Interpreting the Big Daddy of Option Greeks: Delta

05/10/2010 10:10 am EST


John Jagerson

Co-Founder and Contributor,

Option Greeks are a way to measure an option's sensitivity to the underlying stock, interest rates, market volatility, and the passage of time. In this series, we will be looking at each of the common “Greeks” used by investors. This article will begin our discussion of the first of these “Greeks,” delta.

Delta is a measure of the rate of change in an option's price for a $1 move in the underlying stock or index. If a particular option contract has a delta of .5 and the underlying stock moves by $1.00, then the option's price should increase by $.50 per share, or $50 per contract.

It gets a little more complicated because delta will grow as a stock option goes further in the money. For example, if the $25 strike price call has a delta of .50 on a stock that is currently worth $25 per share, we could expect a $.50 move in the option for a $1.00 move in the stock. But if the option subsequently becomes "in the money," delta will increase and could rise to .70, .90, or even 1.00 for a very deep-in-the-money call.

Conversely, delta will fall as an option becomes "out of the money." Using the same numbers above, if the stock falls to $20, the $25 strike call may have a delta of .2 or less.

Delta works the same way for puts with an important difference. A put's delta will always be negative. What this means is that if the stock rises by one dollar, the negative-put delta shows how much value we should expect the put to fall.

Conversely, the negative delta also predicts how much value we expect to gain in the put's premium if the stock falls a dollar in value. In-the-money puts have a larger negative delta and out-of-the-money puts have a lower negative delta. Besides this minor notational difference, this Greek works the same way for both calls and puts.

Despite this fairly straightforward explanation, delta can be a little tricky from a practical perspective. First, using it to forecast price changes only works if everything else in the market stays constant. That means that delta is at best only an estimate of what price changes should be expected if the underlying stock or index only moves $1 in a very constant market over a very short period.

Another way to look at delta is that it is an efficient estimate by the "market" of the probability that an option will expire "in the money" by expiration. This makes sense for an at the money option to have a delta of .50 because reasonably it has a 50% chance of closing in the money by expiration. Similarly, the more out of the money an option is, the lower the probability is has of expiring in the money.

Because there is no way to determine the real likelihood of an option's chances of expiring in or out of the money, delta is a great way to create an estimate. This can be helpful for option buyers or sellers who want to model their chances of success in a given trade relative to the amount of risk they are taking. This is a subject we have expanded on in our articles on position sizing and money management. 

By John Jagerson of

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