What are the theoretical underpinnings of the Black-Scholes model for pricing derivatives? Explain the assumptions and limitations of the model.
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Detailed Solution & Explanation
The Black-Scholes model is a theoretical framework for pricing derivatives, such as options and warrants. The model is based on several assumptions, including the assumption of a constant risk-free interest rate, a constant volatility, and the ability to buy or sell the underlying asset at any time. The model also assumes that the price of the underlying asset follows a geometric Brownian motion. The limitations of the Black-Scholes model include its assumption of constant volatility, which is not always realistic, and its failure to account for other factors that can affect the price of the underlying asset, such as dividends and interest rates. Despite these limitations, the Black-Scholes model remains a widely used and influential framework for pricing derivatives.
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