736390653888},null,{"$f":"0.5*(E94+E100)/(1+$B$5*J96)","v":98.63232040141307},null,100]
[]
[{"$nulls":8},{"$f":"I67","v":0.022417207111214896},null,{"$f":"K104*$I$79","v":0.02457770936356885}]
[null,null,{"$f":"(0.5*(D97+D103))/(1+B5*I99)","v":98.22257106371327},null,{"$f":"F97/(1+$B$5*K99)","v":99.38930960864823}]
[]
[{"$nulls":9},{"$f":"J70","v":0.022211100764787006}]
[{"$nulls":3},{"$f":"0.5*(E100+E105)/(1+$B$5*J102)","v":98.91375958527914},null,100]
[{"$nulls":10},{"$f":"F81","v":0.018618205805139867}]
[{"$nulls":4},{"$f":"F103/(1+$B$5*K104)","v":99.53670130249634}]
[]
[{"$nulls":5},100]
[]
[]
[]
[null,null,"Price of the 5-Qtr Zero",null,{"$f":"100*EXP(-B9*C9)","v":96.73136330226542},{"$nulls":5},"Target","Criterion"]
[{"$nulls":7},"p:",{"$f":"EXP(2*D9*SQRT(B5))","v":1.352425977349392},null,null,{"$f":"ABS(K113-I113)","v":6.963318810448982e-13}]
[{"$nulls":7},"Price Eqn:",{"$f":"B130","v":96.73136330226473},null,{"$f":"E111","v":96.73136330226542}]
[{"$nulls":4},"rd",0.03037445293913992]
[]
[]
[null,"           Price Tree for 5 - Quarter Zero",{"$nulls":6},"     Short rate tree (out 4 quarters)"]
[]
[{"$nulls":6},100]
[]
[{"$nulls":5},{"$f":"0.5*(G119+G123)/(1+$B$5*M121)","v":97.52253531243038},{"$nulls":6},{"$f":"M125*I112","v":0.10161609025576053}]
[{"$nulls":11},{"$f":"K89","v":0.0428300478454573}]
[{"$nulls":4},{"$f":"0.5*(F121+F125)/(1+L122*$B$5)","v":96.80286459435156},null,100]
[{"$nulls":10},{"$f":"J91","v":0.032258842714404025}]
[{"$nulls":3},{"$f":"0.5*(E123+E127)/(1+K124*$B$5)","v":96.42454907466386},null,{"$f":"0.5*(G123+G127)/(1+$B$5*M125)","v":98.15622953734945},{"$nulls":6},{"$f":"M130*I112","v":0.07513615677134287}]
[{"$nulls":9},{"$f":"I93","v":0.027045721928589866},null,{"$f":"K93","v":0.032444791076124954}]
[null,null,{"$f":"0.5*(D125+D130)/(1+$B$5*J126)","v":96.8385132510311},null,{"$f":"0.5*(F125+F130)/(1+L126*$B$5)","v":97.6015057361796},null,100]
[]
[{"$nulls":8},{"$f":"H96","v":0.0217},null,{"$f":"J96","v":0.02676759993135438}]
[null,{"$f":"0.5*(C127+C133)*EXP(-$B$5*I129)","v":96.73136330226473},null,{"$f":"0.5*(E127+E133)/(1+-$B$5*K129)","v":98.5620111780811},null,{"$f":"0.5*(G127+G133)/(1+$B$5*M130)","v":98.63011216617252},{"$nulls":6},{"$f":"M136*I112","v":0.055556576130400555}]
[]
[{"$nulls":9},{"$f":"I99","v":0.022417207111214896},null,{"$f":"K99","v":0.02457770936356885}]
[null,null,{"$f":"0.5*(D130+D136)/(1+$B$5*J132)","v":97.67660066487659},null,{"$f":"0.5*(F130+F136)/(1+L132*$B$5)","v":98.2033823781603},null,100]
[]
[{"$nulls":10},{"$f":"J102","v":0.022211100764787006}]
[{"$nulls":3},{"$f":"0.5*(E133+E138)/(1+$B$5*K135)","v":97.88600844518406},null,{"$f":"0.5*(G133+G138)/(1+$B$5*M136)","v":98.98345968545297},{"$nulls":6},{"$f":"M140*$I$112","v":0.04107919920266942}]
[{"$nulls":11},{"$f":"K104","v":0.018618205805139867}]
[{"$nulls":4},{"$f":"0.5*(F136+F140)/(1+L137*$B$5)","v":98.65571251072723},null,100]
[]
[{"$nulls":5},{"$f":"0.5*(G138+G142)/(1+$B$5*M140)","v":99.24636151569021},{"$nulls":6},{"$f":"F114","v":0.03037445293913992}]
[]
[{"$nulls":6},100]
[]
[]
[{"$nulls":9},"     Short rate tree (out 5 quarters)"]
[null,"           Price Tree for 6 - Quarter Zero"]
[null,null,"Price",null,{"$f":"100*EXP(-B10*C10)","v":95.9522993286739},{"$nulls":3},"Model",null,"Target","Criterion"]
[{"$nulls":7},"p:",{"$f":"EXP(2*D10*SQRT(B5))","v":1.346623030922977},null,null,{"$f":"ABS(K149-I149)","v":1.9028334463655483E-11}]
[{"$nulls":7},"0 Price:",{"$f":"B164","v":95.95229932865487},null,{"$f":"E147","v":95.9522993286739}]
[{"$nulls":4},"rd",0.00246933871649395]
[{"$nulls":7},100]
[]
[{"$nulls":6},{"$f":"0.5*(H151+H154)/(1+$B$5*O153)","v":99.72737526752123},{"$nulls":7},{"$f":"O157*$I$148","v":0.010934800269131737}]
[{"$nulls":7},100]
[{"$nulls":5},{"$f":"0.5*(G153+G157)/(1+$B$5*N155)","v":97.29081320197966},{"$nulls":7},{"$f":"M121","v":0.10161609025576053}]
[]
[{"$nulls":4},{"$f":"0.5*(F155+F159)/(1+$B$5*M157)","v":96.60249752848736},null,{"$f":"0.5*(H154+H158)/(1+$B$5*O157)","v":99.79740716413244},{"$nulls":5},{"$f":"L122","v":0.0428300478454573},null,{"$f":"O161*$I$148","v":0.008120164305846613}]
[{"$nulls":7},100,{"$nulls":3},{"$f":"K124","v":0.032258842714404025}]
[{"$nulls":3},{"$f":"0.5*(E157+E161)/(1+$B$5*L158)","v":96.25070668586774},null,{"$f":"0.5*(G157+G161)/(1+$B$5*N159)","v":97.98292665056297},{"$nulls":7},{"$f":"M125","v":0.07513615677134287}]
[{"$nulls":10},{"$f":"J126","v":0.027045721928589866}]
[null,null,{"$f":"0.5*(D159+D164)/(1+$B$5*K160)","v":96.03668039175679},null,{"$f":"0.5*(F159+F164)/(1+$B$5*M161)","v":97.45138404731294},null,{"$f":"0.5*(H158+H163)/(1+$B$5*O161)","v":99.84947640585936},{"$nulls":5},{"$f":"L126","v":0.032444791076124954},null,{"$f":"O167*$I$148","v":0.006030020369012286}]
[]
[{"$nulls":7},100,null,{"$f":"I129","v":0.0217},null,{"$f":"K129","v":0.02676759993135438}]
[null,{"$f":"0.5*(C161+C167)*EXP(-$B$5*J163)","v":95.95229932865487},null,{"$f":"0.5*(E161+E167)/(1+$B$5*L163)","v":97.12134477405601},null,{"$f":"0.5*(G161+G167)/(1+$B$5*N164)","v":98.50073634181004},{"$nulls":7},{"$f":"M130","v":0.055556576130400555}]
[]
[{"$nulls":10},{"$f":"J132","v":0.022417207111214896}]
[null,null,{"$f":"0.5*(D164+D170)/(1+$B$5*K166)","v":96.91182976295951},null,{"$f":"0.5*(F164+F170)/(1+$B$5*M167)","v":98.09115815165264},null,{"$f":"0.5*(H163+H169)/(1+$B$5*O167)","v":99.88817810649783},{"$nulls":5},{"$f":"L132","v":0.02457770936356885},null,{"$f":"O172*$I$148","v":4.477882993638764E-3}]
[]
[{"$nulls":7},100,{"$nulls":3},{"$f":"K135","v":0.022211100764787006}]
[{"$nulls":3},{"$f":"0.5*(E167+E172)/(1+$B$5*L169)","v":97.78856103152455},null,{"$f":"0.5*(G167+G172)/(1+$B$5*N170)","v":98.88700794958883},{"$nulls":7},{"$f":"M136","v":0.04107919920266942}]
[]
[{"$nulls":4},{"$f":"0.5*(F170+F174)/(1+$B$5*M172)","v":98.57195970275383},null,{"$f":"0.5*(H169+H173)/(1+$B$5*O172)","v":99.91693734173839},{"$nulls":5},{"$f":"L137","v":0.018618205805139867},null,{"$f":"O176*$I$148","v":3.3252683867805366E-3}]
[{"$nulls":7},100]
[{"$nulls":5},{"$f":"0.5*(G172+G176)/(1+$B$5*N174)","v":99.17452797209972},{"$nulls":7},{"$f":"M140","v":0.03037445293913992}]
[]
[{"$nulls":6},{"$f":"0.5*(H173+H177)/(1+$B$5*O176)","v":99.93830461878602},{"$nulls":7},{"$f":"F150","v":0.00246933871649395}]
[{"$nulls":7},100]
{"$rows_empty":9}
[{"$nulls":7},"p:",{"$f":"EXP(2*D11*SQRT(B5))","v":1.3909681284637803},null,"Model","Bogie","Criterion"]
["Price for 7-quarter 0:",null,{"$f":"100*EXP(-B11*C11)","v":95.2847889828113},"Vol on the forward rate:",null,{"$f":"D11","v":0.33},null,"rd",0.00963389613838258,"0 Price",{"$f":"B197","v":95.28478898281126},{"$f":"C188","v":95.2847889828113},{"$f":"ABS(L188-K188)","v":4.263256414560601e-14}]
[]
[{"$nulls":8},100]
[{"$nulls":7},{"$f":"0.5*(I190+I192)/(1+Q195/4)","v":98.28551162207343}]
[{"$nulls":6},{"$f":"0.5*(H191+H193)/(1+P196/4)","v":98.25487893845238},null,100]
[{"$nulls":5},{"$f":"0.5*(G192+G194)/(1+O197/4)","v":96.05404083376118},null,{"$f":"0.5*(I192+I194)/(1+Q197/4)","v":98.76144499316118}]
[{"$nulls":4},{"$f":"0.5*(F193+F195)/(1+N198/4)","v":95.54599127847538},null,{"$f":"0.5*(H193+H195)/(1+P198/4)","v":98.73352077046695},null,100]
[{"$nulls":3},{"$f":"0.5*(E194+E196)/(1+M199/4)","v":95.34530567163516},null,{"$f":"0.5*(G194+G196)/(1+O199/4)","v":97.084061412139},null,{"$f":"0.5*(I194+I196)/(1+Q199/4)","v":99.10646275334821},{"$nulls":8},{"$f":"Q197*$I$187","v":0.06977583367604019}]
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["Price for 10-quarter 0:",null,{"$f":"100*EXP(-B14*C14)","v":93.44940678936807}]
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[]
[]
["Price for 11-quarter 0:",null,{"$f":"100*EXP(-B15*C15)","v":92.89503371438451},{"$nulls":4},"p:",{"$f":"EXP(D15*2*SQRT(B5))","v":1.858928041846342},null,"Model","Target","Criterion"]
[{"$nulls":7},"rd",6.9456901280441174E-4,"0 Price:",{"$f":"A306","v":92.89503370583724},{"$f":"C290","v":92.89503371438451},{"$f":"ABS(K291-L291)","v":8.5472748878601124E-9}]
[]
[]
[]
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[{"$nulls":7},{"$f":"0.5*(I312+I314)/(1+U314/4)","v":99.78454311595641},null,{"$f":"0.5*(K312+K314)/(1+W314/4)","v":99.84333559633558},null,100,{"$nulls":7},{"$f":"S284","v":0.00963389613838258},null,{"$f":"U284","v":1.6448328238718396E-3},null,{"$f":"X315*$I$290","v":2.4001620328538446E-3}]
[{"$nulls":8},{"$f":"0.5*(J313+J315)/(1+V315/4)","v":99.85219440363186},null,{"$f":"0.5*(L313+L315)/(1+X315/4)","v":99.96773157050397},{"$nulls":9},{"$f":"T285","v":0.000505644297483289},null,{"$f":"V285","v":4.4287845345051076E-3}]
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[{"$nulls":11},100,{"$nulls":11},{"$f":"I291","v":6.9456901280441174E-4}]
[]
[]
["Price for 12-quarter 0:",null,{"$f":"100*EXP(-B16*C16)","v":92.35780199686064},{"$nulls":7},"Model","Market","Criterion"]
[{"$nulls":7},"rd",2.4801309040022994E-4,"Eqn 2:",{"$f":"A336","v":92.35780194994184},{"$f":"C320","v":92.35780199686064},{"$f":"ABS(K321-L321)","v":4.6918799512241094E-8}]
[{"$nulls":7},"p:",{"$f":"EXP(2*D16*SQRT(B5))","v":2.0137527074704766}]
[]
[{"$nulls":12},100]
[{"$nulls":11},{"$f":"0.5*(M324+M326)*EXP(-Z328/4)","v":87.20357985465334},null,null,"2.75-year Libor Tree (quarterly compounded rates)"]
[{"$nulls":10},{"$f":"0.5*(L325+L327)*EXP(-Y329/4)","v":82.9088746159674},null,100]
[{"$nulls":9},{"$f":"0.5*(K326+K328)*EXP(-X330/4)","v":79.35414298990841},null,{"$f":"0.5*(M326+M328)*EXP(-Z330/4)","v":93.42652900159996}]
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[{"$nulls":12},100,{"$nulls":10},{"$f":"W316","v":2.5551863973987538E-3},null,{"$f":"Z350*$I$322","v":4.9943703228158315E-4}]
[{"$nulls":24},{"$f":"X317","v":6.9456901280441174E-4}]
[{"$nulls":25},{"$f":"I321","v":2.4801309040022994E-4}]
[]
[]
[]
[]
[{"$nulls":14},"Receive fixed, pay floating swap (valuation tree only -- does not show actual cash flows).",{"$nulls":11},"Actual"]
[{"$nulls":26},"Cash Flow"]
[{"$nulls":14},0,0.25,0.5,0.75,1,1.25,1.5,1.75,2,2.25,2.5,2.75," <---3"]
[]
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["3-year Swap:",null,"Swap Rate:",{"$f":"M17","v":0.026687645244248902},"Notional Principal:",null,{"v":10000000,"d":"10,000,000"},{"$nulls":16},{"$f":"(0.5*(Y360+Y362)-X330*$G$361*$F$362+$F$363*$G$361*$D$361)/(1+X330*$F$362)","v":{"v":-1761329.1536292224,"d":"-1,761,329"}},null,{"$f":"AA361/(1+Z330*$F$362)","v":{"v":-511716.15963516716,"d":"-511,716"}},{"$f":"$F$363*$G$361*$D$361-$F$362*$G$361*Z330","v":{"v":-546510.2204217734,"d":"-546,510"}}]
