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CFA Level I · CFA Level I Exam · Simulation of Financial Asset Prices and Returns

An analyst simulates a stock price using a geometric Brownian motion model in which the continuously compounded return over each step is normally distributed. Which feature of the simulated prices is most likely a result of this specification?

Simulated prices can never become negative. Normally distributed continuously compounded returns imply prices equal the starting price multiplied by an exponential term, which is always positive. Prices are lognormal and right-skewed, and individual simulated returns can still be negative.

  1. ASimulated prices can never become negativeCorrect
  2. BSimulated prices have a symmetric distribution
  3. CSimulated returns are always positive

Explanation

If continuously compounded returns are normal, the price is the starting price times an exponential, so it is always positive and lognormally distributed. The price distribution is right-skewed, not symmetric. Returns can be negative because the normal distribution has negative values.

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