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

A stock index is at 100 and pays a continuous dividend yield of 3% per year. The risk-free rate is 5% (continuously compounded). For a two-year European option, the Black-Scholes-Merton model with a continuous yield replaces S0 with which value?

The input becomes about 94.18. With a continuous dividend yield, the stock price is reduced by e raised to minus yield times maturity. Here 100 × e^(-0.03×2) = 100 × e^(-0.06), which equals roughly 94.18, reflecting the dividends that option holders will not receive.

  1. A97.04
  2. B94.18Correct
  3. C106.18
  4. D100.00

Explanation

With a continuous dividend yield q, the model uses S0 × e^(-qT) = 100 × e^(-0.03×2) = 100 × e^(-0.06) = 94.18. 97.04 results from using one year instead of two. 106.18 has the wrong sign in the exponent.

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