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Unformatted text preview: Valuation Lecture 21 BlackScholes and Option Trading Strategies Materials from Smart, et al. Ch. 18 & Grinblatt & Titman Ch.7 BlackScholes Model Reasoning behind Black and Scholes is similar to that of the binomial model: Does a combination of option and shares exist that provides a riskfree payoff? Assumption s of the model • Stock prices can move at every moment in time. • Movements of stock prices are random, and therefore unpredictable. • Volatility (standard deviation) of stock’s movements is known. September 23, 2009 Calculating BS Call Options S = current market price of underlying stock X = strike price of option t = amount of time before option expires (in years) r = annual riskfree interest rate = annual standard deviation of underlying stock’s returns e = 2.718 N(X) = probability of drawing a value less than or equal to X from standard normal distribution σ t d d t t r X S d σ σ σ = + + = 1 2 2 1 2 ln C = SN(d 1 ) – Xert N(d 2 ) September 23, 2009 An Example Price of Stock Holm Inc. is currently $28 A European call option on Stock Holm Inc. has expiration date three months in the future and strike price of $25. Estimate of standard deviation on Stock Holm Inc. is 40% and the riskfree rate is 3%. 5041 . 7041 . 4 / 1 4 . 4 1 2 4 . 03 . 25 28 ln 1 2 2 1 = = = + + = t d d d σ What should the call price be? N(0.7041) = 0.7593 N(0.5041) = 0.6929 C = 28(0.7593) – 25( 2.718 (.03)(0.25) )(0.6929) = $4.07 September 23, 2009 BS Call Values for Stock Holm Inc. 0 15 28 45 60 5 10 15 20 25 30 35 40 45 50 Stock Price ($) Value of Call Option ($) Call Price Now Call Payoff at expiration C = SN(d 1 ) – Xert N(d 2 ) September 23, 2009 Option’s Delta Measures how much the call price changes as the underlying stock price changes: Delta is equal to the slope of the solid line in previous graph. Delta equals the value N(d1) from BS formula. When call is far out of the money, delta is close to zero....
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This note was uploaded on 09/23/2009 for the course AEM 4280 taught by Professor Ng,d. during the Spring '08 term at Cornell.
 Spring '08
 NG,D.

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