Flaws in the Black-Scholes Pricing Model

A turning point in the evolution of options trading was in the year 1973, when professors Fischer Black and Myron Scholes write a paper titled, "Pricing of Options and Corporate Liabilities."

This was viewed as a significant effort at articulating pricing of options and corporate bonds based on the assumption that a risk-free interest rate existed. It is still used today for estimating what options should be worth, but it is applied mostly in institutional portfolio management departments and in academia. Most individual traders have long since recognized that the model is flawed, in several ways:

1. The model was developed in 1973, when calls were traded on only 16 stocks, and there were no puts at all. The market was so young that many of today’s strategies did not yet exist.

In addition, the “population” of options trading was extremely limited. This means the assumptions in use for the model do not apply in the more complex modern options industry.

2. The Internet had not yet been invented. Without the ability to crunch numbers easily and automatically, the Black-Scholes model depended on manual calculations.

With thousands more options to trade and with faster, more detailed, and more widely used formulas for tracking value, the whole options market is a different animal today than it was in 1973. Even open contracts levels have changed, growing in the billions since 1973 to a volume today that was unimaginable in the past. This also affects valuation very directly. The use of delta, gamma and vega are far more reliable measurements of implied volatility and option pricing than the more obscure Black-Scholes model with its impractical variables.

3. Some of the assumptions in the formula are questionable under today’s economic and market conditions. For example, the calculationuses an assumed risk-free interest rate to compare to buying or selling options. It is questionable whether such a rate exists today.

The formula is also based on European-style options, those that can be exercised only on the last trading day. Other than some index options, the majority of publicly traded options can be closed at any time before expiration; this changes the calculation. Finally, the Black-Scholes model makes one assumption that is fatally flawed: the assumption is that implied volatility on the date of the analysis will remain unchanged until expiration. Every trader knows this is simply inaccurate.

4. Dividends are not calculated in the equation, which assumes no dividends are applicable.

Today, anyone trading in options along with related stock positions has to consider the impact of dividend yield on overall return. In fact, in comparing values among two or more underlyings, dividend yield often is the determining factor in deciding which one is a better value.

The problems with Black-Scholes are numerous. Since it was first published, several additional theories have been put forth to expand Black-Scholes and make it more applicable to realistic market conditions. Even so, it is not likely that an accurate market model will be developed in the near future.

The formula does contain too many variables, and the more variables you use, the less reliable a formula becomes. These include the assumption of a risk-free interest rate, European expiration, unchanging implied volatility, and the lack of dividend. When one variable is used in a formula, it is troubling to a degree. When two or three apply, the inaccuracy is exponentially greater.

A solution may be to focus on the only true variable in option pricing, which is implied volatility. If this is isolated from the two other formats of pricing (intrinsic value and time value), a better and simpler model may evolve. Today, “time value” often is defined inaccurately as the entire option premium except intrinsic value. In fact, time value is just as predictable as intrinsic value, and implied volatility (“extrinsic value”) is where all the variables reside.

The solution to the pricing problem should be limited to studies of implied volatility. Thus, the historical volatility of the underlying, market conditions, and the proximity between current market value of stock and strike of the option, are the true determining factors in placing value on an option.

Trading strategies invariably rely on a study of volatility, and this is where all of the variability is found in premium value. The real test of options should not be to arrive at a “fair” estimated total premium value, but to identify levels of volatility to better time entry and exit. This is a difficult task, you will benefit by getting help just focusing on volatility for this important timing of trades. To improve your option trade timing, check the Benzinga service Options & Volatility Edge which is designed to help you improve selection of options as well as timing of your trades