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IAI Actuarial Core Principles · Economic Modelling · Principles of option pricing

Which of the following is an assumption underlying the standard Black-Scholes model for a European option?

The standard Black-Scholes model assumes the underlying follows geometric Brownian motion with constant volatility, along with a constant risk-free rate and frictionless continuous trading. Stochastic volatility, jumps, transaction costs and random interest rates all contradict the model's assumptions.

  1. AThe underlying price follows a geometric Brownian motion with constant volatilityCorrect
  2. BThe volatility of the underlying follows its own random process
  3. CThe underlying price can jump discontinuously at random times
  4. DBuying and selling the underlying incurs proportional transaction costs
  5. The risk-free rate changes randomly over the life of the option

Explanation

Black-Scholes assumes log-prices follow a Brownian motion with constant drift and volatility, a constant risk-free rate, continuous frictionless trading and no arbitrage. Stochastic volatility, jumps, transaction costs and random interest rates are extensions or violations of the model, not assumptions of it.

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