If you plan to write a covered call option which will expire does traditional option pricing theory apply and, if not, what can replace the Greeks?

Abstract

The primary goal of option pricing theory is to calculate the probability that an option will be exercised at expiration. These calculations are often summarized using "the Greeks", for example, theta is the expected change in the price of the option associated with a 1-unit change in time.  Options can either be traded or held until expiration.  If the investor's intention is to write a covered call option which will expire, and is indifferent between whether or not the option is exercised, then option pricing theory in general and the Greeks in particular are not directly relevant to them.   Here, we consider the question of what information in fact is important to an investor who writes such a covered call option, and then explore the extent to which an analogy between that investor's analysis and the Greeks can be developed.  A case study is presented, and then it is demonstrated that an analogue of theta addresses the same general construct of time value decay.  The degree to which the writing of covered calls is an investment strategy versus a speculative strategy is also considered.  In conclusion, for an investor who intends to write a covered call option with the intention of allowing it to expire, even though the Greeks are not directly helpful, the principles which underpin their derivation very much are.