Assumptions of Black-Scholes-Merton Model
We will cover following topics
Introduction
The Black-Scholes-Merton (BSM) option pricing model is a foundational tool in finance for valuing European-style options. To use the model effectively, it’s crucial to understand the underlying assumptions that form the basis of its calculations. In this chapter, we will explore the key assumptions behind the BSM model, which help us make reasonable estimations of option prices and guide our understanding of its limitations.
Assumption 1: Efficient Markets
The BSM model assumes that financial markets are perfectly efficient. This implies that all available information is already reflected in asset prices. In such markets, it is impossible to consistently earn above-average returns using any trading strategy. The BSM model is rooted in this assumption, as it relies on the concept of no arbitrage, where opportunities for risk-free profits do not exist.
Assumption 2: Constant Volatility
Another crucial assumption is that the volatility of the underlying asset’s returns remains constant over the life of the option. This assumption is necessary to calculate option prices accurately. In reality, volatility can fluctuate, especially in response to news and events. However, for simplicity, BSM assumes constant volatility.
Assumption 3: Lognormal Distribution
The BSM model assumes that the returns of the underlying asset follow a lognormal distribution. This distribution is asymmetric and captures the property that asset prices cannot fall below zero. It’s a reasonable approximation for many assets but may not hold for all. The lognormal assumption simplifies the mathematics of option pricing.
Assumption 4: Risk-Free Interest Rate
The model assumes the existence of a risk-free interest rate, which is constant and known with certainty throughout the life of the option. This rate is used to discount future cash flows back to their present value. In practice, finding a risk-free rate that matches the term of the option can be challenging, but the BSM model relies on this assumption for its calculations.
Assumption 5: No Dividends
The BSM model assumes that the underlying asset does not pay any dividends during the life of the option. In reality, many assets, such as stocks, pay dividends. To account for dividends, an adjusted version of the BSM model, known as the Black-Scholes-Merton Dividend Model, is used.
Conclusion
Understanding the assumptions underpinning the Black-Scholes-Merton option pricing model is essential for its proper application and interpretation. While these assumptions simplify the model and make it tractable, they may not always hold in real-world situations. It’s crucial for financial professionals to be aware of these assumptions and their potential limitations when using the BSM model for option pricing. In practice, adjustments and alternative models may be necessary to accommodate specific market conditions and asset characteristics.