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

A stock trades at 100 and will pay a dividend of 3 in exactly three months. A European call has strike 95, expiry in four months, and r = 4% continuously compounded. Using the dividend-adjusted Black-Scholes-Merton approach, what stock price should be used as S0 in the formula, and which statement about early exercise of an American call is correct?

The adjusted price is 100 minus the present value of the dividend, 3e^(-0.01) = 2.97, giving 97.03. Because a dividend is paid, an American call can be optimally exercised early, but only just before the ex-dividend date.

  1. AS0 = 100; early exercise is never optimal
  2. BS0 = 97.03; early exercise may be optimal just before the ex-dividend dateCorrect
  3. CS0 = 97.00; early exercise is optimal immediately
  4. DS0 = 97.03; early exercise is never optimal because dividends are known

Explanation

Subtract the PV of the dividend: 3 e^(-0.04*0.25) = 3(0.99005) = 2.970. S0 = 100 - 2.970 = 97.03. With a dividend, an American call may be exercised early, but only immediately before an ex-dividend date. Using 97.00 undiscounts the dividend; using 100 ignores it.

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