What Are the Key Limitations of the Original Black-Scholes Model in a Volatile Market like Crypto?

The original Black-Scholes model has several key limitations that are exacerbated in the volatile crypto market. It assumes volatility is constant, asset prices follow a log-normal distribution, and trading is continuous, none of which perfectly hold true for crypto.

Crypto markets exhibit high, non-constant volatility, price jumps, and "fat tails" (more extreme price movements than log-normal predicts). These violations mean the model can systematically misprice options, particularly those far out-of-the-money, leading to the "volatility smile" phenomenon.