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FRM Part I · FRM Exam Part I · The Black-Scholes-Merton Model

A stock trades at $50.00 and will pay one dividend of $2.00 in three months. A European option on it expires in six months, and the continuously compounded risk-free rate is 4% per year. To price the option with the Black-Scholes-Merton model, which stock price should be used as the model input?

The input is about $48.02. For a European option on a stock with a known discrete dividend, you subtract the present value of the dividend from the current price. The $2 dividend discounted three months at 4% is about $1.98, so 50 minus 1.98 gives 48.02.

  1. A$48.00
  2. B$48.02Correct
  3. C$51.98
  4. D$50.00

Explanation

For a known discrete dividend during the option's life, the model input is S0 minus the present value of the dividend. PV = 2 × e^(-0.04×0.25) = 2 × 0.99005 = 1.9801, so the input is 50 − 1.98 = 48.02. Subtracting the undiscounted $2.00 gives 48.00, which ignores the time value of the dividend.

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