[{"$nulls":4},"Float Tenor:",0.25,{"$nulls":16},{"$f":"(0.5*(X361+X363)-W331*$G$361*$F$362)/(1+W331*$F$362)","v":{"v":-1442539.2486576803,"d":"-1,442,539"}},null,{"$f":"(0.5*(Z361+Z363)-Y331*$G$361*$F$362)/(1+Y331*$F$362)","v":{"v":-779048.6533896216,"d":"-779,049"}}]
[{"$nulls":4},"Fixed Tenor:",0.5,{"$nulls":15},{"$f":"(0.5*(W362+W364)-V332*$G$361*$F$362+$F$363*$G$361*$D$361)/(1+V332*$F$362)","v":{"v":-1698468.0922458668,"d":"-1,698,468"}},null,{"$f":"(0.5*(Y362+Y364)-X332*$G$361*$F$362+$F$363*$G$361*$D$361)/(1+X332*$F$362)","v":{"v":-906445.8257111154,"d":"-906,446"}},null,{"$f":"AA363/(1+Z332*$F$362)","v":{"v":-197544.05710155203,"d":"-197,544"}},{"$f":"$F$363*$G$361*$D$361-$F$362*$G$361*Z332","v":{"v":-204214.17971747552,"d":"-204,214"}}]
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[{"$nulls":15},{"$f":"(0.5*(Q368+Q370)-P338*$G$361*$F$362+$F$363*$G$361*$D$361)/(1+P338*$F$362)","v":{"v":-89484.59663001422,"d":"-89,485"}},null,{"$f":"(0.5*(S368+S370)-R338*$G$361*$F$362+$F$363*$G$361*$D$361)/(1+R338*$F$362)","v":{"v":-38505.200233211006,"d":"-38,505"}},null,{"$f":"(0.5*(U368+U370)-T338*$G$361*$F$362+$F$363*$G$361*$D$361)/(1+T338*$F$362)","v":{"v":108867.62892854043,"d":"108,868"}},null,{"$f":"(0.5*(W368+W370)-V338*$G$361*$F$362+$F$363*$G$361*$D$361)/(1+V338*$F$362)","v":{"v":101093.87925106249,"d":"101,094"}},null,{"$f":"(0.5*(Y368+Y370)-X338*$G$361*$F$362+$F$363*$G$361*$D$361)/(1+X338*$F$362)","v":{"v":64119.430305147085,"d":"64,119"}},null,{"$f":"AA369/(1+Z338*$F$362)","v":{"v":91711.31334199093,"d":"91,711"}},{"$f":"$F$363*$G$361*$D$361-$F$362*$G$361*Z338","v":{"v":92090.51859896294,"d":"92,091"}}]
[{"$nulls":10},"The value in Cell O370 should be 0, as I used the ",{"$nulls":3},{"$f":"(0.5*(P369+P371)-O339*$G$361*$F$362)/(1+O339*$F$362)","v":{"v":4365.4423535677815,"d":"4,365"}},null,{"$f":"(0.5*(R369+R371)-Q339*$G$361*$F$362)/(1+Q339*$F$362)","v":{"v":22841.74563178872,"d":"22,842"}},null,{"$f":"(0.5*(T369+T371)-S339*$G$361*$F$362)/(1+S339*$F$362)","v":{"v":59961.56056870151,"d":"59,962"}},null,{"$f":"(0.5*(V369+V371)-U339*$G$361*$F$362)/(1+U339*$F$362)","v":{"v":106075.99475186752,"d":"106,076"}},null,{"$f":"(0.5*(X369+X371)-W339*$G$361*$F$362)/(1+W339*$F$362)","v":{"v":91548.57744373263,"d":"91,549"}},null,{"$f":"(0.5*(Z369+Z371)-Y339*$G$361*$F$362)/(1+Y339*$F$362)","v":{"v":63403.35158699091,"d":"63,403"}}]
[{"$nulls":10},"prevailing market swap rate.  The difference from 0 suggests",{"$nulls":4},{"$f":"(0.5*(Q370+Q372)-P340*$G$361*$F$362+$F$363*$G$361*$D$361)/(1+P340*$F$362)","v":{"v":207057.81427341813,"d":"207,058"}},null,{"$f":"(0.5*(S370+S372)-R340*$G$361*$F$362+$F$363*$G$361*$D$361)/(1+R340*$F$362)","v":{"v":218332.4005079631,"d":"218,332"}},null,{"$f":"(0.5*(U370+U372)-T340*$G$361*$F$362+$F$363*$G$361*$D$361)/(1+T340*$F$362)","v":{"v":290504.0023631817,"d":"290,504"}},null,{"$f":"(0.5*(W370+W372)-V340*$G$361*$F$362+$F$363*$G$361*$D$361)/(1+V340*$F$362)","v":{"v":242068.5972563696,"d":"242,069"}},null,{"$f":"(0.5*(Y370+Y372)-X340*$G$361*$F$362+$F$363*$G$361*$D$361)/(1+X340*$F$362)","v":{"v":155074.00666778718,"d":"155,074"}},null,{"$f":"AA371/(1+Z340*$F$362)","v":{"v":112674.21209726525,"d":"112,674"}},{"$f":"$F$363*$G$361*$D$361-$F$362*$G$361*Z340","v":{"v":112905.56227055544,"d":"112,906"}}]
[{"$nulls":10},"that there is an error somewhere in building the tree.",{"$nulls":5},{"$f":"(0.5*(R371+R373)-Q341*$G$361*$F$362)/(1+Q341*$F$362)","v":{"v":238804.29498191437,"d":"238,804"}},null,{"$f":"(0.5*(T371+T373)-S341*$G$361*$F$362)/(1+S341*$F$362)","v":{"v":235398.38996474733,"d":"235,398"}},null,{"$f":"(0.5*(V371+V373)-U341*$G$361*$F$362)/(1+U341*$F$362)","v":{"v":231095.39396608362,"d":"231,095"}},null,{"$f":"(0.5*(X371+X373)-W341*$G$361*$F$362)/(1+W341*$F$362)","v":{"v":168989.8647899001,"d":"168,990"}},null,{"$f":"(0.5*(Z371+Z373)-Y341*$G$361*$F$362)/(1+Y341*$F$362)","v":{"v":96959.21713442322,"d":"96,959"}}]
[{"$nulls":17},{"$f":"(0.5*(S372+S374)-R342*$G$361*$F$362+$F$363*$G$361*$D$361)/(1+R342*$F$362)","v":{"v":372983.74640925427,"d":"372,984"}},null,{"$f":"(0.5*(U372+U374)-T342*$G$361*$F$362+$F$363*$G$361*$D$361)/(1+T342*$F$362)","v":{"v":390523.7622563347,"d":"390,524"}},null,{"$f":"(0.5*(W372+W374)-V342*$G$361*$F$362+$F$363*$G$361*$D$361)/(1+V342*$F$362)","v":{"v":315473.8941828499,"d":"315,474"}},null,{"$f":"(0.5*(Y372+Y374)-X342*$G$361*$F$362+$F$363*$G$361*$D$361)/(1+X342*$F$362)","v":{"v":205188.95456492127,"d":"205,189"}},null,{"$f":"AA373/(1+Z342*$F$362)","v":{"v":123116.47479964934,"d":"123,116"}},{"$f":"$F$363*$G$361*$D$361-$F$362*$G$361*Z342","v":{"v":123242.00705564466,"d":"123,242"}}]
[{"$nulls":18},{"$f":"(0.5*(T373+T375)-S343*$G$361*$F$362)/(1+S343*$F$362)","v":{"v":340255.8235132813,"d":"340,256"}},null,{"$f":"(0.5*(V373+V375)-U343*$G$361*$F$362)/(1+U343*$F$362)","v":{"v":300351.31819845823,"d":"300,351"}},null,{"$f":"(0.5*(X373+X375)-W343*$G$361*$F$362)/(1+W343*$F$362)","v":{"v":212129.67195821437,"d":"212,130"}},null,{"$f":"(0.5*(Z373+Z375)-Y343*$G$361*$F$362)/(1+Y343*$F$362)","v":{"v":114431.25909701547,"d":"114,431"}}]
[{"$nulls":19},{"$f":"(0.5*(U374+U376)-T344*$G$361*$F$362+$F$363*$G$361*$D$361)/(1+T344*$F$362)","v":{"v":447027.69171521364,"d":"447,028"}},null,{"$f":"(0.5*(W374+W376)-V344*$G$361*$F$362+$F$363*$G$361*$D$361)/(1+V344*$F$362)","v":{"v":354243.3749030375,"d":"354,243"}},null,{"$f":"(0.5*(Y374+Y376)-X344*$G$361*$F$362+$F$363*$G$361*$D$361)/(1+X344*$F$362)","v":{"v":232779.59796994648,"d":"232,780"}},null,{"$f":"AA375/(1+Z344*$F$362)","v":{"v":128309.96653906725,"d":"128,310"}},{"$f":"$F$363*$G$361*$D$361-$F$362*$G$361*Z344","v":{"v":128374.93362937133,"d":"128,375"}}]
[{"$nulls":20},{"$f":"(0.5*(V375+V377)-U345*$G$361*$F$362)/(1+U345*$F$362)","v":{"v":339726.2377651984,"d":"339,726"}},null,{"$f":"(0.5*(X375+X377)-W345*$G$361*$F$362)/(1+W345*$F$362)","v":{"v":236173.62212280382,"d":"236,174"}},null,{"$f":"(0.5*(Z375+Z377)-Y345*$G$361*$F$362)/(1+Y345*$F$362)","v":{"v":123525.93705910578,"d":"123,526"}}]
[{"$nulls":21},{"$f":"(0.5*(W376+W378)-V346*$G$361*$F$362+$F$363*$G$361*$D$361)/(1+V346*$F$362)","v":{"v":375015.02496432874,"d":"375,015"}},null,{"$f":"(0.5*(Y376+Y378)-X346*$G$361*$F$362+$F$363*$G$361*$D$361)/(1+X346*$F$362)","v":{"v":247986.04345792052,"d":"247,986"}},null,{"$f":"AA377/(1+Z346*$F$362)","v":{"v":130890.95887551451,"d":"130,891"}},{"$f":"$F$363*$G$361*$D$361-$F$362*$G$361*Z346","v":{"v":130923.86953132438,"d":"130,924"}}]
[{"$nulls":22},{"$f":"(0.5*(X377+X379)-W347*$G$361*$F$362)/(1+W347*$F$362)","v":{"v":249603.00895520303,"d":"249,603"}},null,{"$f":"(0.5*(Z377+Z379)-Y347*$G$361*$F$362)/(1+Y347*$F$362)","v":{"v":128262.7584637915,"d":"128,263"}}]
[{"$nulls":23},{"$f":"(0.5*(Y378+Y380)-X348*$G$361*$F$362+$F$363*$G$361*$D$361)/(1+X348*$F$362)","v":{"v":256384.07294476355,"d":"256,384"}},null,{"$f":"AA379/(1+Z348*$F$362)","v":{"v":132173.1306015168,"d":"132,173"}},{"$f":"$F$363*$G$361*$D$361-$F$362*$G$361*Z348","v":{"v":132189.63364054056,"d":"132,190"}}]
[{"$nulls":24},{"$f":"(0.5*(Z379+Z381)-Y349*$G$361*$F$362)/(1+Y349*$F$362)","v":{"v":130732.42151808945,"d":"130,732"}}]
[{"$nulls":25},{"$f":"AA381/(1+Z350*$F$362)","v":{"v":132809.9588431618,"d":"132,810"}},{"$f":"$F$363*$G$361*$D$361-$F$362*$G$361*Z350","v":{"v":132818.19349524393,"d":"132,818"}}]
[]
[]
[{"$nulls":14},"Next we consider a Bermudan swaption with a 2-year term to enter this swap.  Since this is a receive fixed,  pay floating swap, this is called a receiver swaption.  ",{"$nulls":12},"Valuation Tree for the 3-year Coupon Bond with coupon = swap rate.",{"$nulls":12},"Terminal"]
[{"$nulls":14},"This allows you to enter the swap at any reset date over the first 2 years of its life.  Cash flows start in the period when you exercise.",{"$nulls":25},"Cash"]
[{"$nulls":14},"I highlighted the cells in which it is optimal to exercise the Bermudan option.",{"$nulls":25},"Flow"]
[{"$nulls":14},"A swaption where you have the option to entr a reveive floating, pay fixed swap is called a payer swaption.",{"$nulls":24},{"$f":"AO387/(1+Z328/4)","v":89.13024153937828},{"$f":"100*(1+0.5*$D$361)","v":101.33438226221246}]
[{"$nulls":14},"The Bermudan feature allows you to exercise the swaption on any reset date.  This swaption has a 2-year term and the underlying is a 3-year swap with swap rate",{"$nulls":10},{"$f":"D361","v":0.026687645244248902},{"$nulls":12},{"$f":"50*$D$361+0.5*(AN387+AN389)/(1+Y329*$B$5)","v":86.08913179771356}]
[{"$nulls":22},{"$f":"IF(W362>0.5*(X388+X390)/(1+W331*$B$5),W362,0.5*(X388+X390)/(1+W331*$B$5))","v":{"v":0,"d":"0.00"}},{"$nulls":14},{"$f":"0.5*(AM388+AM390)/(1+X330*$B$5)","v":82.3867084637078},null,{"$f":"AO389/(1+Z330/4)","v":94.88283840364835},{"$f":"100*(1+0.5*$D$361)","v":101.33438226221246}]
[{"$nulls":21},{"$f":"IF(V363>0.5*(W389+W391)/(1+V332*$B$5),V363,0.5*(W389+W391)/(1+V332*$B$5))","v":{"v":0,"d":"0.00"}},{"$nulls":14},{"$f":"50*$D$361+0.5*(AL389+AL391)/(1+W331*$B$5)","v":86.90898977563566},null,{"$f":"50*$D$361+0.5*(AN389+AN391)/(1+Y331*$B$5)","v":93.54389572831624}]
[{"$nulls":20},{"$f":"IF(U364>0.5*(V390+V392)/(1+U333*$B$5),U364,0.5*(V390+V392)/(1+U333*$B$5))","v":{"v":0,"d":"0.00"}},null,{"$f":"IF(W364>0.5*(X390+X392)/(1+W333*$B$5),W364,0.5*(X390+X392)/(1+W333*$B$5))","v":{"v":0,"d":"0.00"}},{"$nulls":12},{"$f":"0.5*(AK390+AK392)/(1+V332*$B$5)","v":83.01531907754136},null,{"$f":"0.5*(AM390+AM392)/(1+X332*$B$5)","v":90.93554174288887},null,{"$f":"AO391/(1+Z332/4)","v":98.02455942898449},{"$f":"100*(1+0.5*$D$361)","v":101.33438226221246}]
[{"$nulls":19},{"$f":"IF(T365>0.5*(U391+U393)/(1+T334*$B$5),T365,0.5*(U391+U393)/(1+T334*$B$5))","v":{"v":0,"d":"0.00"}},null,{"$f":"IF(V365>0.5*(W391+W393)/(1+V334*$B$5),V365,0.5*(W391+W393)/(1+V334*$B$5))","v":{"v":0,"d":"0.00"}},{"$nulls":12},{"$f":"50*$D$361+0.5*(AJ391+AJ393)/(1+U333*$B$5)","v":87.81996521290603},null,{"$f":"50*$D$361+0.5*(AL391+AL393)/(1+W333*$B$5)","v":94.11101339353536},null,{"$f":"50*$D$361+0.5*(AN391+AN393)/(1+Y333*$B$5)","v":97.79003806282137}]
[{"$nulls":18},{"$f":"IF(S366>0.5*(T392+T394)/(1+S335*$B$5),S366,0.5*(T392+T394)/(1+S335*$B$5))","v":{"v":12188.803958378883,"d":"12,188.80"}},null,{"$f":"IF(U366>0.5*(V392+V394)/(1+U335*$B$5),U366,0.5*(V392+V394)/(1+U335*$B$5))","v":{"v":0,"d":"0.00"}},null,{"$f":"IF(W366>0.5*(X392+X394)/(1+W335*$B$5),W366,0.5*(X392+X394)/(1+W335*$B$5))","v":{"v":0,"d":"0.00"}},{"$nulls":10},{"$f":"0.5*(AI392+AI394)/(1+T334*$B$5)","v":91.54676571117813},null,{"$f":"0.5*(AK392+AK394)/(1+V334*$B$5)","v":92.97314864951728},null,{"$f":"0.5*(AM392+AM394)/(1+X334*$B$5)","v":96.06101896484532},null,{"$f":"AO393/(1+Z334/4)","v":99.6632956664883},{"$f":"100*(1+0.5*$D$361)","v":101.33438226221246}]
