Option Pricing Fundamentals
Gamma is listed next in most contexts and it is equivalent to the change in the Delta of an option with respect to the change in price of its underlying security. In short, Gamma is the "Delta of the Delta" and it is used primarily by professional traders in portfolio hedging calculations. While Gamma is a key factor in managing institutional positions, it is not used regularly by retail option traders and requires no further discussion in this forum.
Theta is the third component and it is most commonly defined as the change in the price of an option with respect to a change in its time to expiration. In laymen's terms, it is a measure of "premium" decay and although seemingly complex, the erosion of time value is one of the easiest aspects of option pricing to understand. The time value of any option can be simply expressed as everything but its intrinsic value. Intrinsic value is not affected by time passage however the extrinsic portion of an option's value decays each day the option is in existence and the closer the option gets to expiration, the faster it decays. In a strictly mathematical sense, time value decays at its square root and that's why the simple passing of a day can substantially affect the overall value of an option. Since more time equals more money, long-term options have greater extrinsic value at equivalent strike prices. In addition, time value is highest in at-the-money (ATM) options; a very important fact for option writers. Consequently, time value decreases as options move in- or out-of-the-money (ITM-OTM) and strike prices which are deep in- or out-of-the-money have the lowest time value of all options.
Finally, the two lesser-used components of option pricing theory: Vega and Rho. Vega, which is the change in option price given a one percentage point change in volatility, is utilized by professional traders in hedging calculations. Rho is a measure of an option's sensitivity to changes in the risk-free interest rate and it is used to help compare the holding costs and risk-reward outlook for various strategies.
The Black-Scholes model and the Cox, Ross and Rubinstein binomial model are the primary pricing models used by most professionals to evaluate equity and equity-index options. For retail traders, it is adequate to know that both of these models are based on similar theoretical foundations and assumptions. However, there are also some important differences between the two, the most important of which is the fact that the Black-Scholes model cannot be used to accurately price options with an American-style exercise (because it only calculates the option price at expiration). Even so, it offers an expeditious means to calculate a large number of option prices in a short time which, in contrast, is the main disadvantage of the binomial model.
Option traders need to have a firm grasp of pricing theory because the primary attraction of derivatives is the leverage they offer. A trader can achieve an exponential percentage profit with only a moderate change in the price of the underlying issue but to attain this goal, he (or she) has to know which option provides the best results in a given situation. Choosing the correct time frame for a specific play is also vital to long-term success, therefore traders should have a fundamental understanding of Theta and how it affects the value of an option. In the next segment, we'll discuss the effects of volatility on option pricing.