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  UN-13B1234567891011121314151617181920212223242526272829303132 ABCDEFGHIJKS 0 100Current stock priceX90Exercise priceT0.50000Time to maturity of option (in years)r4.00%Risk-free rate of interestSigma35%Stock volatilityd 1 0.6303<-- (LN(S 0 /X)+(r+0.5*sigma^2)*T)/(sigma*SQRT(T))d 2 0.3828<-- d 1 -sigma*SQRT(T)N(d 1 )0.7357<-- Uses formula NormSDist(d 1 )N(d 2 )0.6491<-- Uses formula NormSDist(d 2 )Call price, C 0 16.32<-- S 0 *N(d 1 )-X*exp(-r*T)*N(d 2 )Put price, P 0 4.53<-- call price - S 0  + X*Exp(-r*T): by Put-Call parity4.53<-- X*exp(-r*T)*N(-d 2 ) - S*N(-d 1 ): direct formula StockCallIntrinsicpricepricevalue 450.015380470.027650490.047300510.077430530.121840550.185010570.272040590.388530610.540420630.733840650.974880 The Black-Scholes Option-Pricing Formula 00.20.40.60.811.2455055606570 Stock price S ($) Black-Scholes Price versus Intrinsic Value Call priceIntrinsic value  1234567 ABCCurrent date2/8/2002<-- =DATE(2002,2,8)Expiration date7/19/2002<-- =DATE(2002,7,19)Days between dates161<-- =B3-B2T, time in years to expiration0.441096<-- =B4/365 COMPUTING T USING EXCEL DATE FUNCTION Note: We formatted cell B4 to give a number, using Format|Cells|Number|General  UN-13B1234567891011121314151617181920212223242526272829303132 ABCDEFGHIJKS 0 100Current stock priceX90Exercise priceT0.50000Time to maturity of option (in years)r4.00%Risk-free rate of interestSigma35%Stock volatilityd 1 0.6303<-- =(LN(B2/B3)+(B5+0.5*B6^2)*B4)/(B6*SQRT(B4))d 2 0.3828<-- =B8-SQRT(B4)*B6N(d 1 )0.7357<-- =NORMSDIST(B8)N(d 2 )0.6491<-- =NORMSDIST(B9)Call price, C 0 16.32<-- =B2*B11-B3*EXP(-B5*B4)*B12Put price, P 0 4.53<-- =B14-B2+B3*EXP(-B5*B4)4.53<-- =B3*EXP(-B5*B4)*NORMSDIST(-B9)-B2*NORMSDIST(-B8) StockCallIntrinsicpricepricevalue 450.015380470.027650490.047300510.077430530.121840550.185010570.272040590.388530610.540420630.733840650.974880 The Black-Scholes Option-Pricing FormulaThis version shows the actual Excel formulas 00.20.40.60.811.2455055606570 Stock price S ($) Black-Scholes Price versus Intrinsic Value Call priceIntrinsic value  123456789101112131415161718 ABCD DateClosingstock priceReturn 31-Dec-902.725731-Dec-915.010460.88%<-- =LN(B4/B3)31-Dec-925.40627.60%31-Dec-935.3203-1.60%31-Dec-947.421933.29%31-Dec-9511.562544.33%31-Dec-9625.500079.09%31-Dec-9737.296938.02%31-Dec-9887.500085.27%31-Dec-9997.875011.21%31-Dec-0061.0625-47.18%31-Dec-0166.25008.15% Average return29.01%<-- =AVERAGE(C4:C14)Return variance13.61%<-- =VARP(C4:C14)Return standard deviation36.90%<-- =STDEVP(C4:C14) MICROSOFT STOCK PRICES--ANNUAL DATA
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