## Delta, Like Everything, Decays

Mon, Oct 4, 2010 | Jared Woodard

Standard accounts of the option Greeks will explain that delta measures the rate of change in the price of an option per unit change in the underlying asset. The text I use with mentoring clients, Natenberg’s *Option Volatility and Pricing*, provides some additional helpful ways of thinking about delta:

- as a ratio of underlying contracts to options required to establish a neutral position, e.g. for every five 40-delta calls purchased, two underlying contracts (or two hundred shares of stock) should be sold short;
- as an equivalent to the underlying, e.g. a 40-delta call is equivalent to owning 40 shares of stock;
- as the probability that an option will expire in-the-money.

But even the Natenberg book (and, if I remember correctly, McMillan) don’t discuss the difference between the deltas of options with identical strike prices but different expirations. As expiration approaches, the delta of in-the-money options approaches one, while the delta of out-of-the-money options approaches zero. Known also as “charm,” delta decay is a second-order Greek that measures the rate of change of delta per day.

The chart below illustrates the phenomenon of delta decay nicely. With DIA near $108, the 114 call options expiring in October have hardly any delta at all, while the 114 calls expiring in June have a delta above 30. The converse is true for ITM options: October DIA 100 calls have a delta above 90, but that number drops to just above 60 for the 100 calls expiring in June. Delta decay is of particular interest to traders holding ATM or OTM options near expiration, especially when those options are serving as portfolio hedges.

October 4th, 2010 at 4:37 pm

Charm and Color are two very under-subscribed concepts.