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

A stock trades at 50 and pays a continuous dividend yield of 4% per year. A European option on it expires in 6 months. When the option is priced with the Black-Scholes-Merton model adjusted for the dividend yield, what value replaces the stock price in the formula?

The adjusted stock price is 49.01. With a continuous dividend yield, the stock price is reduced to S0 times e to the power of minus qT, which is 50 times e to the power of minus 0.02. The yield lowers the effective price because holders of the option do not receive the dividends.

  1. A48.04
  2. B49.01Correct
  3. C50.00
  4. D51.01

Explanation

With a continuous yield q, the stock price is replaced by S0*e^(-qT) = 50*e^(-0.04*0.5) = 50*e^(-0.02) = 50*0.9802 = 49.01. The 48.04 figure comes from using the full year, e^(-0.04), instead of T = 0.5. The 51.01 figure applies the wrong sign to the exponent.

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