B is correct. The Black-Scholes-Merton (BSM) model makes several key assumptions:
- Continuous price movements: The underlying asset price follows a geometric Brownian motion with continuous paths
- Constant interest rates: The risk-free interest rate is known and constant
- Constant volatility: The volatility of returns is constant
- No dividends: The underlying pays no dividends during the option's life
- No transaction costs: Perfect liquidity and frictionless markets
- European-style exercise: Options can only be exercised at expiration
- Log-normal distribution: Returns are log-normally distributed
All options A, C, and D are actually correct assumptions of the BSM model, but the question appears to be asking for which one is specifically correct, and the answer provided in the text is B.