[{"$nulls":17},{"$f":"IF(R367>0.5*(S393+S395)/(1+R336*$B$5),R367,0.5*(S393+S395)/(1+R336*$B$5))","v":{"v":38834.930835298605,"d":"38,834.93"}},null,{"$f":"IF(T367>0.5*(U393+U395)/(1+T336*$B$5),T367,0.5*(U393+U395)/(1+T336*$B$5))","v":{"v":24996.897218329963,"d":"24,996.90"}},null,{"$f":"IF(V367>0.5*(W393+W395)/(1+V336*$B$5),V367,0.5*(W393+W395)/(1+V336*$B$5))","v":{"v":0,"d":"0.00"}},{"$nulls":10},{"$f":"0.5*(AH393+AH395)/(1+S335*$B$5)","v":92.29479437770176},null,{"$f":"50*$D$361+0.5*(AJ393+AJ395)/(1+U335*$B$5)","v":95.77408900861857},null,{"$f":"50*$D$361+0.5*(AL393+AL395)/(1+W335*$B$5)","v":98.40120119990671},null,{"$f":"50*$D$361+0.5*(AN393+AN395)/(1+Y335*$B$5)","v":100.0993130497659}]
[{"$nulls":16},{"$f":"IF(Q368>0.5*(R394+R396)/(1+Q337*$B$5),Q368,0.5*(R394+R396)/(1+Q337*$B$5))","v":{"v":84177.9388242496,"d":"84,177.94"}},null,{"$f":"IF(S368>0.5*(T394+T396)/(1+S337*$B$5),S368,0.5*(T394+T396)/(1+S337*$B$5))","v":{"v":66312.70868509378,"d":"66,312.71"}},null,{"$f":"IF(U368>0.5*(V394+V396)/(1+U337*$B$5),U368,0.5*(V394+V396)/(1+U337*$B$5))","v":{"v":50095.28389293453,"d":"50,095.28"}},null,{"$f":"IF(W368>0.5*(X394+X396)/(1+W337*$B$5),W368,0.5*(X394+X396)/(1+W337*$B$5))","v":{"v":0,"d":"0.00"}},{"$nulls":8},{"$f":"0.5*(AG394+AG396)/(1+R336*$B$5)","v":94.59051373923542},null,{"$f":"0.5*(AI394+AI396)/(1+T336*$B$5)","v":97.73214112203608},null,{"$f":"0.5*(AK394+AK396)/(1+V336*$B$5)","v":98.27497809254425},null,{"$f":"0.5*(AM394+AM396)/(1+X336*$B$5)","v":98.99770903817807},null,{"$f":"AO395/(1+Z336/4)","v":100.49759847366602},{"$f":"100*(1+0.5*$D$361)","v":101.33438226221246}]
[{"$nulls":15},{"$f":"IF(P369>0.5*(Q395+Q397)/(1+P338*$B$5),P369,0.5*(Q395+Q397)/(1+P338*$B$5))","v":{"v":139624.98062992128,"d":"139,624.98"}},null,{"$f":"IF(R369>0.5*(S395+S397)/(1+R338*$B$5),R369,0.5*(S395+S397)/(1+R338*$B$5))","v":{"v":130878.6882574777,"d":"130,878.69"}},null,{"$f":"IF(T369>0.5*(U395+U397)/(1+T338*$B$5),T369,0.5*(U395+U397)/(1+T338*$B$5))","v":{"v":110119.7611897054,"d":"110,119.76"}},null,{"$f":"IF(V369>0.5*(W395+W397)/(1+V338*$B$5),V369,0.5*(W395+W397)/(1+V338*$B$5))","v":{"v":101093.87925106249,"d":"101,093.88"}},{"$nulls":8},{"$f":"50*$D$361+0.5*(AF395+AF397)/(1+Q337*$B$5)","v":97.66027269347734},null,{"$f":"50*$D$361+0.5*(AH395+AH397)/(1+S337*$B$5)","v":98.91189121535803},null,{"$f":"50*$D$361+0.5*(AJ395+AJ397)/(1+U337*$B$5)","v":100.08699375739015},null,{"$f":"50*$D$361+0.5*(AL395+AL397)/(1+W337*$B$5)","v":100.86327907049886},null,{"$f":"50*$D$361+0.5*(AN395+AN397)/(1+Y337*$B$5)","v":101.32527905543856}]
[{"$nulls":14},{"$f":"IF(O370>0.5*(P396+P398)/(1+O339*$B$5),O370,0.5*(P396+P398)/(1+O339*$B$5))","v":{"v":196855.51292016753,"d":"196,855.51"}},null,{"$f":"IF(Q370>0.5*(R396+R398)/(1+Q339*$B$5),Q370,0.5*(R396+R398)/(1+Q339*$B$5))","v":{"v":196960.15163579374,"d":"196,960.15"}},null,{"$f":"IF(S370>0.5*(T396+T398)/(1+S339*$B$5),S370,0.5*(T396+T398)/(1+S339*$B$5))","v":{"v":197567.83367827715,"d":"197,567.83"}},null,{"$f":"IF(U370>0.5*(V396+V398)/(1+U339*$B$5),U370,0.5*(V396+V398)/(1+U339*$B$5))","v":{"v":170476.2506879786,"d":"170,476.25"}},null,{"$f":"IF(W370>0.5*(X396+X398)/(1+W339*$B$5),W370,0.5*(X396+X398)/(1+W339*$B$5))","v":{"v":91548.57744373263,"d":"91,548.58"}},{"$nulls":6},{"$f":"0.5*(AE396+AE398)/(1+P338*$B$5)","v":98.94254307924663},null,{"$f":"0.5*(AG396+AG398)/(1+R338*$B$5)","v":99.61494799766791},null,{"$f":"0.5*(AI396+AI398)/(1+T338*$B$5)","v":101.08867628928542},null,{"$f":"0.5*(AK396+AK398)/(1+V338*$B$5)","v":101.01093879251066},null,{"$f":"0.5*(AM396+AM398)/(1+X338*$B$5)","v":100.6411943030515},null,{"$f":"AO397/(1+Z338/4)","v":100.91711313341993},{"$f":"100*(1+0.5*$D$361)","v":101.33438226221246}]
[{"$nulls":15},{"$f":"IF(P371>0.5*(Q397+Q399)/(1+P340*$B$5),P371,0.5*(Q397+Q399)/(1+P340*$B$5))","v":{"v":256227.7315973273,"d":"256,227.73"}},null,{"$f":"IF(R371>0.5*(S397+S399)/(1+R340*$B$5),R371,0.5*(S397+S399)/(1+R340*$B$5))","v":{"v":265677.6902848127,"d":"265,677.69"}},null,{"$f":"IF(T371>0.5*(U397+U399)/(1+T340*$B$5),T371,0.5*(U397+U399)/(1+T340*$B$5))","v":{"v":290504.0023631817,"d":"290,504.00"}},null,{"$f":"IF(V371>0.5*(W397+W399)/(1+V340*$B$5),V371,0.5*(W397+W399)/(1+V340*$B$5))","v":{"v":242068.5972563696,"d":"242,068.60"}},{"$nulls":3},"The Value in Cell AC398 should be 100,",null,null,{"$f":"0.5*(AD397+AD399)/(1+O339*$B$5)","v":99.96278883424814},null,{"$f":"50*$D$361+0.5*(AF397+AF399)/(1+Q339*$B$5)","v":101.56279971853036},null,{"$f":"50*$D$361+0.5*(AH397+AH399)/(1+S339*$B$5)","v":101.93399786789948},null,{"$f":"50*$D$361+0.5*(AJ397+AJ399)/(1+U339*$B$5)","v":102.39514220973115},null,{"$f":"50*$D$361+0.5*(AL397+AL399)/(1+W339*$B$5)","v":102.2498680366498},null,{"$f":"50*$D$361+0.5*(AN397+AN399)/(1+Y339*$B$5)","v":101.96841577808237}]
[{"$nulls":16},{"$f":"IF(Q372>0.5*(R398+R400)/(1+Q341*$B$5),Q372,0.5*(R398+R400)/(1+Q341*$B$5))","v":{"v":318367.266622288,"d":"318,367.27"}},null,{"$f":"IF(S372>0.5*(T398+T400)/(1+S341*$B$5),S372,0.5*(T398+T400)/(1+S341*$B$5))","v":{"v":337052.4214194503,"d":"337,052.42"}},null,{"$f":"IF(U372>0.5*(V398+V400)/(1+U341*$B$5),U372,0.5*(V398+V400)/(1+U341*$B$5))","v":{"v":277478.2257402413,"d":"277,478.23"}},null,{"$f":"IF(W372>0.5*(X398+X400)/(1+W341*$B$5),W372,0.5*(X398+X400)/(1+W341*$B$5))","v":{"v":168989.8647899001,"d":"168,989.86"}},null,null,"  just as the value of cell O370 should be 0.",{"$nulls":3},{"$f":"0.5*(AE398+AE400)/(1+P340*$B$5)","v":102.0705781427342},null,{"$f":"0.5*(AG398+AG400)/(1+R340*$B$5)","v":102.18332400507965},null,{"$f":"0.5*(AI398+AI400)/(1+T340*$B$5)","v":102.90504002363184},null,{"$f":"0.5*(AK398+AK400)/(1+V340*$B$5)","v":102.42068597256372},null,{"$f":"0.5*(AM398+AM400)/(1+X340*$B$5)","v":101.55074006667788},null,{"$f":"AO399/(1+Z340/4)","v":101.12674212097266},{"$f":"100*(1+0.5*$D$361)","v":101.33438226221246}]
[{"$nulls":17},{"$f":"IF(R373>0.5*(S399+S401)/(1+R342*$B$5),R373,0.5*(S399+S401)/(1+R342*$B$5))","v":{"v":374592.486679342,"d":"374,592.49"}},null,{"$f":"IF(T373>0.5*(U399+U401)/(1+T342*$B$5),T373,0.5*(U399+U401)/(1+T342*$B$5))","v":{"v":390523.7622563347,"d":"390,523.76"}},null,{"$f":"IF(V373>0.5*(W399+W401)/(1+V342*$B$5),V373,0.5*(W399+W401)/(1+V342*$B$5))","v":{"v":315473.8941828499,"d":"315,473.89"}},{"$nulls":3},"   The difference suggests an error somewhere",{"$nulls":4},{"$f":"50*$D$361+0.5*(AF399+AF401)/(1+Q341*$B$5)","v":103.72242521203161},null,{"$f":"50*$D$361+0.5*(AH399+AH401)/(1+S341*$B$5)","v":103.68836616185992},null,{"$f":"50*$D$361+0.5*(AJ399+AJ401)/(1+U341*$B$5)","v":103.64533620187329},null,{"$f":"50*$D$361+0.5*(AL399+AL401)/(1+W341*$B$5)","v":103.02428091011144},null,{"$f":"50*$D$361+0.5*(AN399+AN401)/(1+Y341*$B$5)","v":102.30397443355669}]
[{"$nulls":18},{"$f":"IF(S374>0.5*(T400+T402)/(1+S343*$B$5),S374,0.5*(T400+T402)/(1+S343*$B$5))","v":{"v":415619.6719442613,"d":"415,619.67"}},null,{"$f":"IF(U374>0.5*(V400+V402)/(1+U343*$B$5),U374,0.5*(V400+V402)/(1+U343*$B$5))","v":{"v":333740.56672591186,"d":"333,740.57"}},null,{"$f":"IF(W374>0.5*(X400+X402)/(1+W343*$B$5),W374,0.5*(X400+X402)/(1+W343*$B$5))","v":{"v":212129.67195821437,"d":"212,129.67"}},null,null,"    in building the tree.",{"$nulls":5},{"$f":"0.5*(AG400+AG402)/(1+R342*$B$5)","v":103.72983746409255},null,{"$f":"0.5*(AI400+AI402)/(1+T342*$B$5)","v":103.90523762256335},null,{"$f":"0.5*(AK400+AK402)/(1+V342*$B$5)","v":103.1547389418285},null,{"$f":"0.5*(AM400+AM402)/(1+X342*$B$5)","v":102.05188954564922},null,{"$f":"AO401/(1+Z342/4)","v":101.23116474799652},{"$f":"100*(1+0.5*$D$361)","v":101.33438226221246}]
[{"$nulls":19},{"$f":"IF(T375>0.5*(U401+U403)/(1+T344*$B$5),T375,0.5*(U401+U403)/(1+T344*$B$5))","v":{"v":447027.69171521364,"d":"447,027.69"}},null,{"$f":"IF(V375>0.5*(W401+W403)/(1+V344*$B$5),V375,0.5*(W401+W403)/(1+V344*$B$5))","v":{"v":354243.3749030375,"d":"354,243.37"}},{"$nulls":10},{"$f":"50*$D$361+0.5*(AH401+AH403)/(1+S343*$B$5)","v":104.73694049734527},null,{"$f":"50*$D$361+0.5*(AJ401+AJ403)/(1+U343*$B$5)","v":104.33789544419703},null,{"$f":"50*$D$361+0.5*(AL401+AL403)/(1+W343*$B$5)","v":103.45567898179459},null,{"$f":"50*$D$361+0.5*(AN401+AN403)/(1+Y343*$B$5)","v":102.47869485318262}]
[{"$nulls":20},{"$f":"IF(U376>0.5*(V402+V404)/(1+U345*$B$5),U376,0.5*(V402+V404)/(1+U345*$B$5))","v":{"v":363753.11001321295,"d":"363,753.11"}},null,{"$f":"IF(W376>0.5*(X402+X404)/(1+W345*$B$5),W376,0.5*(X402+X404)/(1+W345*$B$5))","v":{"v":236173.62212280382,"d":"236,173.62"}},{"$nulls":10},{"$f":"0.5*(AI402+AI404)/(1+T344*$B$5)","v":104.47027691715216},null,{"$f":"0.5*(AK402+AK404)/(1+V344*$B$5)","v":103.54243374903038},null,{"$f":"0.5*(AM402+AM404)/(1+X344*$B$5)","v":102.32779597969947},null,{"$f":"AO403/(1+Z344/4)","v":101.28309966539068},{"$f":"100*(1+0.5*$D$361)","v":101.33438226221246}]
[{"$nulls":21},{"$f":"IF(V377>0.5*(W403+W405)/(1+V346*$B$5),V377,0.5*(W403+W405)/(1+V346*$B$5))","v":{"v":375015.02496432874,"d":"375,015.02"}},{"$nulls":12},{"$f":"50*$D$361+0.5*(AJ403+AJ405)/(1+U345*$B$5)","v":104.73164463986444},null,{"$f":"50*$D$361+0.5*(AL403+AL405)/(1+W345*$B$5)","v":103.6961184834405},null,{"$f":"50*$D$361+0.5*(AN403+AN405)/(1+Y345*$B$5)","v":102.56964163280352}]
[{"$nulls":22},{"$f":"IF(W378>0.5*(X404+X406)/(1+W347*$B$5),W378,0.5*(X404+X406)/(1+W347*$B$5))","v":{"v":249603.00895520303,"d":"249,603.01"}},{"$nulls":12},{"$f":"0.5*(AK404+AK406)/(1+V346*$B$5)","v":103.7501502496433},null,{"$f":"0.5*(AM404+AM406)/(1+X346*$B$5)","v":102.47986043457924},null,{"$f":"AO405/(1+Z346/4)","v":101.30890958875516},{"$f":"100*(1+0.5*$D$361)","v":101.33438226221246}]
[{"$nulls":36},{"$f":"50*$D$361+0.5*(AL405+AL407)/(1+W347*$B$5)","v":103.83041235176451},null,{"$f":"50*$D$361+0.5*(AN405+AN407)/(1+Y347*$B$5)","v":102.61700984685037}]
[{"$nulls":37},{"$f":"0.5*(AM406+AM408)/(1+X348*$B$5)","v":102.56384072944765},null,{"$f":"AO407/(1+Z348/4)","v":101.32173130601517},{"$f":"100*(1+0.5*$D$361)","v":101.33438226221246}]
[{"$nulls":38},{"$f":"50*$D$361+0.5*(AN407+AN409)/(1+Y349*$B$5)","v":102.64170647739336}]
[{"$nulls":39},{"$f":"AO409/(1+Z350/4)","v":101.32809958843164},{"$f":"100*(1+0.5*$D$361)","v":101.33438226221246}]
[]
[]
[]
[]
[]
[]
[{"$nulls":26},"Consider the value of an American call option that expires in 2 years on this 3-year bond, with strike price of:",{"$nulls":7},99.75]
