Ch13HullFundamentals7thEd - Fundamentals of Futures and...

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Unformatted text preview: Fundamentals of Futures and Options Markets, 7th Ed, Ch 13, Copyright John C. Hull 2010 Valuing Stock Options: The Black-Scholes-Merton Model Chapter 13 1 Fundamentals of Futures and Options Markets, 7th Ed, Ch 13, Copyright John C. Hull 2010 The Black-Scholes-Merton Random Walk Assumption Consider a stock whose price is S In a short period of time of length t the return on the stock ( S / S ) is assumed to be normal with mean t and standard deviation is expected return and is volatility t 2 Fundamentals of Futures and Options Markets, 7th Ed, Ch 13, Copyright John C. Hull 2010 The Lognormal Property These assumptions imply ln S T is normally distributed with mean: and standard deviation : Because the logarithm of S T is normal, S T is lognormally distributed T S ) 2 / ( ln 2 - + T 3 Fundamentals of Futures and Options Markets, 7th Ed, Ch 13, Copyright John C. Hull 2010 The Lognormal Property continued where [ m , v ] is a normal distribution with mean m and variance v [ ] [ ] T T S S T T S S T T 2 2 2 2 , ) 2 ( ln , ) 2 ( ln ln - - + or 4 Fundamentals of Futures and Options Markets, 7th Ed, Ch 13, Copyright John C. Hull 2010 The Lognormal Distribution E S S e S S e e T T T T T ( ) ( ) ( ) = = - 2 2 2 1 var 5 Fundamentals of Futures and Options Markets, 7th Ed, Ch 13, Copyright John C. Hull 2010 The Expected Return The expected value of the stock price is S e T The return in a short period t is t But the expected return on the stock with continuous compounding is 2 /2 This reflects the difference between arithmetic and geometric means 6 Fundamentals of Futures and Options Markets, 7th Ed, Ch 13, Copyright John C. Hull 2010 7 Mutual Fund Returns (See Business Snapshot 13.1 on page 294)Snapshot 13....
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This note was uploaded on 08/22/2011 for the course FINANCE 422 taught by Professor Jiang during the Spring '11 term at University of Arizona- Tucson.

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Ch13HullFundamentals7thEd - Fundamentals of Futures and...

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