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fm3_chapter21

# fm3_chapter21 - UN-14E A 1 2 3 4 5 6 7 8 9 10 11 12 13 14...

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UN-14E S 56 Stock price X 50 Exercise price T 1 Time remaining r 8.00% Risk-free rate of interest Sigma 30% Stock volatility 0.7944 <-- (LN(S/X)+(r+0.5*sigma^2)*T)/(sigma*SQRT(T)) 0.4944 0.7865 0.6895 Call price 12.22 Put price 2.38 <-- call price - S + X*Exp(-r*T): by Put-Call parity Black-Scholes Option Pricing Formula Applied to General Pills Put d 1 d 2 <-- d 1 -Sigma*SQRT(T) N(d 1 ) <-- Uses formula NormSDist(d 1 ) N(d 2 ) <-- Uses formula NormSDist(d 2 ) <-- S*N(d 1 )-X*exp(-r*T)*N(d 2 ) A B C 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

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UN-14E S 56 Stock price X 50 Exercise price T 1 Time remaining r 8.00% Risk-free rate of interest Sigma 30% Stock volatility 0.7944 <-- (LN(S/X)+(r+0.5*sigma^2)*T)/(sigma*SQRT(T)) 0.4944 0.7865 0.6895 Call price 12.22 Put price 2.38 <-- call price - S + X*Exp(-r*T): by Put-Call parity Calculating the portfolio insurance proportions Omega 75.45% #MACRO? 1-omega 24.55% #MACRO? Black-Scholes Option Pricing Formula Applied to General Pills Put d 1 d 2 <-- d 1 -Sigma*SQRT(T) N(d 1 ) <-- Uses formula NormSDist(d 1 ) N(d 2 ) <-- Uses formula NormSDist(d 2 ) <-- S*N(d 1 )-X*exp(-r*T)*N(d 2 ) A B C 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
UN-14E S 60 Stock price X 50 Exercise price T 0.9808 #MACRO? r 8.00% Risk-free rate of interest Sigma 30% Stock volatility 1.0263 <-- (LN(S/X)+(r+0.5*sigma^2)*T)/(sigma*SQRT(T)) 0.7292 0.8476 0.7671 Call price 15.40 Put price 1.63 <-- call price - S + X*Exp(-r*T): by Put-Call parity Calculating the portfolio insurance proportions Omega 82.53% #MACRO? 1-omega 17.47% #MACRO? Black-Scholes Option Pricing Formula Applied to General Pills Put d 1 d 2 <-- d 1 -Sigma*SQRT(T) N(d 1 ) <-- Uses formula NormSDist(d 1 ) N(d 2 ) <-- Uses formula NormSDist(d 2 ) <-- S*N(d 1 )-X*exp(-r*T)*N(d 2 ) A B C 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

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Pages 581-583 Page 4 PORTFOLIO INSURANCE SIMULATION X 50 Exercise price of puts in strategy 15% Mean of lognormal distribution 30% Sigma of lognormal distribution r 8% Interest rate Initial 1000 Initial investment Portfolio value, beginning of week Week Stocks Bonds 0 56.00 60.00 0.7944 0.7545 754.50 245.50 1000.00 1 60.00 52.00 1.0263 0.8253 870.06 184.22 1054.27 2 52.00 ??? 0.5419 0.6635 622.73 315.82 938.55 Mean, μ Sigma, σ Stock price at begin. of week Stock price at end of week d 1 , begining of week Omega, beginning of week Portfolio value
Pages 581-583 Page 5 Portfolio value, end of week Stocks Bonds 808.39 245.88 1054.27 754.05 184.50 938.55 ??? 316.30 ??? Portfolio value

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Page 585-86 Page 6 PORTFOLIO INSURANCE SIMULATION X 50 Exercise price of puts in strategy 15% Mean of lognormal distribution 30% Sigma of lognormal distribution r 8% Interest rate Initial 1000 Initial investment Portfolio value, begin Week Stocks Bonds 0 56.00 53.61 0.7944 0.7545 754.50 245.50 1 53.61 50.96 0.6470 0.7029 680.53 287.58 2 50.96 50.51 0.4734 0.6364 595.04 339.96 3 50.51 47.70 0.4392 0.6232 579.68 350.55 4 47.70 47.68 0.2366 0.5394 484.61 413.87 5 47.68 45.33 0.2295 0.5370 482.71 416.25 6 45.33 46.71 0.0440 0.4588 401.77 474.00 7 46.71 48.31 0.1434 0.5016 445.83 442.90 8 48.31 49.11 0.2587 0.5512 498.68 406.06 9 49.11 48.02 0.3134 0.5747 525.10 388.56 10 48.02 45.45 0.2245 0.5380 485.59 416.95 11 45.45 47.19 0.0117 0.4486 393.51 483.68 12 47.19 47.85 0.1454 0.5059 451.73 441.26 13 47.85 48.50 0.1920 0.5263 473.68 426.37 14 48.50 44.49 0.2373 0.5460 495.30 411.78 15 44.49 42.46 -0.1096 0.4012 347.79 519.03 16 42.46 43.19 -0.3083 0.3234 275.45 576.27 17 43.19 43.46 -0.2534 0.3453 296.04 561.28 18 43.46 42.55 -0.2408 0.3510 301.91 558.17 19 42.55 44.13 -0.3434 0.3126 267.14 587.44 20 44.13 42.79 -0.2042 0.3671 317.70 547.70 21 42.79 38.00 -0.3504 0.3116 266.96 589.67 22 38.00 37.27 -0.8876 0.1467 121.40 706.26 23 37.27 37.11 -1.0003 0.1220 100.82 725.59 24 37.11 36.76 -1.0483 0.1128 93.28 733.82 25 36.76 37.72 -1.1223 0.0993 82.17 745.19 26 37.72 40.11 -1.0343 0.1168 96.99 733.64 27 40.11 37.71 -0.7711 0.1801 150.89 687.02 28 37.71 39.18 -1.1007 0.1050 87.14 742.82 29 39.18 37.16 -0.9446 0.1381 115.25 719.25 30 37.16 35.92 -1.2504 0.0806 66.87 762.78 31 35.92 33.18 -1.4697 0.0523 43.37 785.23 32 33.18 33.54 -1.9461 0.0176 14.59 811.91 33 33.54 35.22 -1.9497 0.0177 14.63 813.28 34 35.22 34.58 -1.7405 0.0296 24.52 805.36 35 34.58 33.14 -1.9121 0.0198 16.45 814.23 36 33.14 33.15 -2.2399 0.0085 7.08 824.17 37 33.15 33.47 -2.3266 0.0068 5.64 826.88 Mean, μ Sigma, σ Stock price at begin. of week Stock price at end of week d 1 , beginning of week Omega,
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• Spring '09
• EDWARDCHANG
• Prime number, portfolio value, 0.2209 0.3580 306.68 Week, 0.9808 8.00%, 5.28 6.03 7.24 5.94 15.40 7.23 6.17 2.53 2.59 0.14 0.35 0.26 0.01 0.01 L

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