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What Is the Core Assumption of the Black-Scholes Model?

The Black-Scholes model makes several core assumptions, including that the underlying asset price follows a geometric Brownian motion, volatility and interest rates are constant, and there are no transaction costs. Crucially, it assumes the option is European-style and cannot be exercised early.

How Does the Early Exercise Feature of American Options Affect Their Pricing Relative to European Options?
Does the Early Exercise Rule Apply Equally to American-Style Put Options?
How Does the Black-Scholes Model Handle the Early Exercise Feature of American Options?
What Is the Concept of ‘Early Exercise Premium’ in American Options?