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Options: Calculating Delta, Part 1


The most basic, and most necessary, of all the Greeks.


Knowing an Option's Delta

I've received a lot of questions on delta, including: How do I calculate an options delta? How does volatility effect an option's delta? Can a delta be negative? 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 2 parts. Today I'll focus mainly on what delta is, and how you can determine a specific option's delta.

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 $0.50, and the value of the $50 put to decline by $0.50.

Most online brokers will provide a choice of ways to view an option chain that can display the Greeks - including delta, along with other items, such as implied volatility or current volume and open interest.

Delta as a Road Map

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 multi-strike combinations.

In descending order, the components that factor into an option's delta are underlying price, strike price, time remaining and interest rates. You can use an option calculator to plug in different variables to see how they affect delta. For instance, you should note that as a function of time, the delta of in-the-money options increases as expiration approaches, while the delta of out-of-the-money options decreases.

While the above exercise will reveal many nuances, the most important concept is that an option's delta isn't linear. 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 something of a road map that will help tell what an option's price will be, should the value of the underlying move to different location.

The table below provides a quick rule-of-thumb guide to gauging an option's delta. These are approximations based on option studies using the strike relative to the underlying stock.

Again, the values and option's price will also be dependent on the other elements, such as time and implied volatility -- which, while it has no direct bearing on delta, does have a big impact on the option's overall price -- not changing radically.

But assuming all else being equal, if XYZ stock goes from $30 to $31, we'd expect the $30 call to gain $0.50 and the $30 put to drop $0.50. 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.

Note: An option's delta has little connection to its absolute value or price. That means that 2 different options -- one priced at $0.50 and one priced at $6.50 -- can both have the same delta.

Next time I'll take a look at how to use delta when hedging, or in multi-strike positions.

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