Looking at Options Greeks: Delta

January 7, 2014
By Vlad Karpel

Last week we introduced you to options Greeks, indispensable tools for any serious option trader. Because the price of an option is influenced by several variables, it’s important to isolate the effect of each variable on price. This helps us understand the impact a change in interest rates, underlying asset price, volatility, and time-to-maturity can all have on the price of options. Today we look at the most important Greek letter for an options trader — delta.

Delta measures the sensitivity of the options price to a change in the underlying assets price. More than anything, important factors to consider when choosing an option include the price of the underlying and the prospects for its evolution. In this sense delta is an excellent tool to evaluate how much change is expected in the price of an option for the change we estimate in the price of the underlying asset.

If you’re used to stock trading and beta, it’s easy to understand the option delta. Let’s say Microsoft has a beta of 0.75. That means Microsoft tends to rise 0.75% for each 1% rise in the market. Higher betas correspond to higher leverage, so the stock will eventually move more than proportionally to market changes. The definition of delta is similar, but we usually speak about dollar change instead of percentages. A delta of 0.75 means the option moves $0.75 for each $1 change in the underlying security.

Unlike betas, which can assume any value, delta varies between 0 and 1 for a call option and between -1 and 0 for a put option. At the extreme, the price of an option can move by the same dollar amount as the underlying asset moves, which occurs as maturity nears or when the option is deep in the money. Under such circumstances, the option value is near its intrinsic value and a call will have a delta near 1 while a put will have a delta near -1.

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The following figure shows option prices for Microsoft for two different maturity dates. At the time the information was collected, Microsoft was trading at $37.20.


If you look carefully at the figure, you’ll notice that for the same strike prices, delta is higher for options with 35 days-to-maturity than for 749 days-to-maturity. Delta is also higher for in-the-money options (in absolute value). Look at the first maturity, for example: Delta is 0.98 for a call with a strike of $30 but 0.55 for a strike of $37. The same applies to put options. The more in-the-money $45 strike carries a delta of -0.97, while the out-of-the-money $28 strike shows a delta of -0.01.

It can be useful to express delta as a percentage, like beta. In this case, delta would show the percentage change expected in the option price for each 1% change in the price of the underlying, just like for beta. Stating delta as a percentage has the advantage of expressing the expected return on the option in relative terms.

In graphical terms, if you represent the price of an option as a function of the underlying’s price, the value of delta is represented by the slope of the curve.


As you can see in the chart, the slope of the curve varies, so the value of delta depends on the exact point at which you’re examining the curve.   The higher the stock price and the higher the price of the option will result in higher delta.

However, having a value for delta is sometimes not enough to understand how the option responds to changes in the underlying. Next week we’ll look at another important Greek letter — gamma – which us helps understand the rate at which delta changes. Stay tuned!

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