The Black Scholes Model Option Pricing

The previously mentioned variables can be combined in an equation to arrive at a theoretical price for an option. Various models have been created to determine the price of an option. Fisher Black and Myron Scholes made a great contribution to the understanding of options when they developed the Black Scholes theoretical equation to evaluate option prices. Before their work in the 1970's, traders had little information and few models to use in determining the theoretical price of an option.

The basic option model for a call is:

Different models are used to evaluate different kinds of options. For example, a model may be used for calls and another variation of the model for puts. Different markets may require separate models. For instance, stock option models may need to include a dividend for a stock, whereas futures do not pay dividends. The bibliography suggests references for further study in this area.

Much work is being done to create a better model but do not be mislead into thinking a slightly more accurate model will predict the proper price of an option. The difficult work of option evaluation is determining the proper input variables and specifically the future volatility of the underlying security price. Anyone trading with a crude evaluation model, but correct volatility estimates, will probably achieve better results than another person trading with a more accurate and so­phisticated model, but incorrect volatility estimates.

More sophisticated models have been developed in the ensuing years to compensate for various shortfalls in the Black Scholes model, but it is still one of the most widely used models for option evaluation. Any shortfalls in the model are relatively minor and do not affect the theoretical option prices substantially. This is especially true when you compare how uncertain the input variable volatility is and how large an effect it has on option pricing.

Why Use The Option Models?

How do you know which method to use and if the options are priced correctly? For example, if you are bul1ish on a market should you buy a call, sell a put, buy a call spread, sell a put spread, buy a straddle, etc.? The option valuation models will help in determining which options are undervalued, fairly valued, and overvalued. The models are a valuable resource in determining which options are correctly priced which will help in implementing a strategy.

If you are bullish and options are under priced then buying calls outright, straddles, or backspreads may be appropriate trading strategies. If options are expensive then selling puts, buying call spreads, or selling put spreads may be the better way to trade the market. If options are fairly valued then any method is equally appropriate.

Theoretical models allow us to determine the value of spreads and more sophisticated strategies quite easily that would otherwise be difficult to evaluate. Theoretical models also help in estimating the delta, gamma, theta, vega, and rho of an option. These important concepts are actually derived from the option valuation models.