# <I>TSC</I> Options Forum: Facts About Delta

*Hello Steve. How do I find out or calculate the delta of a call?*

I've received a lot of questions on delta, ranging from "Does volatility effect an option's delta?" to "Can a delta be negative?" and "I'm a small investor who usually just buys LEAPs, so why do I need to even know an option's delta?"

Of all the "greeks" that are used to define the characteristics of an option, delta is probably the most basic and necessary. Since an option's delta is so fundamental, I want to address this in two parts. This week I'll focus mainly on what delta is and how you can determine a specific option's delta. Next week we'll see how it can be applied to trading strategies and help you determine hedging requirements.

Delta measures the expected change in an option's value for a unit change in the price of the underlying security. Options have deltas that range from 0 to 1.00. For practical purposes call options have positive deltas, while put options' deltas are negative. For example, if a stock moves from $50 up to $51, and the at-the-money options have a 0.50 delta, you can expect the value of the $50 call to increase 50 cents and the value of the $50 put to decline by 50 cents.

Knowing how an option's value will change relative to the underlying price is crucial when making investment decisions, not only for speculative single strike positions, but even more so when used for hedging purposes or in multistrike combinations.

An option's delta is a function of four of the five variables that go into

valuing an option's price using the Black-Scholes pricing method. Implied volatility has virtually no measurable impact on an option's delta.

In descending order, the components that factor into an option's delta are underlying price, strike price, time remaining and interest rates. I recommend using an option calculator such as the one provided at the

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Chicago Board Options Exchange, plugging in different variables and seeing how they affect delta. For instance, you should note that as a function of time, the delta of in-the-money options increase as expiration approaches, while out-of-the-money options' delta decreases.

An option's delta isn't linear. The rate of change in an option's delta is called its gamma. This is a secondary derivative of the underlying price, and it has little meaning to the nonprofessional trader. For the people who don't deal with options for a living, we need a good method by which we can gauge delta and therefore an option's expected move relative to the underlying security.

You don't need to understand the lift and thrust that propels a plane into flight in order to purchase an airline ticket, but it's still important to know when and where you're going to land. Cleveland on May 3 is very different from Bora Bora on April 28.

To stretch the analogy, a schedule of an option's delta configuration is presented in the table below. These are approximations based on option studies using the strike relative to the underlying stock.

If XYZ stock goes from $30 to $31, we would expect the $30 call to gain 50 cents and the $30 put to drop 50 cents. But again, delta isn't linear, so if XYZ moved to $35 we should expect the call, which is now one strike in the money, to gain roughly $3, or 60%, of the $5 change in the stock. Conversely, the $30 put should lose only $2, or 40%, of the $5 move.

Again, these values are predicated on the other elements, such as time and volatility (which while it has no direct bearing on delta does figure into the option's overall price) not changing radically. Remember, an option's delta has little connection to its absolute value or price. That means that two different options, one priced at 50 cents and one priced at $6.50, can both have the same delta.

Next week I'll show how multiple-strike deltas are calculated on a cumulative basis and how to analyze an overall position for hedging purposes.

Steven Smith writes regularly for TheStreet.com. In keeping with TSC's editorial policy, he doesn't own or short individual stocks. He also doesn't invest in hedge funds or other private investment partnerships. He was a seatholding member of the Chicago Board of Trade (CBOT) and the Chicago Board Options Exchange (CBOE) from May 1989 to August 1995. During that six-year period, he traded multiple markets for his own personal account and acted as an executing broker for third-party accounts. He invites you to send your feedback to

Steve Smith.