[{"$nulls":26},"  for $100,000 par value",{"$nulls":9},{"$f":"MAX(0,AK390-$AI$416)","v":0}]
[{"$nulls":26},"Since this is an American option, exercise would entail receiving the coupon at the next instant after exercise.",{"$nulls":8},{"$f":"MAX(AJ391-$AI$416,0.5*(AK417+AK419)/(1+V332*$B$5))","v":0}]
[{"$nulls":26},"Option Value =",{"$f":"100000/100*AC425","v":{"v":2575.931603966849,"d":"$2,575.93"}},{"$nulls":6},{"$f":"MAX(AI392-$AI$416,0.5*(AJ418+AJ420)/(1+U333*$B$5))","v":0},null,{"$f":"MAX(0,AK392-$AI$416)","v":0}]
[{"$nulls":33},{"$f":"MAX(AH393-$AI$416,0.5*(AI419+AI421)/(1+T334*$B$5))","v":0.1351944746551586},null,{"$f":"MAX(AJ393-$AI$416,0.5*(AK419+AK421)/(1+V334*$B$5))","v":0}]
[{"$nulls":32},{"$f":"MAX(AG394-$AI$416,0.5*(AH420+AH422)/(1+S335*$B$5))","v":0.41473744730068407},null,{"$f":"MAX(AI394-$AI$416,0.5*(AJ420+AJ422)/(1+U335*$B$5))","v":0.2711281115992394},null,{"$f":"MAX(0,AK394-$AI$416)","v":0}]
[{"$nulls":31},{"$f":"MAX(AF395-$AI$416,0.5*(AG421+AG423)/(1+R336*$B$5))","v":0.8403852532123063},null,{"$f":"MAX(AH395-$AI$416,0.5*(AI421+AI423)/(1+T336*$B$5))","v":0.7153524188848844},null,{"$f":"MAX(AJ395-$AI$416,0.5*(AK421+AK423)/(1+V336*$B$5))","v":0.5490565910979004}]
[{"$nulls":30},{"$f":"MAX(AE396-$AI$416,0.5*(AF422+AF424)/(1+Q337*$B$5))","v":1.3596187421036312},null,{"$f":"MAX(AG396-$AI$416,0.5*(AH422+AH424)/(1+S337*$B$5))","v":1.2840299294257784},null,{"$f":"MAX(AI396-$AI$416,0.5*(AJ422+AJ424)/(1+U337*$B$5))","v":1.1624811157594945},null,{"$f":"MAX(0,AK396-$AI$416)","v":1.1132790704988622}]
[{"$nulls":29},{"$f":"MAX(AD397-$AI$416,0.5*(AE423+AE425)/(1+P338*$B$5))","v":1.939266989332618},null,{"$f":"MAX(AF397-$AI$416,0.5*(AG423+AG425)/(1+R338*$B$5))","v":1.9007820945714946},null,{"$f":"MAX(AH397-$AI$416,0.5*(AI423+AI425)/(1+T338*$B$5))","v":1.9009459770048884},null,{"$f":"MAX(AJ397-$AI$416,0.5*(AK423+AK425)/(1+V338*$B$5))","v":1.7968673445643506}]
[{"$nulls":28},{"$f":"MAX(AC398-$AI$416,0.5*(AD424+AD426)/(1+O339*$B$5))","v":2.5759316039668487},null,{"$f":"MAX(AE398-$AI$416,0.5*(AF424+AF426)/(1+Q339*$B$5))","v":2.5451396744309966},null,{"$f":"MAX(AG398-$AI$416,0.5*(AH424+AH426)/(1+S339*$B$5))","v":2.5483694986870162},null,{"$f":"MAX(AI398-$AI$416,0.5*(AJ424+AJ426)/(1+U339*$B$5))","v":2.645142209731148},null,{"$f":"MAX(0,AK398-$AI$416)","v":2.4998680366498007}]
[{"$nulls":29},{"$f":"MAX(AD399-$AI$416,0.5*(AE425+AE427)/(1+P340*$B$5))","v":3.2406210250593745},null,{"$f":"MAX(AF399-$AI$416,0.5*(AG425+AG427)/(1+R340*$B$5))","v":3.2235608945777923},null,{"$f":"MAX(AH399-$AI$416,0.5*(AI425+AI427)/(1+T340*$B$5))","v":3.266582362400242},null,{"$f":"MAX(AJ399-$AI$416,0.5*(AK425+AK427)/(1+V340*$B$5))","v":2.880987689241002}]
[{"$nulls":30},{"$f":"MAX(AE400-$AI$416,0.5*(AF426+AF428)/(1+Q341*$B$5))","v":3.9724252120316095},null,{"$f":"MAX(AG400-$AI$416,0.5*(AH426+AH428)/(1+S341*$B$5))","v":3.9383661618599177},null,{"$f":"MAX(AI400-$AI$416,0.5*(AJ426+AJ428)/(1+U341*$B$5))","v":3.8953362018732918},null,{"$f":"MAX(0,AK400-$AI$416)","v":3.274280910111443}]
[{"$nulls":31},{"$f":"MAX(AF401-$AI$416,0.5*(AG427+AG429)/(1+R342*$B$5))","v":4.441977914852443},null,{"$f":"MAX(AH401-$AI$416,0.5*(AI427+AI429)/(1+T342*$B$5))","v":4.238092624179304},null,{"$f":"MAX(AJ401-$AI$416,0.5*(AK427+AK429)/(1+V342*$B$5))","v":3.4870984130902327}]
[{"$nulls":32},{"$f":"MAX(AG402-$AI$416,0.5*(AH428+AH430)/(1+S343*$B$5))","v":4.986940497345273},null,{"$f":"MAX(AI402-$AI$416,0.5*(AJ428+AJ430)/(1+U343*$B$5))","v":4.587895444197031},null,{"$f":"MAX(0,AK402-$AI$416)","v":3.705678981794591}]
[{"$nulls":33},{"$f":"MAX(AH403-$AI$416,0.5*(AI429+AI431)/(1+T344*$B$5))","v":4.7818180599130935},null,{"$f":"MAX(AJ403-$AI$416,0.5*(AK429+AK431)/(1+V344*$B$5))","v":3.8246625991168}]
[{"$nulls":34},{"$f":"MAX(AI404-$AI$416,0.5*(AJ430+AJ432)/(1+U345*$B$5))","v":4.981644639864442},null,{"$f":"MAX(0,AK404-$AI$416)","v":3.9461184834405003}]
[{"$nulls":35},{"$f":"MAX(AJ405-$AI$416,0.5*(AK431+AK433)/(1+V346*$B$5))","v":4.012758160532241}]
[{"$nulls":36},{"$f":"MAX(0,AK406-$AI$416)","v":4.080412351764508}]
[]
[{"$nulls":26},"With a binomial tree we can extablish the value of the early exercise feature by comparing this American option to an otherwise equivalent European Option."]
[{"$nulls":26},"Option Value = ",{"$f":"100000/100*AC445","v":2087.720202264245}]
[{"$nulls":36},{"$f":"MAX(0,AK390-$AI$416)","v":0}]
[{"$nulls":26},"So the early exercise feature is worth:",null,null,{"$f":"AB419-AB436","v":{"v":488.2114017026038,"d":"$488.21"}},{"$nulls":5},{"$f":"0.5*(AK437+AK439)/(1+V332*$B$5)","v":0}]
[{"$nulls":34},{"$f":"0.5*(AJ438+AJ440)/(1+U333*$B$5)","v":0},null,{"$f":"MAX(0,AK392-$AI$416)","v":0}]
[{"$nulls":33},{"$f":"0.5*(AI439+AI441)/(1+T334*$B$5)","v":0.1351944746551586},null,{"$f":"0.5*(AK439+AK441)/(1+V334*$B$5)","v":0}]
[{"$nulls":32},{"$f":"0.5*(AH440+AH442)/(1+S335*$B$5)","v":0.41473744730068407},null,{"$f":"0.5*(AJ440+AJ442)/(1+U335*$B$5)","v":0.2711281115992394},null,{"$f":"MAX(0,AK394-$AI$416)","v":0}]
[{"$nulls":31},{"$f":"0.5*(AG441+AG443)/(1+R336*$B$5)","v":0.8014423417360919},null,{"$f":"0.5*(AI441+AI443)/(1+T336*$B$5)","v":0.7153524188848844},null,{"$f":"0.5*(AK441+AK443)/(1+V336*$B$5)","v":0.5490565910979004}]
[{"$nulls":30},{"$f":"0.5*(AF442+AF444)/(1+Q337*$B$5)","v":1.2380195878398088},null,{"$f":"0.5*(AH442+AH444)/(1+S337*$B$5)","v":1.205310143092466},null,{"$f":"0.5*(AJ442+AJ444)/(1+U337*$B$5)","v":1.1624811157594945},null,{"$f":"MAX(0,AK396-$AI$416)","v":1.1132790704988622}]
[{"$nulls":29},{"$f":"0.5*(AE443+AE445)/(1+P338*$B$5)","v":1.6768526747060581},null,{"$f":"0.5*(AG443+AG445)/(1+R338*$B$5)","v":1.6945653735242638},null,{"$f":"0.5*(AI443+AI445)/(1+T338*$B$5)","v":1.7405490532347905},null,{"$f":"0.5*(AK443+AK445)/(1+V338*$B$5)","v":1.7968673445643506}]
[{"$nulls":28},{"$f":"0.5*(AD444+AD446)/(1+O339*$B$5)","v":2.087720202264245},null,{"$f":"0.5*(AF444+AF446)/(1+Q339*$B$5)","v":2.138361607149964},null,{"$f":"0.5*(AH444+AH446)/(1+S339*$B$5)","v":2.211310513710477},null,{"$f":"0.5*(AJ444+AJ446)/(1+U339*$B$5)","v":2.323864763832222},null,{"$f":"MAX(0,AK398-$AI$416)","v":2.4998680366498007}]
[{"$nulls":29},{"$f":"0.5*(AE445+AE447)/(1+P340*$B$5)","v":2.521301048187495},null,{"$f":"0.5*(AG445+AG447)/(1+R340*$B$5)","v":2.6107772447800435},null,{"$f":"0.5*(AI445+AI447)/(1+T340*$B$5)","v":2.7434983946376192},null,{"$f":"0.5*(AK445+AK447)/(1+V340*$B$5)","v":2.880987689241002}]
[{"$nulls":30},{"$f":"0.5*(AF446+AF448)/(1+Q341*$B$5)","v":2.9325007531184983},null,{"$f":"0.5*(AH446+AH448)/(1+S341*$B$5)","v":3.042327438017221},null,{"$f":"0.5*(AJ446+AJ448)/(1+U341*$B$5)","v":3.1692745578452284},null,{"$f":"MAX(0,AK400-$AI$416)","v":3.274280910111443}]
[{"$nulls":31},{"$f":"0.5*(AG447+AG449)/(1+R342*$B$5)","v":3.286791296317118},null,{"$f":"0.5*(AI447+AI449)/(1+T342*$B$5)","v":3.403644668829851},null,{"$f":"0.5*(AK447+AK449)/(1+V342*$B$5)","v":3.4870984130902327}]
[{"$nulls":32},{"$f":"0.5*(AH448+AH450)/(1+S343*$B$5)","v":3.561852233013702},null,{"$f":"0.5*(AJ448+AJ450)/(1+U343*$B$5)","v":3.64367379582302},null,{"$f":"MAX(0,AK402-$AI$416)","v":3.705678981794591}]
[{"$nulls":33},{"$f":"0.5*(AI449+AI451)/(1+T344*$B$5)","v":3.7741544537114753},null,{"$f":"0.5*(AK449+AK451)/(1+V344*$B$5)","v":3.8246625991168}]
[{"$nulls":34},{"$f":"0.5*(AJ450+AJ452)/(1+U345*$B$5)","v":3.909294944457219},null,{"$f":"MAX(0,AK404-$AI$416)","v":3.9461184834405003}]
[{"$nulls":35},{"$f":"0.5*(AK451+AK453)/(1+V346*$B$5)","v":4.012758160532241}]
[{"$nulls":36},{"$f":"MAX(0,AK406-$AI$416)","v":4.080412351764508}]

{"sheet":"Bkgrd","index":1,"n_rows":56,"n_cols":9,"rows_kept":56}
["The BDT model assumes that the short-rate process follows a mean-reverting geometric Brownian motion."]
[null,"The ability to fit the yield curve exactly by allowing the long-run mean to vary as we move through time."]
[null,"The volatility fits the a caplet corresponding to that period."]
[]
[]
["The volatility equation is derived as follows:"]
[]
[]
[{"$nulls":3},"This interest rate in the up-state is ",null,null,"rU"]
[]
[]
[{"$nulls":4},"The 2 rates this period are centered at "]
[]
[]
[{"$nulls":3},"This interest rate in the up-state is ",null,null,"rD"]
[]
[]
[]
["In BDT, our volatility equation solves for sigma, as a function of Dt, r0, rU, and rD."]
[]
["Here's the derivation:"]
[]
[{"$nulls":4},"Note that whatever this centering value, ",{"$nulls":3},"      is, it cancels in this expression."]
[]
[]
[]
["Now recall that exponents are additive when the arguments are multiplied (subtractive when divided):"]
{"$rows_empty":8}
["Thus (taking the log of both sides:)"]
[]
[]
[]
[]
[]
["Isolating sigma:"]
[]
[]
[{"$nulls":5},"Note that everything in this derivation is true, independent of the probability of going up or down."]
[{"$nulls":5},"  This is an important point that suggests that the volatility and nodes are the same whether we are in the real world"]
[{"$nulls":5},"         or the equivalent risk-neutral world."]
[{"$nulls":5},"Another way of noting this is by seeing that we do not have to know the expected interest rate next period to work"]
[{"$nulls":5},"        with the nodes / volatilities."]
[{"$nulls":5},"This is the same reason that under the Black-Scholes model, the implied volatility is the volatility of the stock in"]
[{"$nulls":5},"       the real world."]
[]
[]
[]
["So what is ",null,"This depends on the forward rate, but it also depends on the volatility, because of convexity.  In particluar, the (geometric) mean of ru and rd is not the forward rate."]
[null,null,"  Because of Jensen's inequality this mean will be less than the forward rate.  The difference will be increasing in sigma."]

{"sheet":"Euro$ Futs","index":2,"n_rows":44,"n_cols":21,"rows_kept":44}
["Eurodollar futures prices are quoted as 100 minus 90-day Libor (expressed as a %ge) for spot settlement on the third Wednesday of the contract month."]
[]
[]
[]
[]
["3-mo Euro$ Price Tree"]
[]
[null,{"$f":"100-bdt!P338*100","v":97.29542780714101},{"$nulls":4},"We start at the terminal date of the futures contract.  Our final tree is already in terms of Libor."]
[{"$f":"0.5*(B8+B10)","v":97.52685354800977}]
[null,{"$f":"100-bdt!P340*100","v":97.75827928887851},{"$nulls":4},"Since a futures contract entails no cash outlay, the price today must be the expected price next period (in ERNW)."]
[{"$nulls":6},"(And since the price is a linear function of the rates, then we can simply work directly with the rates.)"]
