# Binomial Trees Spreadsheet - A B C D E F G H I J K L M N O...

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Bond Yield Calculations (Citicorp 7-1/8, settles 6/16/95, matures 3/15/04) quote = 101.255 n = 18 coupon rate = 7.125 coupon freq = 2 coupon = 3.5625 u = 91 v = 89 w = 0.4944444 accint = 1.8010417 invoice = 103.05604 Yield Calculation: Manual Method y = 6.928949 <== vary this until b15 equals b10 d = 0.9665153 formula = 103.056 Yield Calculation: Automatic Method (using Solver under Tools) d = 0.9665153 <== have Solver choose this cell until b19 equals invoice price (enter number) formula = 103.056 (Goal Seek works, too) yield = 6.9289489 DV01 Calculations y + .01 = 6.9389489 new d = 0.9664686 new p = 102.9907 DV01 = 0.0653377 Duration Calculations period (j) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 weight (wj) 0.0339913 0.032853 0.031753 0.0306898 0.029662 0.028669 0.027709 0.026781 0.025884 0.025018 0.02418 0.02337 0.022588 0.021831 0.0211 0.020394 0.019711 0.553814 check sum: 1 product (j*wj) 0.0168068 0.049097 0.079206 0.1072438 0.133315 0.15752 0.179954 0.20071 0.219874 0.237529 0.253755 0.268629 0.282221 0.294603 0.305838 0.315991 0.325121 9.688676 Duration = 6.3384509 Duration Calculations: Formula D = 6.3384535 (make sure the d is right in b19)

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Unformatted text preview: A B C D E F G H I J K L M N O P Q R S T U 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 Interest Rate Trees Page 2 Binomial Interest Rate Models Parameters h = 0.25 sigma = 0.5 0.5 0.5 0.25 0.25 0.25 <-- times sqrt(h) r(0,0) = mu1 mu2 mu3 5 5 5 5 5 <-- sum Short Rate Tree 5.750 5.500 5.250 5.250 5.000 4.750 5.000 4.750 4.500 4.250 Discount Factor Tree 0.9857278 0.9863441 0.9869608 0.9869608 0.9875778 0.9881952 0.9875778005 0.9881952 0.988813 0.9894312 State Price Tree (Duffie's Formula) 0.1201738 0.2436751 0.3609724 0.4937889002 0.4876551 0.3614239 1 0.4937889002 0.2439799 0.1206253 Discount Factors and Yields maturity 1 2 3 4 (d) 0.9875778005 0.9753101 0.9631954 0.951232 < --- last one uses a trick! (y) 5 4.9999609 4.9998698 4.9997266 < --- vary mu's until this row equals the next one (data) 4.969 4.999 5.03 5.126 (error^2) 0.000961 9.23E-007 0.0009078 0.015945 (sum) 0.0178147338...
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