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

Which of the following is NOT an assumption of the original Black-Scholes-Merton model for pricing a European option on a stock?

Discontinuous random jumps in the stock price are not part of the original BSM model. It assumes continuous geometric Brownian motion, constant volatility, a constant risk-free rate and permitted short selling, with no transaction costs.

  1. AThe short-selling of securities with full use of proceeds is permitted
  2. BVolatility of the stock price is constant over the option life
  3. CThe risk-free rate is constant and the same for all maturities
  4. DThe stock price can jump discontinuously with random timingCorrect

Explanation

BSM assumes continuous, smooth geometric Brownian motion paths with no jumps. Short selling allowed, constant volatility and a constant risk-free rate are all standard assumptions. Jump processes appear in extensions such as Merton jump-diffusion, not in the original model.

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