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

Which of the following is an assumption of the original Black-Scholes-Merton model for pricing a European option?

The original BSM model assumes frictionless markets in which short selling is allowed and there are no transaction costs or taxes. It also assumes constant volatility and risk-free rate and no dividends. Stochastic volatility or rates and variable dividends are extensions.

  1. AThe stock's volatility changes randomly over time
  2. BThe stock pays a known continuous dividend yield that varies with price
  3. CShort selling is permitted and there are no transaction costs or taxesCorrect
  4. DThe risk-free rate follows a mean-reverting stochastic process

Explanation

The BSM model assumes constant volatility, a constant risk-free rate, no dividends during the option life, and frictionless markets with short selling allowed and no arbitrage. The other options describe extensions such as stochastic volatility, dividend yields and stochastic rates.

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