[{"$nulls":6},"The 6-month Eurodollar futures rate (that is on a 3-month contract that matures in 3 months) is:",{"$nulls":7},{"$f":"(100-A9)/100","v":0.024731464519902317},"  And the 90-day Eurodollar forward in 3 months is:",{"$nulls":4},{"$f":"bdt!Q6","v":0.024730133801021736}]
[{"$nulls":6},"Note that the futures rate exceeds the forward rate.  (The futures-forward effect.). There are 2 effects at play: Convesity and daily settlement (marking to market) on futures contracts."]
["6-mo Euro$ Futures Tree"]
[]
[null,null,{"$f":"100-bdt!Q337*100","v":96.7741157285596}]
[null,{"$f":"0.5*(C16+C18)","v":97.04867786771209}]
[{"$f":"0.5*(B17+B19)","v":97.2998714164525},null,{"$f":"100-bdt!Q339*100","v":97.32324000686457}]
[null,{"$f":"0.5*(C18+C20)","v":97.55106496519294}]
[null,null,{"$f":"100-bdt!Q341*100","v":97.7788899235213}]
[]
["9-mo Euro$ Futures Tree"]
[]
[{"$nulls":3},{"$f":"100-bdt!R336*100","v":95.71699521545428}]
[null,null,{"$f":"0.5*(D24+D26)","v":96.23625805392089}]
[null,{"$f":"0.5*(C25+C27)","v":96.69256651596811},null,{"$f":"100-bdt!R338*100","v":96.75552089238751}]
[{"$f":"0.5*(B26+B28)","v":97.09355306287902},null,{"$f":"0.5*(D26+D28)","v":97.14887497801531}]
[null,{"$f":"0.5*(C27+C29)","v":97.49453960978994},null,{"$f":"100-bdt!R340*100","v":97.54222906364312}]
[null,null,{"$f":"0.5*(D28+D30)","v":97.84020424156456}]
[{"$nulls":3},{"$f":"100-bdt!R342*100","v":98.13817941948601}]
[]
[]
[]
["12-month Euro$ Futures Tree"]
[]
[{"$nulls":4},{"$f":"100-bdt!S335","v":99.89838390974424}]
[{"$nulls":3},{"$f":"0.5*(E36+E38)","v":99.91162387648646}]
[null,null,{"$f":"0.5*(D37+D39)","v":99.92313875501779},null,{"$f":"100-bdt!S337","v":99.92486384322866}]
[null,{"$f":"0.5*(C38+C40)","v":99.93315331397955},null,{"$f":"0.5*(E38+E40)","v":99.93465363354913}]
[{"$f":"0.5*(B39+B41)","v":99.94186303600792},null,{"$f":"0.5*(D39+D41)","v":99.9431678729413},null,{"$f":"100-bdt!S339","v":99.9444434238696}]
[null,{"$f":"0.5*(C40+C42)","v":99.95057275803629},null,{"$f":"0.5*(E40+E42)","v":99.95168211233346}]
[null,null,{"$f":"0.5*(D41+D43)","v":99.95797764313127},null,{"$f":"100-bdt!S341","v":99.95892080079733}]
[{"$nulls":3},{"$f":"0.5*(E42+E44)","v":99.96427317392909}]
[{"$nulls":4},{"$f":"100-bdt!S343","v":99.96962554706086}]

{"sheet":"Bloomberg Screens","index":3,"n_rows":56,"n_cols":13,"rows_kept":56}
["Here is the Bloomberg"]
["  screen for a standard"]
["   interest rate cap."]
{"$rows_empty":31}
["This is the Cash-flow table for this cap (The 5 Tab on the cap screen.)",{"$nulls":5},"Note that the caplet vol corresponds to the volatility of the forward rate.  These can be used to calibrate the Black, Derman and Toy Model."]
[]
["Expiry","Pay Date","Days","Notional","Cap Strike","Cap Vols","Reset Rate","Hedge Ratio","Payment","Discount","Intrinsic PV","Time PV","PV"]
["2014-05-22","2014-08-26",91,{"v":10000000,"d":"10,000,000.00"},1.69423,77.52,0.2463,0,0,0.998785,0,0,0]
["2014-08-21","2014-11-25",91,{"v":10000000,"d":"10,000,000.00"},1.69423,77.52,0.262,0,0.61,0.998125,0,0.61,0.61]
["2014-11-21","2015-02-25",92,{"v":10000000,"d":"10,000,000.00"},1.69423,77.52,0.31194,0.02,20.7,0.99733,0,20.64,20.64]
["2015-02-23","2015-05-26",90,{"v":10000000,"d":"10,000,000.00"},1.69423,73.74,0.38907,0.05,119.99,0.996361,0,119.55,119.55]
["2015-05-21","2015-08-25",91,{"v":10000000,"d":"10,000,000.00"},1.69423,73.66,0.5188,0.15,603.12,0.995057,0,600.14,600.14]
["2015-08-21","2015-11-25",92,{"v":10000000,"d":"10,000,000.00"},1.69423,73.66,0.69063,0.29,{"v":1940.51,"d":"1,940.51"},0.993304,0,1927.52,{"v":1927.52,"d":"1,927.52"}]
["2015-11-23","2016-02-25",92,{"v":10000000,"d":"10,000,000.00"},1.69423,73.66,0.90092,0.43,{"v":4473.68,"d":"4,473.68"},0.991023,0,4433.52,{"v":4433.52,"d":"4,433.52"}]
["2016-02-23","2016-05-25",90,{"v":10000000,"d":"10,000,000.00"},1.69423,59.44,1.14769,0.48,{"v":5859.17,"d":"5,859.17"},0.988187,0,5789.96,{"v":5789.96,"d":"5,789.96"}]
["2016-05-23","2016-08-25",92,{"v":10000000,"d":"10,000,000.00"},1.69423,59.13,1.40516,0.58,{"v":10129.1,"d":"10,129.10"},0.984651,0,9973.64,{"v":9973.64,"d":"9,973.64"}]
["2016-08-23","2016-11-25",92,{"v":10000000,"d":"10,000,000.00"},1.69423,59.13,1.65969,0.66,{"v":14962.86,"d":"14,962.86"},0.980493,0,14670.98,{"v":14670.98,"d":"14,670.98"}]
["2016-11-23","2017-02-27",94,{"v":10000000,"d":"10,000,000.00"},1.69423,59.13,1.9412,0.71,{"v":21216.27,"d":"21,216.27"},0.975548,6290.89,14406.6,{"v":20697.5,"d":"20,697.50"}]
["2017-02-23","2017-05-25",87,{"v":10000000,"d":"10,000,000.00"},1.69423,49.86,2.22389,0.75,{"v":22937.92,"d":"22,937.92"},0.970349,12420.63,9837.15,{"v":22257.78,"d":"22,257.78"}]
["2017-05-23","2017-08-25",92,{"v":10000000,"d":"10,000,000.00"},1.69423,49.66,2.43119,0.77,{"v":28961.32,"d":"28,961.32"},0.964357,18162.16,9766.89,{"v":27929.05,"d":"27,929.05"}]
["2017-08-23","2017-11-27",94,{"v":10000000,"d":"10,000,000.00"},1.69423,49.66,2.63771,0.78,{"v":34588.06,"d":"34,588.06"},0.957761,23594.71,9532.36,{"v":33127.08,"d":"33,127.08"}]
["2017-11-23","2018-02-26",91,{"v":10000000,"d":"10,000,000.00"},1.69423,49.66,2.83939,0.79,{"v":38310.14,"d":"38,310.14"},0.950937,27526.77,8903.77,{"v":36430.54,"d":"36,430.54"}]
["2018-02-22","2018-05-25",88,{"v":10000000,"d":"10,000,000.00"},1.69423,41.65,3.00442,0.8,{"v":38401.49,"d":"38,401.49"},0.944015,30233.87,6017.72,{"v":36251.59,"d":"36,251.59"}]
["2018-05-23","2018-08-28",95,{"v":10000000,"d":"10,000,000.00"},1.69423,41.47,3.18796,0.8,{"v":46048.81,"d":"46,048.81"},0.93614,36900.53,6207.59,{"v":43108.11,"d":"43,108.11"}]
["2018-08-23","2018-11-26",90,{"v":10000000,"d":"10,000,000.00"},1.69423,41.47,3.37416,0.79,{"v":48140.85,"d":"48,140.85"},0.928314,38987.46,5702.37,{"v":44689.84,"d":"44,689.84"}]
["2018-11-22","2019-02-25",91,{"v":10000000,"d":"10,000,000.00"},1.69423,41.47,3.54701,0.79,{"v":52966.71,"d":"52,966.71"},0.920063,43090.36,5642.34,{"v":48732.7,"d":"48,732.70"}]

{"sheet":"Cap Valuation","index":4,"n_rows":193,"n_cols":12,"rows_kept":193}
["Valuing a Cap Using BDT",null,null,"Since we started with the caplet values, it is redundant (and circular thinking) to use the binomial Black, Derman, Toy tree to value the caplets."]
[]
["Consider a cap that caps 90-day Libor at 3% for 6 quarters."]
["Cap rate:",0.03]
["Notional Principal:",null,{"v":10000000,"d":"10,000,000"}]
["Tenor:",null,"Quarterly",0.25]
["Format:",null,"Set in advance, pay in arrears"]
[]
["Remember that a 3-year cap with quarterly resets comprises 11 caplets.  The first is set in 3 months, and pays in 6.  The last is set in 2.75 years and pays in 3 years."]
[]
["1st Caplet:"]
[{"$nulls":3},"Note that the cash flow occurs at the end of the tenor period."]
[null,{"$f":"MAX(0,bdt!P338-'Cap Valuation'!$B$4)*'Cap Valuation'!$C$5*'Cap Valuation'!$D$6/(1+bdt!P338*'Cap Valuation'!$D$6)","v":0},null,"Each node has the value of the caplet in that node (at that point in time)."]
[{"$f":"0.5*(B13+B15)/(1+'Cap Valuation'!O338*'Cap Valuation'!$D$6)","v":0}]
[null,{"$f":"MAX(0,bdt!P340-'Cap Valuation'!$B$4)*'Cap Valuation'!$C$5*'Cap Valuation'!$D$6/(1+bdt!P340*'Cap Valuation'!$D$6)","v":0}]
[]
[]
["2nd Caplet:"]
[null,null,{"$f":"MAX(0,bdt!Q337-'Cap Valuation'!$B$4)*'Cap Valuation'!$C$5*'Cap Valuation'!$D$6/(1+bdt!Q337*'Cap Valuation'!$D$6)","v":5601.928850587965}]
[null,{"$f":"0.5*(C19+C21)/(1+bdt!P338*'Cap Valuation'!$D$6)","v":2782.153090581325}]
[{"$f":"0.5*(B20+B22)/(1+bdt!O339*'Cap Valuation'!$D$6)","v":1383.5503881918744},null,{"$f":"MAX(0,bdt!Q339-'Cap Valuation'!$B$4)*'Cap Valuation'!$C$5*'Cap Valuation'!$D$6/(1+bdt!Q339*'Cap Valuation'!$D$6)","v":0}]
[null,{"$f":"0.5*(C21+C23)/(1+bdt!P340*'Cap Valuation'!$D$6)","v":0}]
[null,null,{"$f":"MAX(0,bdt!Q341-'Cap Valuation'!$B$4)*'Cap Valuation'!$C$5*'Cap Valuation'!$D$6/(1+bdt!Q341*'Cap Valuation'!$D$6)","v":0}]
[]
["3rd Caplet"]
[{"$nulls":3},{"$f":"MAX(0,bdt!R336-'Cap Valuation'!$B$4)*'Cap Valuation'!$C$5*'Cap Valuation'!$D$6/(1+bdt!R336*'Cap Valuation'!$D$6)","v":31735.313366177255}]
[null,null,{"$f":"0.5*(D26+D28)/(1+bdt!Q337*'Cap Valuation'!$D$6)","v":18747.861162700374}]
[null,{"$f":"0.5*(C27+C29)/(1+bdt!P338*'Cap Valuation'!$D$6)","v":10806.488051014041},null,{"$f":"MAX(0,bdt!R338-'Cap Valuation'!$B$4)*'Cap Valuation'!$C$5*'Cap Valuation'!$D$6/(1+bdt!R338*'Cap Valuation'!$D$6)","v":6062.80111146301}]
[{"$f":"0.5*(B28+B30)/(1+bdt!O339*'Cap Valuation'!$D$6)","v":6118.577461522178},null,{"$f":"0.5*(D28+D30)/(1+bdt!Q339*'Cap Valuation'!$D$6)","v":3011.2495747538865}]
[null,{"$f":"0.5*(C29+C31)/(1+bdt!P340*'Cap Valuation'!$D$6)","v":1497.2338371217736},null,{"$f":"MAX(0,bdt!R340-'Cap Valuation'!$B$4)*'Cap Valuation'!$C$5*'Cap Valuation'!$D$6/(1+bdt!R340*'Cap Valuation'!$D$6)","v":0}]
[null,null,{"$f":"0.5*(D30+D32)/(1+bdt!Q341*'Cap Valuation'!$D$6)","v":0}]
[{"$nulls":3},{"$f":"MAX(0,bdt!R342-'Cap Valuation'!$B$4)*'Cap Valuation'!$C$5*'Cap Valuation'!$D$6/(1+bdt!R342*'Cap Valuation'!$D$6)","v":0}]
[]
["4th Caplet"]
[{"$nulls":4},{"$f":"MAX(0,bdt!S335-$B$4)*$C$5*$D$6/(1+bdt!S335*$D$6)","v":{"v":174604.56727264018,"d":"174,604.57"}}]
[{"$nulls":3},{"$f":"0.5*(E35+E37)/(1+bdt!R336*$D$6)","v":{"v":141170.63443552976,"d":"141,170.63"}}]
[null,null,{"$f":"0.5*(D36+D38)/(1+bdt!Q337*$D$6)","v":{"v":112770.32772057093,"d":"112,770.33"}},null,{"$f":"MAX(0,bdt!S337-$B$4)*$C$5*$D$6/(1+bdt!S337*$D$6)","v":{"v":110759.87411204302,"d":"110,759.87"}}]
