fm3_chapter19

fm3_chapter19 - UN-13B A 1 2 3 4 5 6 7 8 9 10 11 12 13 14...

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UN-13B Black-Scholes Option-Pricing Formula S 50 Current stock price X 45 Exercise price r 4.00% Risk-free rate of interest T 0.75 Time to maturity of option (in years) Sigma 30% 0.6509 <-- (LN(S/X)+(r+0.5*sigma^2)*T)/(sigma*SQRT(T)) 0.3911 0.7424 0.6521 Call price 8.64 Put price 2.31 <-- call price - S + X*Exp(-r*T): by Put-Call parity 2.31 8.6434 5 5 0.0000 0 10 0.0000 0 15 0.0000 0 20 0.0029 0 25 0.0484 0 30 0.3101 0 35 1.1077 0 40 2.7319 0 45 5.2777 0 50 8.6434 5 55 12.6307 10 60 17.0378 15 65 21.7056 20 70 26.5256 25 75 31.4304 30 80 36.3811 35 Stock volatility, σ 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 ) <-- X*exp(-r*T)*N(-d 2 ) - S*N(-d 1 ): direct formula Data table: Comparing the Black-Scholes to the intrinsic value Stock Call price Intrinsic value 0 10 20 30 40 50 60 70 80 0 5 10 15 20 25 30 35 Black-Scholes Price Versus Instrinsic Value Call price Intrinsic value Stock price, S Data table header: = B14 Data table header: =Max(B2-B3,0). This is the option's intrinsic value . A B C D E F G H I J K L M 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 39 40
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UN-13C BLACK-SCHOLES MODEL IN VBA S 100 X 100 Stock price Call Put T 1.00 ### ### <--This is the header of the Data Table start 40 Interest 10.00% 40 ### ### step 5 Sigma 40.00% 45 ### ### 50 ### ### Call price ### #MACRO? 55 ### ### Put price ### #MACRO? 60 ### ### 65 ### ### 70 ### ### To the right is a data 75 ### ### table that gives the 80 ### ### call and put values for 85 ### ### various stock 90 ### ### prices. 95 ### ### 100 ### ### 105 ### ### 110 ### ### 115 ### ### 120 ### ### 125 ### ### 130 ### ### =B8 =B9 40 50 60 70 80 90 100 110 120 130 0 5 10 15 20 25 30 35 40 45 50 Call and Put Prices using Black-Scholes Cal Put Stock price, S A B C D E F G H I J K L M 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
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Date Return 30-May-06 38.61 31-May-06 38.79 0.47% #MACRO? Return statistics 1-Jun-06 39.71 2.34% #MACRO? Average daily return -0.09% 2-Jun-06 39.61 -0.25% #MACRO? Standard deviation of daily return 1.31% 5-Jun-06 38.75 -2.20% #MACRO? 6-Jun-06 38.72 -0.08% Annualized mean return -23.59% 7-Jun-06 38.43 -0.75% Annualized sigma 20.66% 8-Jun-06 38.37 -0.16% 9-Jun-06 38.12 -0.65% 12-Jun-06 37.37 -1.99% 13-Jun-06 37.22 -0.40% 14-Jun-06 37.6 1.02% 19-Jul-06 36.62 1.29% 20-Jul-06 36.08 -1.49% 21-Jul-06 35.7 -1.06% 24-Jul-06 36.41 1.97% 25-Jul-06 36.62 0.58% 26-Jul-06 36.59 -0.08% 27-Jul-06 36.35 -0.66% 28-Jul-06 37.11 2.07% QQQQ HISTORICAL PRICES, DAILY DATA and resulting statistics Closing price A B C D E F G 1 2 3 4 5 6 7 8 9 10 11 12 13 14 38 39 40 41 42 43 44 45
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#MACRO? #MACRO? #MACRO? #MACRO? H 1 2 3 4 5 6 7 8 9 10 11 12 13 14 38 39 40 41 42 43 44 45
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Current date 28-Jul-06 Option expiration date 18-Aug-06 S 37.11 X 37 T 0.06 #MACRO? Interest 5.00% Sigma 20.66% Call price #MACRO? #MACRO? Put price #MACRO? #MACRO? Actual prices Call 0.75 Put 0.55 PRICING THE AUGUST 2006 QQQQ OPTIONS Using the historical volatility σ A B C D E 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 39 40 41 42 43 44 45 46 47 48 49 50
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A B C D E 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89
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F G H I J K L M N 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 39 40 41 42 43 44 45 46 47 48 49 50
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F G H I J K L M N 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89
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O P Q R S T U V 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 39 40 41 42 43 44 45 46 47 48 49 50
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O P Q R S T U V 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89
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Date Return 30-Jul-04 34.40 2-Aug-04 33.54 -2.53% Return statistics 1-Sep-04 34.64 3.23% Average monthly return 0.18% 1-Oct-04 36.38 4.90%
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fm3_chapter19 - UN-13B A 1 2 3 4 5 6 7 8 9 10 11 12 13 14...

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