Explanation

C is correct. The no-arbitrage assumption is fundamental to the Black-Scholes-Merton model derivation. This assumption states that risk-free arbitrage opportunities cannot exist in the market, which is essential for the model's risk-neutral pricing framework. Unlike other assumptions that have been relaxed over time (such as dividend payments or early exercise), the no-arbitrage condition remains a core requirement.

A is incorrect because the BSM model has been extended to handle dividend-paying assets through various methods, including discrete dividend adjustments and continuous dividend yield models.

B is incorrect because while BSM was originally derived for European options, it can be applied to American call options on non-dividend paying stocks where early exercise is never optimal.

D is incorrect because the BSM model assumes that stock returns over short periods are normally distributed, but this leads to a lognormal distribution for stock prices over longer periods, not a normal distribution.