An Introduction to the Black-Scholes-Merton Model

Did you know that the Black-Scholes-Merton (BSM) model has revolutionized the economic and finance industry? Developed in the early 1970s by economists Fischer Black, Myron Scholes, and Robert C. Merton, this mathematical framework allows investors and analysts to estimate the price of options.

Considering factors such as the underlying asset price, strike price, time to expiration, risk-free interest rate, and volatility, the BSM model provides a way to estimate the value of options. It has become an essential tool for pricing and trading options, enabling market participants to make informed decisions and manage risk effectively.

How the BSM Model Has Impacted the Financial/Economic Industry

Increased Option Liquidity and Efficiency: The pricing formula of the BSM model has played a vital role in fostering the growth of options markets, resulting in enhanced liquidity and market efficiency.

Option Trading Expansion: The theoretical foundation of the BSM model has promoted the expansion of option trading strategies, empowering investors to engage in various market conditions and better mitigate risk

Financial Innovation: The insights from the BSM model have catalyzed financial innovation, accelerating the development of new derivative instruments and investment strategies.

Academic Advancement: The BSM model has sparked discussions on option pricing, risk management, and quantitative finance, fostering exploration and advancement.

When and How To Use the BSM Model

While a handy tool, the BSM model is only as accurate as the assumptions that feed the model. Most inputs are explicitly defined or easy to estimate, but one of the trickiest (and most sensitive) assumptions is the underlying asset’s volatility (or bounciness). We calculate volatility in one of three ways – historical volatility of the asset, volatility expectations of the market based on other option trades, and the volatility of comparable assets. Depending on the details of a given situation, we may use one, two, or even all three of these estimates for maximum precision. The more accurate we can forecast volatility, our BSM result will be more precise.

Another significant limitation of the BSM model is that it isn’t flexible to model more exotic instruments or awards, such as options with price-vesting conditions or exotic warrants with features such as the liquidation preference and the conversion features (find out more from our article, Warrants on Preferred Stock). We must use a more complex model, like a lattice or Monte Carlo simulation, in those cases. It is essential to ensure we use the right tools for a given job.

Understanding how and when the BSM model works (and, just as importantly, when it doesn’t work) is essential when making important financial decisions. Effective use of the model will aid in navigating the complexities of the options market and enable market participants to make informed decisions.

Equity Methods and the BSM Model

Here at EM, we use this model to help clients value and account for options issued to employees as compensation. For many companies, options are a powerful way to align the interests of employees and shareholders by tying compensation outcomes to stock price growth. The accounting guidance requires that companies recognize a non-cash expense equal to the fair value of the equity instruments they grant to employees. The BSM model provides a straightforward and proven way to do so.