Discuss the assumptions underlying the Black-Scholes model and how these assumptions affect its accuracy in real-world applications.

The Black-Scholes model, a cornerstone of financial modeling, rests upon several key assumptions that significantly influence its accuracy in real-world scenarios. Understanding these assumptions is crucial for appreciating both the model's strengths and its limitations. First, the model assumes that the underlying asset price follows a geometric Brownian motion. This means that price changes are random, normally distributed, and independent of past price movements. This assumption, while simplifying the model, neglects real-world factors like market crashes, jumps, or predictable trends that deviate from this idealized pattern. For example, a significant news event or regulatory change can cause sudden, non-random price fluctuations, deviating from the model's assumptions. Second, the Black-Scholes model assumes that the risk-free rate of return and the volatility of the underlying asset are constant over the option's lifetime. However, interest rates and volatility are ....