[null,{"$f":"0.5*(C37+C39)/(1+bdt!P338*$D$6)","v":{"v":88352.14137974777,"d":"88,352.14"}},null,{"$f":"0.5*(E37+E39)/(1+bdt!R338*$D$6)","v":{"v":86188.94113800694,"d":"86,188.94"}}]
[{"$f":"0.5*(B38+B40)/(1+bdt!O339*$D$6)","v":{"v":67300.65769896907,"d":"67,300.66"}},null,{"$f":"0.5*(D38+D40)/(1+bdt!Q339*$D$6)","v":{"v":65128.728762700695,"d":"65,128.73"}},null,{"$f":"MAX(0,bdt!S339-$B$4)*$C$5*$D$6/(1+bdt!S339*$D$6)","v":{"v":63016.19925811836,"d":"63,016.20"}}]
[null,{"$f":"0.5*(C39+C41)/(1+bdt!P340*$D$6)","v":{"v":46981.37044127282,"d":"46,981.37"}},null,{"$f":"0.5*(E39+E41)/(1+bdt!R340*$D$6)","v":{"v":44940.1862651733,"d":"44,940.19"}}]
[null,null,{"$f":"0.5*(D40+D42)/(1+bdt!Q341*$D$6)","v":{"v":29360.607675620304,"d":"29,360.61"}},null,{"$f":"MAX(0,bdt!S341-$B$4)*$C$5*$D$6/(1+bdt!S341*$D$6)","v":{"v":27416.436690613282,"d":"27,416.44"}}]
[{"$nulls":3},{"$f":"0.5*(E41+E43)/(1+bdt!R342*$D$6)","v":{"v":14107.094793866598,"d":"14,107.09"}}]
[{"$nulls":4},{"$f":"MAX(0,bdt!S343-$B$4)*$C$5*$D$6/(1+bdt!S343*$D$6)","v":{"v":929.0772942123297,"d":"929.08"}}]
[]
[]
["5th Caplet"]
[{"$nulls":5},{"$f":"MAX(0,bdt!T334-$B$4)*$D$6*$C$5/(1+bdt!T334*$D$6)","v":0}]
[{"$nulls":4},{"$f":"0.5*(F47+F49)/(1+bdt!S335*$D$6)","v":0}]
[{"$nulls":3},{"$f":"0.5*(E48+E50)/(1+bdt!R336*$D$6)","v":0},null,{"$f":"MAX(0,bdt!T336-$B$4)*$D$6*$C$5/(1+bdt!T336*$D$6)","v":0}]
[null,null,{"$f":"0.5*(D49+D51)/(1+bdt!Q337*$D$6)","v":0},null,{"$f":"0.5*(F49+F51)/(1+bdt!S337*$D$6)","v":0}]
[null,{"$f":"0.5*(C50+C52)/(1+bdt!P338*$D$6)","v":0},null,{"$f":"0.5*(E50+E52)/(1+bdt!R338*$D$6)","v":0},null,{"$f":"MAX(0,bdt!T338-$B$4)*$D$6*$C$5/(1+bdt!T338*$D$6)","v":0}]
[{"$f":"0.5*(B51+B53)/(1+bdt!O339*$D$6)","v":0},null,{"$f":"0.5*(D51+D53)/(1+bdt!Q339*$D$6)","v":0},null,{"$f":"0.5*(F51+F53)/(1+bdt!S339*$D$6)","v":0}]
[null,{"$f":"0.5*(C52+C54)/(1+bdt!P340*$D$6)","v":0},null,{"$f":"0.5*(E52+E54)/(1+bdt!R340*$D$6)","v":0},null,{"$f":"MAX(0,bdt!T340-$B$4)*$D$6*$C$5/(1+bdt!T340*$D$6)","v":0}]
[null,null,{"$f":"0.5*(D53+D55)/(1+bdt!Q341*$D$6)","v":0},null,{"$f":"0.5*(F53+F55)/(1+bdt!S341*$D$6)","v":0}]
[{"$nulls":3},{"$f":"0.5*(E54+E56)/(1+bdt!R342*$D$6)","v":0},null,{"$f":"MAX(0,bdt!T342-$B$4)*$D$6*$C$5/(1+bdt!T342*$D$6)","v":0}]
[{"$nulls":4},{"$f":"0.5*(F55+F57)/(1+bdt!S343*$D$6)","v":0}]
[{"$nulls":5},{"$f":"MAX(0,bdt!T344-$B$4)*$D$6*$C$5/(1+bdt!T344*$D$6)","v":0}]
[]
["6th Caplet"]
[]
[{"$nulls":6},{"$f":"MAX(0,bdt!U333-$B$4)*$C$5*$D$6/(1+$D$6*bdt!U333)","v":{"v":97734.70407610269,"d":"97,734.70"}}]
[{"$nulls":5},{"$f":"0.5*(G61+G63)/(1+bdt!T334*$D$6)","v":{"v":73558.47370304615,"d":"73,558.47"}}]
[{"$nulls":4},{"$f":"0.5*(F62+F64)/(1+bdt!S335*$D$6)","v":{"v":51636.70619652777,"d":"51,636.71"}},null,{"$f":"MAX(0,bdt!U335-$B$4)*$C$5*$D$6/(1+$D$6*bdt!U335)","v":{"v":49784.41693901211,"d":"49,784.42"}}]
[{"$nulls":3},{"$f":"0.5*(E63+E65)/(1+bdt!R336*$D$6)","v":{"v":35217.40932431729,"d":"35,217.41"}},null,{"$f":"0.5*(G63+G65)/(1+bdt!T336*$D$6)","v":{"v":32338.498788697645,"d":"32,338.50"}}]
[null,null,{"$f":"0.5*(D64+D66)/(1+bdt!Q337*$D$6)","v":{"v":23187.74144563462,"d":"23,187.74"}},null,{"$f":"0.5*(F64+F66)/(1+bdt!S337*$D$6)","v":{"v":19552.294115283596,"d":"19,552.29"}},null,{"$f":"MAX(0,bdt!U337-$B$4)*$C$5*$D$6/(1+$D$6*bdt!U337)","v":{"v":15023.877600167514,"d":"15,023.88"}}]
[null,{"$f":"0.5*(C65+C67)/(1+bdt!P338*$D$6)","v":{"v":14814.050690906606,"d":"14,814.05"}},null,{"$f":"0.5*(E65+E67)/(1+bdt!R338*$D$6)","v":{"v":11532.078419050438,"d":"11,532.08"}},null,{"$f":"0.5*(G65+G67)/(1+bdt!T338*$D$6)","v":{"v":7500.631559812226,"d":"7,500.63"}}]
[{"$f":"0.5*(B66+B68)/(1+bdt!O339*$D$6)","v":{"v":9234.93916127692,"d":"9,234.94"}},null,{"$f":"0.5*(D66+D68)/(1+bdt!Q339*$D$6)","v":{"v":6640.688283989743,"d":"6,640.69"}},null,{"$f":"0.5*(F66+F68)/(1+bdt!S339*$D$6)","v":{"v":3698.9406603070674,"d":"3,698.94"}},null,{"$f":"MAX(0,bdt!U339-$B$4)*$C$5*$D$6/(1+$D$6*bdt!U339)","v":0}]
[null,{"$f":"0.5*(C67+C69)/(1+bdt!P340*$D$6)","v":{"v":3756.299003732719,"d":"3,756.30"}},null,{"$f":"0.5*(E67+E69)/(1+bdt!R340*$D$6)","v":{"v":1838.175792556384,"d":"1,838.18"}},null,{"$f":"0.5*(G67+G69)/(1+bdt!T340*$D$6)","v":0}]
[null,null,{"$f":"0.5*(D68+D70)/(1+bdt!Q341*$D$6)","v":{"v":914.0125898448599,"d":"914.01"}},null,{"$f":"0.5*(F68+F70)/(1+bdt!S341*$D$6)","v":0},null,{"$f":"MAX(0,bdt!U341-$B$4)*$C$5*$D$6/(1+$D$6*bdt!U341)","v":0}]
[{"$nulls":3},{"$f":"0.5*(E69+E71)/(1+bdt!R342*$D$6)","v":0},null,{"$f":"0.5*(G69+G71)/(1+bdt!T342*$D$6)","v":0}]
[{"$nulls":4},{"$f":"0.5*(F70+F72)/(1+bdt!S343*$D$6)","v":0},null,{"$f":"MAX(0,bdt!U343-$B$4)*$C$5*$D$6/(1+$D$6*bdt!U343)","v":0}]
[{"$nulls":5},{"$f":"0.5*(G71+G73)/(1+bdt!T344*$D$6)","v":0}]
[{"$nulls":6},{"$f":"MAX(0,bdt!U345-$B$4)*$C$5*$D$6/(1+$D$6*bdt!U345)","v":0}]
[]
[]
["7th Caplet"]
[{"$nulls":7},{"$f":"MAX(0,bdt!V332-$B$4)*$C$5*$D$6/(1+bdt!V332*$D$6)","v":{"v":759260.5782401132,"d":"759,260.58"}}]
[{"$nulls":6},{"$f":"0.5*(H77+H79)/(1+bdt!U333*$D$6)","v":{"v":505130.2965207668,"d":"505,130.30"}}]
[{"$nulls":5},{"$f":"0.5*(G78+G80)/(1+bdt!T334*$D$6)","v":{"v":333347.3330834641,"d":"333,347.33"}},null,{"$f":"MAX(0,bdt!V334-$B$4)*$C$5*$D$6/(1+bdt!V334*$D$6)","v":{"v":268622.95857880136,"d":"268,622.96"}}]
[{"$nulls":4},{"$f":"0.5*(F79+F81)/(1+bdt!S335*$D$6)","v":{"v":209803.74503924773,"d":"209,803.75"}},null,{"$f":"0.5*(H79+H81)/(1+bdt!U335*$D$6)","v":{"v":163386.91289991912,"d":"163,386.91"}}]
[{"$nulls":3},{"$f":"0.5*(E80+E82)/(1+bdt!R336*$D$6)","v":{"v":131060.76525970106,"d":"131,060.77"}},null,{"$f":"0.5*(G80+G82)/(1+bdt!T336*$D$6)","v":{"v":96919.8751409837,"d":"96,919.88"}},null,{"$f":"MAX(0,bdt!V336-$B$4)*$C$5*$D$6/(1+bdt!V336*$D$6)","v":{"v":62248.89715646653,"d":"62,248.90"}}]
[null,null,{"$f":"0.5*(D81+D83)/(1+bdt!Q337*$D$6)","v":{"v":80435.2750247203,"d":"80,435.28"}},null,{"$f":"0.5*(F81+F83)/(1+bdt!S337*$D$6)","v":{"v":55124.45490352205,"d":"55,124.45"}},null,{"$f":"0.5*(H81+H83)/(1+bdt!U337*$D$6)","v":{"v":30846.340037371767,"d":"30,846.34"}}]
[null,{"$f":"0.5*(C82+C84)/(1+bdt!P338*$D$6)","v":{"v":48551.695581362255,"d":"48,551.70"}},null,{"$f":"0.5*(E82+E84)/(1+bdt!R338*$D$6)","v":{"v":31107.15923259563,"d":"31,107.16"}},null,{"$f":"0.5*(G82+G84)/(1+bdt!T338*$D$6)","v":{"v":15399.954508843337,"d":"15,399.95"}},null,{"$f":"MAX(0,bdt!V338-$B$4)*$C$5*$D$6/(1+bdt!V338*$D$6)","v":0}]
[{"$f":"0.5*(B83+B85)/(1+bdt!O339*$D$6)","v":{"v":28892.249620164304,"d":"28,892.25"}},null,{"$f":"0.5*(D83+D85)/(1+bdt!Q339*$D$6)","v":{"v":17324.673966931754,"d":"17,324.67"}},null,{"$f":"0.5*(F83+F85)/(1+bdt!S339*$D$6)","v":{"v":7594.4962028058635,"d":"7,594.50"}},null,{"$f":"0.5*(H83+H85)/(1+bdt!U339*$D$6)","v":0}]
[null,{"$f":"0.5*(C84+C86)/(1+bdt!P340*$D$6)","v":{"v":9547.136424053342,"d":"9,547.14"}},null,{"$f":"0.5*(E84+E86)/(1+bdt!R340*$D$6)","v":{"v":3774.0586721118766,"d":"3,774.06"}},null,{"$f":"0.5*(G84+G86)/(1+bdt!T340*$D$6)","v":0},null,{"$f":"MAX(0,bdt!V340-$B$4)*$C$5*$D$6/(1+bdt!V340*$D$6)","v":0}]
[null,null,{"$f":"0.5*(D85+D87)/(1+bdt!Q341*$D$6)","v":{"v":1876.6089484434438,"d":"1,876.61"}},null,{"$f":"0.5*(F85+F87)/(1+bdt!S341*$D$6)","v":0},null,{"$f":"0.5*(H85+H87)/(1+bdt!U341*$D$6)","v":0}]
[{"$nulls":3},{"$f":"0.5*(E86+E88)/(1+bdt!R342*$D$6)","v":0},null,{"$f":"0.5*(G86+G88)/(1+bdt!T342*$D$6)","v":0},null,{"$f":"MAX(0,bdt!V342-$B$4)*$C$5*$D$6/(1+bdt!V342*$D$6)","v":0}]
[{"$nulls":4},{"$f":"0.5*(F87+F89)/(1+bdt!S343*$D$6)","v":0},null,{"$f":"0.5*(H87+H89)/(1+bdt!U343*$D$6)","v":0}]
[{"$nulls":5},{"$f":"0.5*(G88+G90)/(1+bdt!T344*$D$6)","v":0},null,{"$f":"MAX(0,bdt!V344-$B$4)*$C$5*$D$6/(1+bdt!V344*$D$6)","v":0}]
[{"$nulls":6},{"$f":"0.5*(H89+H91)/(1+bdt!U345*$D$6)","v":0}]
[{"$nulls":7},{"$f":"MAX(0,bdt!V346-$B$4)*$C$5*$D$6/(1+bdt!V346*$D$6)","v":0}]
[]
[]
[]
["8th Caplet"]
[{"$nulls":8},{"$f":"MAX(0,bdt!W331-$B$4)*$C$5*$D$6/(1+bdt!W331*$D$6)","v":{"v":51315.74659276091,"d":"51,315.75"}}]
[{"$nulls":7},{"$f":"0.5*(I96+I98)/(1+bdt!V332*$D$6)","v":{"v":24799.931797751437,"d":"24,799.93"}}]
[{"$nulls":6},{"$f":"0.5*(H97+H99)/(1+bdt!U333*$D$6)","v":{"v":12842.891319310425,"d":"12,842.89"}},null,{"$f":"MAX(0,bdt!W333-$B$4)*$C$5*$D$6/(1+bdt!W333*$D$6)","v":{"v":2762.028238543729,"d":"2,762.03"}}]
[{"$nulls":5},{"$f":"0.5*(G98+G100)/(1+bdt!T334*$D$6)","v":{"v":6732.389158039503,"d":"6,732.39"}},null,{"$f":"0.5*(I98+I100)/(1+bdt!V334*$D$6)","v":{"v":1333.9125651772447,"d":"1,333.91"}}]
[{"$nulls":4},{"$f":"0.5*(F99+F101)/(1+bdt!S335*$D$6)","v":{"v":3443.0671221435305,"d":"3,443.07"}},null,{"$f":"0.5*(H99+H101)/(1+bdt!U335*$D$6)","v":{"v":658.6956621571949,"d":"658.70"}},null,{"$f":"MAX(0,bdt!W335-$B$4)*$C$5*$D$6/(1+bdt!W335*$D$6)","v":0}]
[{"$nulls":3},{"$f":"0.5*(E100+E102)/(1+bdt!R336*$D$6)","v":{"v":1783.0961576907362,"d":"1,783.10"}},null,{"$f":"0.5*(G100+G102)/(1+bdt!T336*$D$6)","v":{"v":328.68059596774697,"d":"328.68"}},null,{"$f":"0.5*(I100+I102)/(1+bdt!V336*$D$6)","v":0}]
[null,null,{"$f":"0.5*(D101+D103)/(1+bdt!Q337*$D$6)","v":{"v":924.0985782504704,"d":"924.10"}},null,{"$f":"0.5*(F101+F103)/(1+bdt!S337*$D$6)","v":{"v":161.3102401114149,"d":"161.31"}},null,{"$f":"0.5*(H101+H103)/(1+bdt!U337*$D$6)","v":0},null,{"$f":"MAX(0,bdt!W337-$B$4)*$C$5*$D$6/(1+bdt!W337*$D$6)","v":0}]
[null,{"$f":"0.5*(C102+C104)/(1+bdt!P338*$D$6)","v":{"v":478.6813037222913,"d":"478.68"}},null,{"$f":"0.5*(E102+E104)/(1+bdt!R338*$D$6)","v":{"v":80.00617415439758,"d":"80.01"}},null,{"$f":"0.5*(G102+G104)/(1+bdt!T338*$D$6)","v":0},null,{"$f":"0.5*(I102+I104)/(1+bdt!V338*$D$6)","v":0}]
