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

A stock has S_0 = 50, μ = 14% and σ = 30% per year under the lognormal model. What is the expected stock price after 2 years, E[S_2]?

The expected stock price is S_0 times e to the power μT, which is 50 × e^0.28, about 66.15. The volatility adjustment applies to the expected log return and the median price, not to the expected price level itself.

  1. A50 × e^(0.28) ≈ 66.15Correct
  2. B50 × e^(0.28 − 0.09) ≈ 60.46
  3. C50 × e^(0.28 − 0.18) ≈ 55.26
  4. D50 × e^(0.28 + 0.09) ≈ 72.40

Explanation

E[S_T] = S_0 e^{μT} = 50 × e^{0.28}. e^{0.28} ≈ 1.3231, so E[S_2] ≈ 66.16 (about 66.15). The other options subtract or add a variance term, which applies to the median or log mean, not the expected price.

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