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Unformatted text preview: Fundamentals of Futures and Options Markets , 5 th Edition, Copyright © John C. Hull 2004 12.1 Valuing Stock Options:The BlackScholes Model Chapter 12 Fundamentals of Futures and Options Markets, 5th Edition, 12.2 The BlackScholes Random Walk Assumption Consider a stock whose price is S In a short period of time of length ∆ t the change in the stock price is assumed to be normal with mean μ S ∆ t and standard deviation • μ is expected return and σ is volatility t S ∆ σ Fundamentals of Futures and Options Markets, 5th Edition, 12.3 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 σ μ + T σ Fundamentals of Futures and Options Markets, 5th Edition, 12.4 The Lognormal Property continued where φ [ m , s ] is a normal distribution with mean m and standard deviation s [ ] [ ] T T S S T T S S T T σ σ μ φ = σ σ μ + φ ≈ , ) 2 ( ln or , ) 2 ( ln ln 2 2 Fundamentals of Futures and Options Markets, 5th Edition, 12.5 The Lognormal Distribution E S S e S S e e T T T T T ( ) ( ) ( ) = =  2 2 2 1 var μ μ σ Fundamentals of Futures and Options Markets, 5th Edition, 12.6 The Expected Return The expected value of the stock price is S e μ T The expected return on the stock with continuous compounding is μ – σ 2 /2 The arithmetic mean of the returns over short periods of length ∆ t is μ The geometric mean of these returns is μ – σ 2 /2 Fundamentals of Futures and Options Markets, 5th Edition,...
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This note was uploaded on 10/07/2011 for the course FIN 416 taught by Professor Sankarshanacharya during the Fall '11 term at Ill. Chicago.
 Fall '11
 SankarshanAcharya
 Options

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