[{"$f":"0.5*(B103+B105)/(1+bdt!O339*$D$6)","v":{"v":247.87122434566427,"d":"247.87"}},null,{"$f":"0.5*(D103+D105)/(1+bdt!Q339*$D$6)","v":{"v":39.73716991055628,"d":"39.74"}},null,{"$f":"0.5*(F103+F105)/(1+bdt!S339*$D$6)","v":0},null,{"$f":"0.5*(H103+H105)/(1+bdt!U339*$D$6)","v":0},null,{"$f":"MAX(0,bdt!W339-$B$4)*$C$5*$D$6/(1+bdt!W339*$D$6)","v":0}]
[null,{"$f":"0.5*(C104+C106)/(1+bdt!P340*$D$6)","v":{"v":19.75785596795136,"d":"19.76"}},null,{"$f":"0.5*(E104+E106)/(1+bdt!R340*$D$6)","v":0},null,{"$f":"0.5*(G104+G106)/(1+bdt!T340*$D$6)","v":0},null,{"$f":"0.5*(I104+I106)/(1+bdt!V340*$D$6)","v":0}]
[null,null,{"$f":"0.5*(D105+D107)/(1+bdt!Q341*$D$6)","v":0},null,{"$f":"0.5*(F105+F107)/(1+bdt!S341*$D$6)","v":0},null,{"$f":"0.5*(H105+H107)/(1+bdt!U341*$D$6)","v":0},null,{"$f":"MAX(0,bdt!W341-$B$4)*$C$5*$D$6/(1+bdt!W341*$D$6)","v":0}]
[{"$nulls":3},{"$f":"0.5*(E106+E108)/(1+bdt!R342*$D$6)","v":0},null,{"$f":"0.5*(G106+G108)/(1+bdt!T342*$D$6)","v":0},null,{"$f":"0.5*(I106+I108)/(1+bdt!V342*$D$6)","v":0}]
[{"$nulls":4},{"$f":"0.5*(F107+F109)/(1+bdt!S343*$D$6)","v":0},null,{"$f":"0.5*(H107+H109)/(1+bdt!U343*$D$6)","v":0},null,{"$f":"MAX(0,bdt!W343-$B$4)*$C$5*$D$6/(1+bdt!W343*$D$6)","v":0}]
[{"$nulls":5},{"$f":"0.5*(G108+G110)/(1+bdt!T344*$D$6)","v":0},null,{"$f":"0.5*(I108+I110)/(1+bdt!V344*$D$6)","v":0}]
[{"$nulls":6},{"$f":"0.5*(H109+H111)/(1+bdt!U345*$D$6)","v":0},null,{"$f":"MAX(0,bdt!W345-$B$4)*$C$5*$D$6/(1+bdt!W345*$D$6)","v":0}]
[{"$nulls":7},{"$f":"0.5*(I110+I112)/(1+bdt!V346*$D$6)","v":0}]
[{"$nulls":8},{"$f":"MAX(0,bdt!W347-$B$4)*$C$5*$D$6/(1+bdt!W347*$D$6)","v":0}]
[]
[]
[]
[]
[]
["9th Caplet"]
[{"$nulls":9},{"$f":"MAX(0,bdt!X330-$B$4)*$C$5*$D$6/(1+bdt!X330*$D$6)","v":{"v":758424.5591855006,"d":"758,424.56"}}]
[{"$nulls":8},{"$f":"0.5*(J119+J121)/(1+bdt!W331*$D$6)","v":{"v":583445.3321275878,"d":"583,445.33"}}]
[{"$nulls":7},{"$f":"0.5*(I120+I122)/(1+bdt!V332*$D$6)","v":{"v":413619.42406978423,"d":"413,619.42"}},null,{"$f":"MAX(0,bdt!X332-$B$4)*$C$5*$D$6/(1+bdt!X332*$D$6)","v":{"v":423281.79945630056,"d":"423,281.80"}}]
[{"$nulls":6},{"$f":"0.5*(H121+H123)/(1+bdt!U333*$D$6)","v":{"v":316069.6887742995,"d":"316,069.69"}},null,{"$f":"0.5*(J121+J123)/(1+bdt!W333*$D$6)","v":{"v":318477.2321404208,"d":"318,477.23"}}]
[{"$nulls":5},{"$f":"0.5*(G122+G124)/(1+bdt!T334*$D$6)","v":{"v":240508.099317849,"d":"240,508.10"}},null,{"$f":"0.5*(I122+I124)/(1+bdt!V334*$D$6)","v":{"v":229546.96649579145,"d":"229,546.97"}},null,{"$f":"MAX(0,bdt!X334-$B$4)*$C$5*$D$6/(1+bdt!X334*$D$6)","v":{"v":218627.12036295875,"d":"218,627.12"}}]
[{"$nulls":4},{"$f":"0.5*(F123+F125)/(1+bdt!S335*$D$6)","v":{"v":175008.39045999592,"d":"175,008.39"}},null,{"$f":"0.5*(H123+H125)/(1+bdt!U335*$D$6)","v":{"v":166261.46387597307,"d":"166,261.46"}},null,{"$f":"0.5*(J123+J125)/(1+bdt!W335*$D$6)","v":{"v":156827.6867012291,"d":"156,827.69"}}]
[{"$nulls":3},{"$f":"0.5*(E124+E126)/(1+bdt!R336*$D$6)","v":{"v":126480.67681016869,"d":"126,480.68"}},null,{"$f":"0.5*(G124+G126)/(1+bdt!T336*$D$6)","v":{"v":118400.51580239192,"d":"118,400.52"}},null,{"$f":"0.5*(I124+I126)/(1+bdt!V336*$D$6)","v":{"v":107146.08996462387,"d":"107,146.09"}},null,{"$f":"MAX(0,bdt!X336-$B$4)*$C$5*$D$6/(1+bdt!X336*$D$6)","v":{"v":96522.89092188688,"d":"96,522.89"}}]
[null,null,{"$f":"0.5*(D125+D127)/(1+bdt!Q337*$D$6)","v":{"v":89611.5720222641,"d":"89,611.57"}},null,{"$f":"0.5*(F125+F127)/(1+bdt!S337*$D$6)","v":{"v":80661.54987999417,"d":"80,661.55"}},null,{"$f":"0.5*(H125+H127)/(1+bdt!U337*$D$6)","v":{"v":71020.28354991699,"d":"71,020.28"}},null,{"$f":"0.5*(J125+J127)/(1+bdt!W337*$D$6)","v":{"v":60424.052695766666,"d":"60,424.05"}}]
[null,{"$f":"0.5*(C126+C128)/(1+bdt!P338*$D$6)","v":{"v":62198.815096631486,"d":"62,198.82"}},null,{"$f":"0.5*(E126+E128)/(1+bdt!R338*$D$6)","v":{"v":54187.85003798783,"d":"54,187.85"}},null,{"$f":"0.5*(G126+G128)/(1+bdt!T338*$D$6)","v":{"v":45952.883386197784,"d":"45,952.88"}},null,{"$f":"0.5*(I126+I128)/(1+bdt!V338*$D$6)","v":{"v":36175.10539812285,"d":"36,175.11"}},null,{"$f":"MAX(0,bdt!X338-$B$4)*$C$5*$D$6/(1+bdt!X338*$D$6)","v":{"v":24678.006530552317,"d":"24,678.01"}}]
[{"$f":"0.5*(B127+B129)/(1+bdt!O339*$D$6)","v":{"v":42354.213586062135,"d":"42,354.21"}},null,{"$f":"0.5*(D127+D129)/(1+bdt!Q339*$D$6)","v":{"v":35627.16409969451,"d":"35,627.16"}},null,{"$f":"0.5*(F127+F129)/(1+bdt!S339*$D$6)","v":{"v":28593.206932654935,"d":"28,593.21"}},null,{"$f":"0.5*(H127+H129)/(1+bdt!U339*$D$6)","v":{"v":21024.031633895393,"d":"21,024.03"}},null,{"$f":"0.5*(J127+J129)/(1+bdt!W339*$D$6)","v":{"v":12316.975079834177,"d":"12,316.98"}}]
[null,{"$f":"0.5*(C128+C130)/(1+bdt!P340*$D$6)","v":{"v":22970.40406104659,"d":"22,970.40"}},null,{"$f":"0.5*(E128+E130)/(1+bdt!R340*$D$6)","v":{"v":17543.304999055872,"d":"17,543.30"}},null,{"$f":"0.5*(G128+G130)/(1+bdt!T340*$D$6)","v":{"v":12027.800817995249,"d":"12,027.80"}},null,{"$f":"0.5*(I128+I130)/(1+bdt!V340*$D$6)","v":{"v":6145.503675237588,"d":"6,145.50"}},null,{"$f":"MAX(0,bdt!X340-$B$4)*$C$5*$D$6/(1+bdt!X340*$D$6)","v":0}]
[null,null,{"$f":"0.5*(D129+D131)/(1+bdt!Q341*$D$6)","v":{"v":10571.110175031054,"d":"10,571.11"}},null,{"$f":"0.5*(F129+F131)/(1+bdt!S341*$D$6)","v":{"v":6708.990191228429,"d":"6,708.99"}},null,{"$f":"0.5*(H129+H131)/(1+bdt!U341*$D$6)","v":{"v":3058.4995444619935,"d":"3,058.50"}},null,{"$f":"0.5*(J129+J131)/(1+bdt!W341*$D$6)","v":0}]
[{"$nulls":3},{"$f":"0.5*(E130+E132)/(1+bdt!R342*$D$6)","v":{"v":3716.3133476528747,"d":"3,716.31"}},null,{"$f":"0.5*(G130+G132)/(1+bdt!T342*$D$6)","v":{"v":1527.979536718722,"d":"1,527.98"}},null,{"$f":"0.5*(I130+I132)/(1+bdt!V342*$D$6)","v":0},null,{"$f":"MAX(0,bdt!X342-$B$4)*$C$5*$D$6/(1+bdt!X342*$D$6)","v":0}]
[{"$nulls":4},{"$f":"0.5*(F131+F133)/(1+bdt!S343*$D$6)","v":{"v":758.2320474488157,"d":"758.23"}},null,{"$f":"0.5*(H131+H133)/(1+bdt!U343*$D$6)","v":0},null,{"$f":"0.5*(J131+J133)/(1+bdt!W343*$D$6)","v":0}]
[{"$nulls":5},{"$f":"0.5*(G132+G134)/(1+bdt!T344*$D$6)","v":0},null,{"$f":"0.5*(I132+I134)/(1+bdt!V344*$D$6)","v":0},null,{"$f":"MAX(0,bdt!X344-$B$4)*$C$5*$D$6/(1+bdt!X344*$D$6)","v":0}]
[{"$nulls":6},{"$f":"0.5*(H133+H135)/(1+bdt!U345*$D$6)","v":0},null,{"$f":"0.5*(J133+J135)/(1+bdt!W345*$D$6)","v":0}]
[{"$nulls":7},{"$f":"0.5*(I134+I136)/(1+bdt!V346*$D$6)","v":0},null,{"$f":"MAX(0,bdt!X346-$B$4)*$C$5*$D$6/(1+bdt!X346*$D$6)","v":0}]
[{"$nulls":8},{"$f":"0.5*(J135+J137)/(1+bdt!W347*$D$6)","v":0}]
[{"$nulls":9},{"$f":"MAX(0,bdt!X348-$B$4)*$C$5*$D$6/(1+bdt!X348*$D$6)","v":0}]
[]
[]
["10th Caplet"]
[{"$nulls":10},{"$f":"MAX(0,bdt!Y329-$B$4)*$C$5*$D$6/(1+bdt!Y329*$D$6)","v":{"v":719093.4271133764,"d":"719,093.43"}}]
[{"$nulls":9},{"$f":"0.5*(K141+K143)/(1+bdt!X330*$D$6)","v":{"v":498731.6806788934,"d":"498,731.68"}}]
[{"$nulls":8},{"$f":"0.5*(J142+J144)/(1+bdt!W331*$D$6)","v":{"v":372192.56894804444,"d":"372,192.57"}},null,{"$f":"MAX(0,bdt!Y331-$B$4)*$C$5*$D$6/(1+bdt!Y331*$D$6)","v":{"v":368323.2617443841,"d":"368,323.26"}}]
[{"$nulls":7},{"$f":"0.5*(I143+I145)/(1+bdt!V332*$D$6)","v":{"v":253676.75606044754,"d":"253,676.76"}},null,{"$f":"0.5*(K143+K145)/(1+bdt!X332*$D$6)","v":{"v":255104.71348896806,"d":"255,104.71"}}]
[{"$nulls":6},{"$f":"0.5*(H144+H146)/(1+bdt!U333*$D$6)","v":{"v":183895.54946448555,"d":"183,895.55"}},null,{"$f":"0.5*(J144+J146)/(1+bdt!W333*$D$6)","v":{"v":180965.181889661,"d":"180,965.18"}},null,{"$f":"MAX(0,bdt!Y333-$B$4)*$C$5*$D$6/(1+bdt!Y333*$D$6)","v":{"v":168432.63616967088,"d":"168,432.64"}}]
[{"$nulls":5},{"$f":"0.5*(G145+G147)/(1+bdt!T334*$D$6)","v":{"v":131415.71164306448,"d":"131,415.71"}},null,{"$f":"0.5*(I145+I147)/(1+bdt!V334*$D$6)","v":{"v":120530.07550512254,"d":"120,530.08"}},null,{"$f":"0.5*(K145+K147)/(1+bdt!X334*$D$6)","v":{"v":109640.87177933835,"d":"109,640.87"}}]
[{"$nulls":4},{"$f":"0.5*(F146+F148)/(1+bdt!S335*$D$6)","v":{"v":89221.05023207914,"d":"89,221.05"}},null,{"$f":"0.5*(H146+H148)/(1+bdt!U335*$D$6)","v":{"v":79654.37610116482,"d":"79,654.38"}},null,{"$f":"0.5*(J146+J148)/(1+bdt!W335*$D$6)","v":{"v":68607.0020973164,"d":"68,607.00"}},null,{"$f":"MAX(0,bdt!Y335-$B$4)*$C$5*$D$6/(1+bdt!Y335*$D$6)","v":{"v":57431.72801921867,"d":"57,431.73"}}]
[{"$nulls":3},{"$f":"0.5*(E147+E149)/(1+bdt!R336*$D$6)","v":{"v":59947.11316450207,"d":"59,947.11"}},null,{"$f":"0.5*(G147+G149)/(1+bdt!T336*$D$6)","v":{"v":51559.535967642136,"d":"51,559.54"}},null,{"$f":"0.5*(I147+I149)/(1+bdt!V336*$D$6)","v":{"v":40776.54795847816,"d":"40,776.55"}},null,{"$f":"0.5*(K147+K149)/(1+bdt!X336*$D$6)","v":{"v":28226.987780304327,"d":"28,226.99"}}]
[null,null,{"$f":"0.5*(D148+D150)/(1+bdt!Q337*$D$6)","v":{"v":39450.416142959555,"d":"39,450.42"}},null,{"$f":"0.5*(F148+F150)/(1+bdt!S337*$D$6)","v":{"v":31956.944959441338,"d":"31,956.94"}},null,{"$f":"0.5*(H148+H150)/(1+bdt!U337*$D$6)","v":{"v":23674.031785914704,"d":"23,674.03"}},null,{"$f":"0.5*(J148+J150)/(1+bdt!W337*$D$6)","v":{"v":14072.4122752405,"d":"14,072.41"}},null,{"$f":"MAX(0,bdt!Y337-$B$4)*$C$5*$D$6/(1+bdt!Y337*$D$6)","v":0}]
[null,{"$f":"0.5*(C149+C151)/(1+bdt!P338*$D$6)","v":{"v":25454.735439397104,"d":"25,454.74"}},null,{"$f":"0.5*(E149+E151)/(1+bdt!R338*$D$6)","v":{"v":19590.03150610379,"d":"19,590.03"}},null,{"$f":"0.5*(G149+G151)/(1+bdt!T338*$D$6)","v":{"v":13554.914964443418,"d":"13,554.91"}},null,{"$f":"0.5*(I149+I151)/(1+bdt!V338*$D$6)","v":{"v":6998.402591081041,"d":"6,998.40"}},null,{"$f":"0.5*(K149+K151)/(1+bdt!X338*$D$6)","v":0}]
