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IAI Actuarial Core Principles · Economic Modelling · Black-Scholes derivative-pricing model

Which of the following is one of the standard assumptions underlying the Black-Scholes model for pricing a European option on a non-dividend-paying share?

The Black-Scholes model assumes the share price follows geometric Brownian motion with constant volatility. It does not allow jumps, stochastic interest rates, transaction costs or price-dependent volatility, since it assumes constant rates and frictionless markets.

  1. AThe share price follows geometric Brownian motion with constant volatilityCorrect
  2. BThe share price can jump by a fixed amount at random times
  3. CThe risk-free rate follows a mean-reverting stochastic process
  4. DTransaction costs are proportional to the size of each trade
  5. Volatility increases with the level of the share price

Explanation

Black-Scholes assumes the share price follows geometric Brownian motion, so log returns are normal with constant volatility. Jumps, stochastic interest rates, transaction costs and price-dependent volatility are all outside the model, which assumes a constant risk-free rate and frictionless trading.

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