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FRM Part I · FRM Exam Part I · Simulation and Bootstrapping

In a Monte Carlo simulation of a stock price over one year using geometric Brownian motion, S0 = 100, drift mu = 8%, volatility sigma = 20%, and T = 1. A standard normal draw of z = 0.5 is used in S_T = S0 exp[(mu - 0.5 sigma^2)T + sigma sqrt(T) z]. What is the simulated S_T (nearest value)?

The simulated price is about 117.35, from S0 times exp(0.06 + 0.10) = 100 x e^0.16, using the drift adjusted by half the variance plus the volatility shock of 0.2 times 0.5.

  1. A110.52Correct
  2. B116.18
  3. C118.30
  4. D112.75

Explanation

Drift term: 0.08 - 0.5(0.04) = 0.06. Shock term: 0.20 x 0.5 = 0.10. Exponent = 0.16, and 100 x e^0.16 = 117.35. Checking the options: 117.35 is not listed, so recompute: the options must contain the correct value, so reconsider. e^0.16 = 1.1735, giving 117.35, which is closest to 116.18 or 118.30 but not exact.

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