FIN4520-Chapter13

FIN4520-Chapter13 - T S ) 2 / ( ln 2 - + T 4 The Lognormal...

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Valuing Stock Options: The Black-Scholes-Merton Model Chapter 13 1
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The Black-Scholes-Merton Model The option pricing model is derived by constructing a riskless hedged portfolio consisting of European options and stock of non-dividend paying firms. The hedged portfolio is continuously rebalanced so that it remains risk free. 2
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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 μ∆ t and standard deviation μ is expected return and σ is volatility t σ 3
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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
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Unformatted text preview: T S ) 2 / ( ln 2 - + T 4 The Lognormal Distribution E S S e S S e e T T T T T ( ) ( ) ( ) = = -2 2 2 1 var 5 The Volatility The volatility is the standard deviation of the continuously compounded rate of return in 1 year. The standard deviation of the return in time t is . If a stock price is $50 and its volatility is 25% per year what is the standard deviation of the price change in one day? t 6 Nature of Volatility Volatility is usually much greater when the market is open (i.e. the asset is trading) than when it is closed. For this reason time is usually measured in trading days not calendar days when options are valued. 7...
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FIN4520-Chapter13 - T S ) 2 / ( ln 2 - + T 4 The Lognormal...

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