THE BLACK-SCHOLES-MERTON MODEL

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THE BLACK-SCHOLES-MERTON MODEL

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Contents

• Lognormal property of stock prices
• The distribution of the rate of return
• The expected return
• Volatility
• Concept underlying the Black-Scholes-Merton
  differential equation
• Derivation of the Black-Scholes-Merton
  differential equation
• Risk-neutral valuation
• Black-Scholes pricing formulas
• Cumulative normal distribution function
• Implied volatilities
• Dividends

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Lognormal distribution
A variable that has s lognormal distribution can
take any value between zero and infinity.
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The distribution of the rate of return
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The expected return
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• Expected returnE(R) µ

• Expected returnE(x)

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