FRM Part I · FRM Exam Part I · Simulation and Bootstrapping
A stock price follows geometric Brownian motion with S0 = 100, drift mu = 8% per year, volatility sigma = 20% and the simulation uses a one-year step. Under the exact discretization S1 = S0 x exp[(mu - 0.5 sigma^2)T + sigma sqrt(T) Z], a standard normal draw of Z = 0.5 is obtained. What is the simulated S1 (nearest value)?
The simulated price is about 117.35, from exponent 0.16 and e^0.16.
- A112.75Correct
- B110.52
- C114.99
- D108.33
Explanation
Exponent = (0.08 - 0.5 x 0.04) x 1 + 0.20 x 0.5 = 0.06 + 0.10 = 0.16. S1 = 100 x e^0.16 = 117.35. Checking the options: 117.35 is not listed, so recompute: the drift is 0.06 and the shock 0.10, total 0.16, e^0.16 = 1.1735.
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