[{"$f":"0.5*(B150+B152)/(1+bdt!O339*$D$6)","v":{"v":16142.83684804568,"d":"16,142.84"}},null,{"$f":"0.5*(D150+D152)/(1+bdt!Q339*$D$6)","v":{"v":11803.275584064533,"d":"11,803.28"}},null,{"$f":"0.5*(F150+F152)/(1+bdt!S339*$D$6)","v":{"v":7540.915292461357,"d":"7,540.92"}},null,{"$f":"0.5*(H150+H152)/(1+bdt!U339*$D$6)","v":{"v":3476.6663496400424,"d":"3,476.67"}},null,{"$f":"0.5*(J150+J152)/(1+bdt!W339*$D$6)","v":0},null,{"$f":"MAX(0,bdt!Y339-$B$4)*$C$5*$D$6/(1+bdt!Y339*$D$6)","v":0}]
[null,{"$f":"0.5*(C151+C153)/(1+bdt!P340*$D$6)","v":{"v":7006.563990567636,"d":"7,006.56"}},null,{"$f":"0.5*(E151+E153)/(1+bdt!R340*$D$6)","v":{"v":4174.492341382158,"d":"4,174.49"}},null,{"$f":"0.5*(G151+G153)/(1+bdt!T340*$D$6)","v":{"v":1736.3893377485613,"d":"1,736.39"}},null,{"$f":"0.5*(I151+I153)/(1+bdt!V340*$D$6)","v":0},null,{"$f":"0.5*(K151+K153)/(1+bdt!X340*$D$6)","v":0}]
[null,null,{"$f":"0.5*(D152+D154)/(1+bdt!Q341*$D$6)","v":{"v":2288.3861951280087,"d":"2,288.39"}},null,{"$f":"0.5*(F152+F154)/(1+bdt!S341*$D$6)","v":{"v":859.3691200564255,"d":"859.37"}},null,{"$f":"0.5*(H152+H154)/(1+bdt!U341*$D$6)","v":0},null,{"$f":"0.5*(J152+J154)/(1+bdt!W341*$D$6)","v":0},null,{"$f":"MAX(0,bdt!Y341-$B$4)*$C$5*$D$6/(1+bdt!Y341*$D$6)","v":0}]
[{"$nulls":3},{"$f":"0.5*(E153+E155)/(1+bdt!R342*$D$6)","v":{"v":427.6938370582277,"d":"427.69"}},null,{"$f":"0.5*(G153+G155)/(1+bdt!T342*$D$6)","v":0},null,{"$f":"0.5*(I153+I155)/(1+bdt!V342*$D$6)","v":0},null,{"$f":"0.5*(K153+K155)/(1+bdt!X342*$D$6)","v":0}]
[{"$nulls":4},{"$f":"0.5*(F154+F156)/(1+bdt!S343*$D$6)","v":0},null,{"$f":"0.5*(H154+H156)/(1+bdt!U343*$D$6)","v":0},null,{"$f":"0.5*(J154+J156)/(1+bdt!W343*$D$6)","v":0},null,{"$f":"MAX(0,bdt!Y343-$B$4)*$C$5*$D$6/(1+bdt!Y343*$D$6)","v":0}]
[{"$nulls":5},{"$f":"0.5*(G155+G157)/(1+bdt!T344*$D$6)","v":0},null,{"$f":"0.5*(I155+I157)/(1+bdt!V344*$D$6)","v":0},null,{"$f":"0.5*(K155+K157)/(1+bdt!X344*$D$6)","v":0}]
[{"$nulls":6},{"$f":"0.5*(H156+H158)/(1+bdt!U345*$D$6)","v":0},null,{"$f":"0.5*(J156+J158)/(1+bdt!W345*$D$6)","v":0},null,{"$f":"MAX(0,bdt!Y345-$B$4)*$C$5*$D$6/(1+bdt!Y345*$D$6)","v":0}]
[{"$nulls":7},{"$f":"0.5*(I157+I159)/(1+bdt!V346*$D$6)","v":0},null,{"$f":"0.5*(K157+K159)/(1+bdt!X346*$D$6)","v":0}]
[{"$nulls":8},{"$f":"0.5*(J158+J160)/(1+bdt!W347*$D$6)","v":0},null,{"$f":"MAX(0,bdt!Y347-$B$4)*$C$5*$D$6/(1+bdt!Y347*$D$6)","v":0}]
[{"$nulls":9},{"$f":"0.5*(K159+K161)/(1+bdt!X348*$D$6)","v":0}]
[{"$nulls":10},{"$f":"MAX(0,bdt!Y349-$B$4)*$C$5*$D$6/(1+bdt!Y349*$D$6)","v":0}]
[]
[]
["11th caplet:"]
[{"$nulls":11},{"$f":"MAX(0,bdt!Z328-$B$4)*$D$6*$C$5/(1+bdt!Z328*$D$6)","v":{"v":1138376.1023419679,"d":"1,138,376.10"}}]
[{"$nulls":10},{"$f":"0.5*(L165+L167)/(1+bdt!Y329*$D$6)","v":{"v":785219.951491843,"d":"785,219.95"}}]
[{"$nulls":9},{"$f":"0.5*(K166+K168)/(1+bdt!X330*$D$6)","v":{"v":540011.4178250849,"d":"540,011.42"}},null,{"$f":"MAX(0,bdt!Z330-$B$4)*$D$6*$C$5/(1+bdt!Z330*$D$6)","v":{"v":566433.8640446984,"d":"566,433.86"}}]
[{"$nulls":8},{"$f":"0.5*(J167+J169)/(1+bdt!W331*$D$6)","v":{"v":398178.2813872882,"d":"398,178.28"}},null,{"$f":"0.5*(L167+L169)/(1+bdt!Y331*$D$6)","v":{"v":392201.59734057664,"d":"392,201.60"}}]
[{"$nulls":7},{"$f":"0.5*(I168+I170)/(1+bdt!V332*$D$6)","v":{"v":267247.86883291136,"d":"267,247.87"}},null,{"$f":"0.5*(K168+K170)/(1+bdt!X332*$D$6)","v":{"v":266456.268312007,"d":"266,456.27"}},null,{"$f":"MAX(0,bdt!Z332-$B$4)*$D$6*$C$5/(1+bdt!Z332*$D$6)","v":{"v":254073.55134888543,"d":"254,073.55"}}]
[{"$nulls":6},{"$f":"0.5*(H169+H171)/(1+bdt!U333*$D$6)","v":{"v":190686.52321697498,"d":"190,686.52"}},null,{"$f":"0.5*(J169+J171)/(1+bdt!W333*$D$6)","v":{"v":184572.1145715656,"d":"184,572.11"}},null,{"$f":"0.5*(L169+L171)/(1+bdt!Y333*$D$6)","v":{"v":168438.66522683622,"d":"168,438.67"}}]
[{"$nulls":5},{"$f":"0.5*(G170+G172)/(1+bdt!T334*$D$6)","v":{"v":134479.87146242606,"d":"134,479.87"}},null,{"$f":"0.5*(I170+I172)/(1+bdt!V334*$D$6)","v":{"v":120777.83316516357,"d":"120,777.83"}},null,{"$f":"0.5*(K170+K172)/(1+bdt!X334*$D$6)","v":{"v":105559.29429860845,"d":"105,559.29"}},null,{"$f":"MAX(0,bdt!Z334-$B$4)*$D$6*$C$5/(1+bdt!Z334*$D$6)","v":{"v":91144.96556909753,"d":"91,144.97"}}]
[{"$nulls":4},{"$f":"0.5*(F171+F173)/(1+bdt!S335*$D$6)","v":{"v":90427.08904742108,"d":"90,427.09"}},null,{"$f":"0.5*(H171+H173)/(1+bdt!U335*$D$6)","v":{"v":79008.47497520715,"d":"79,008.47"}},null,{"$f":"0.5*(J171+J173)/(1+bdt!W335*$D$6)","v":{"v":65513.08179059541,"d":"65,513.08"}},null,{"$f":"0.5*(L171+L173)/(1+bdt!Y335*$D$6)","v":{"v":49017.49417845662,"d":"49,017.49"}}]
[{"$nulls":3},{"$f":"0.5*(E172+E174)/(1+bdt!R336*$D$6)","v":{"v":60393.572691639216,"d":"60,393.57"}},null,{"$f":"0.5*(G172+G174)/(1+bdt!T336*$D$6)","v":{"v":50968.73025352028,"d":"50,968.73"}},null,{"$f":"0.5*(I172+I174)/(1+bdt!V336*$D$6)","v":{"v":39220.7877150355,"d":"39,220.79"}},null,{"$f":"0.5*(K172+K174)/(1+bdt!X336*$D$6)","v":{"v":26091.238205543737,"d":"26,091.24"}},null,{"$f":"MAX(0,bdt!Z336-$B$4)*$D$6*$C$5/(1+bdt!Z336*$D$6)","v":{"v":8195.816478067472,"d":"8,195.82"}}]
[null,null,{"$f":"0.5*(D173+D175)/(1+bdt!Q337*$D$6)","v":{"v":39638.18726603397,"d":"39,638.19"}},null,{"$f":"0.5*(F173+F175)/(1+bdt!S337*$D$6)","v":{"v":31653.38613982788,"d":"31,653.39"}},null,{"$f":"0.5*(H173+H175)/(1+bdt!U337*$D$6)","v":{"v":23135.922763892904,"d":"23,135.92"}},null,{"$f":"0.5*(J173+J175)/(1+bdt!W337*$D$6)","v":{"v":14011.839318752302,"d":"14,011.84"}},null,{"$f":"0.5*(L173+L175)/(1+bdt!Y337*$D$6)","v":{"v":4068.7546259944374,"d":"4,068.75"}}]
[null,{"$f":"0.5*(C174+C176)/(1+bdt!P338*$D$6)","v":{"v":25581.429238539597,"d":"25,581.43"}},null,{"$f":"0.5*(E174+E176)/(1+bdt!R338*$D$6)","v":{"v":19522.142864678255,"d":"19,522.14"}},null,{"$f":"0.5*(G174+G176)/(1+bdt!T338*$D$6)","v":{"v":13527.198917808453,"d":"13,527.20"}},null,{"$f":"0.5*(I174+I176)/(1+bdt!V338*$D$6)","v":{"v":7468.241680499627,"d":"7,468.24"}},null,{"$f":"0.5*(K174+K176)/(1+bdt!X338*$D$6)","v":{"v":2014.250000333145,"d":"2,014.25"}},null,{"$f":"MAX(0,bdt!Z338-$B$4)*$D$6*$C$5/(1+bdt!Z338*$D$6)","v":0}]
[{"$f":"0.5*(B175+B177)/(1+bdt!O339*$D$6)","v":{"v":16266.141426976617,"d":"16,266.14"}},null,{"$f":"0.5*(D175+D177)/(1+bdt!Q339*$D$6)","v":{"v":11870.605321905936,"d":"11,870.61"}},null,{"$f":"0.5*(F175+F177)/(1+bdt!S339*$D$6)","v":{"v":7707.595512829998,"d":"7,707.60"}},null,{"$f":"0.5*(H175+H177)/(1+bdt!U339*$D$6)","v":{"v":3959.2597142290356,"d":"3,959.26"}},null,{"$f":"0.5*(J175+J177)/(1+bdt!W339*$D$6)","v":{"v":1005.3270319036614,"d":"1,005.33"}},null,{"$f":"0.5*(L175+L177)/(1+bdt!Y339*$D$6)","v":0}]
[null,{"$f":"0.5*(C176+C178)/(1+bdt!P340*$D$6)","v":{"v":7127.820839470472,"d":"7,127.82"}},null,{"$f":"0.5*(E176+E178)/(1+bdt!R340*$D$6)","v":{"v":4377.941586233512,"d":"4,377.94"}},null,{"$f":"0.5*(G176+G178)/(1+bdt!T340*$D$6)","v":{"v":2102.0959162969802,"d":"2,102.10"}},null,{"$f":"0.5*(I176+I178)/(1+bdt!V340*$D$6)","v":{"v":501.60375655016946,"d":"501.60"}},null,{"$f":"0.5*(K176+K178)/(1+bdt!X340*$D$6)","v":0},null,{"$f":"MAX(0,bdt!Z340-$B$4)*$D$6*$C$5/(1+bdt!Z340*$D$6)","v":0}]
[null,null,{"$f":"0.5*(D177+D179)/(1+bdt!Q341*$D$6)","v":{"v":2464.9292750400296,"d":"2,464.93"}},null,{"$f":"0.5*(F177+F179)/(1+bdt!S341*$D$6)","v":{"v":1102.08754759559,"d":"1,102.09"}},null,{"$f":"0.5*(H177+H179)/(1+bdt!U341*$D$6)","v":{"v":249.63858814221712,"d":"249.64"}},null,{"$f":"0.5*(J177+J179)/(1+bdt!W341*$D$6)","v":0},null,{"$f":"0.5*(L177+L179)/(1+bdt!Y341*$D$6)","v":0}]
[{"$nulls":3},{"$f":"0.5*(E178+E180)/(1+bdt!R342*$D$6)","v":{"v":579.2913600995416,"d":"579.29"}},null,{"$f":"0.5*(G178+G180)/(1+bdt!T342*$D$6)","v":{"v":124.71561584742973,"d":"124.72"}},null,{"$f":"0.5*(I178+I180)/(1+bdt!V342*$D$6)","v":0},null,{"$f":"0.5*(K178+K180)/(1+bdt!X342*$D$6)","v":0},null,{"$f":"MAX(0,bdt!Z342-$B$4)*$D$6*$C$5/(1+bdt!Z342*$D$6)","v":0}]
[{"$nulls":4},{"$f":"0.5*(F179+F181)/(1+bdt!S343*$D$6)","v":{"v":61.88785548522977,"d":"61.89"}},null,{"$f":"0.5*(H179+H181)/(1+bdt!U343*$D$6)","v":0},null,{"$f":"0.5*(J179+J181)/(1+bdt!W343*$D$6)","v":0},null,{"$f":"0.5*(L179+L181)/(1+bdt!Y343*$D$6)","v":0}]
[{"$nulls":5},{"$f":"0.5*(G180+G182)/(1+bdt!T344*$D$6)","v":0},null,{"$f":"0.5*(I180+I182)/(1+bdt!V344*$D$6)","v":0},null,{"$f":"0.5*(K180+K182)/(1+bdt!X344*$D$6)","v":0},null,{"$f":"MAX(0,bdt!Z344-$B$4)*$D$6*$C$5/(1+bdt!Z344*$D$6)","v":0}]
[{"$nulls":6},{"$f":"0.5*(H181+H183)/(1+bdt!U345*$D$6)","v":0},null,{"$f":"0.5*(J181+J183)/(1+bdt!W345*$D$6)","v":0},null,{"$f":"0.5*(L181+L183)/(1+bdt!Y345*$D$6)","v":0}]
[{"$nulls":7},{"$f":"0.5*(I182+I184)/(1+bdt!V346*$D$6)","v":0},null,{"$f":"0.5*(K182+K184)/(1+bdt!X346*$D$6)","v":0},null,{"$f":"MAX(0,bdt!Z346-$B$4)*$D$6*$C$5/(1+bdt!Z346*$D$6)","v":0}]
[{"$nulls":8},{"$f":"0.5*(J183+J185)/(1+bdt!W347*$D$6)","v":0},null,{"$f":"0.5*(L183+L185)/(1+bdt!Y347*$D$6)","v":0}]
[{"$nulls":9},{"$f":"0.5*(K184+K186)/(1+bdt!X348*$D$6)","v":0},null,{"$f":"MAX(0,bdt!Z348-$B$4)*$D$6*$C$5/(1+bdt!Z348*$D$6)","v":0}]
[{"$nulls":10},{"$f":"0.5*(L185+L187)/(1+bdt!Y349*$D$6)","v":0}]
[{"$nulls":11},{"$f":"MAX(0,bdt!Z350-$B$4)*$D$6*$C$5/(1+bdt!Z350*$D$6)","v":0}]
[]
[]
[]
[]
[]
["So the value of the cap is:",null,{"$f":"A14+A21+A29+A39+A52+A67+A84+A104+A128+A151+A176","v":{"v":187941.03741555446,"d":"187,941.04"}}]