Lecture%2024 - Lecture 24 Stock Options Continued I. More...

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Lecture 24 Stock Options Continued I. More Black-Scholes A) Implied Volatility C = S*N(d1) – Ee -rT N(d2) N(.) is the normal distribution d1 = {ln(S/E) + (r + .5 σ 2 29 T}/ σ T 1/2 d2 = d1 - σ T 1/2 The one unknown in the Black-Scholes model is the volatility of the underlying asset. This is NOT the historical volatility, but the actual volatility between now and the time the option expires. Given the options price we can use the Black-Scholes model to predict the volatility between now and the time the option expires. This is known as Implied Volatility Implied Volatility The expected volatility between now and the time of expiration of an option’s underling asset. The following table contains the option prices and implied volatility of Microsoft options In November 2000 Microsoft was trading at 56 7/16. Strike Price Jan Call Option Price B-S Implied Volatility 45 13.625 76.04 50 9.6875 69.23 55 6.3125 63.57 60 3.625 58.05 65 2.03125 56.99 70 1.0625 56.21 75 .59375 57.22 80 .375 60.1 85 .21875 62.09 90 .1875 66.91
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Notice the implied volatility is not constant. In fact, the implied volatility is u-
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Lecture%2024 - Lecture 24 Stock Options Continued I. More...

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