Option Delta

Option Delta: The King of the Greeks

Delta, probably the best known of the option Greeks, measures an option’s directional exposure. Just by looking at delta, you can quickly tell whether an option or a portfolio of options will go up or down given a particular move in the underlying stock, and approximately by how much. This makes delta a powerful and popular tool for position management and hedging.

Option Delta Definition

Mathematically, delta is the first derivative of the option’s market price with respect to the underlying asset’s price. In other words, change in market price of an option is the product of change in the underlying’s price and the option’s delta.

Option Delta Value Range

Delta of call options can reach values between 0 and +1. Delta or put options ranges from -1 to 0. The value depends mainly on the moneyness of the particular option (in the money vs. out of the money). Read more about delta and moneyness of calls and puts.

How to Estimate an Option’s Market Price Change Using Delta

Let’s see how to estimate an option’s price move given a particular stock price change. In this example I will throw a bunch of numbers at you, but don’t be scared. Most of them will be used logically and very easily, and others will not be needed at all.

You hold a call option slightly in the money with a delta of 0.60 and market price of 1.80. This call option gives you the right to buy 100 shares in Microsoft for 20 dollars each (the strike price). Let’s say Microsoft stock is now trading at 22 (the underlying’s market price). What will happen if the stock price increases to 22.50?

The option’s delta (the number 0.60) tells you that when the underlying stock goes up by 1 dollar, the option’s market price will go up approximately by 60 cents. In our example, the stock goes up by 50 cents. What will be the increase in the option’s market price?

50 cents times the delta, or 0.50 x 0.60 = 0.30. You can expect this option to go up by 30 cents. If Microsoft stock goes to 22.50, your call option will be worth approximately 1.80 + 0.30 = 2.10.

What you need for this calculation:

What you don’t need at all:

Besides a single option (like in this example), you can use delta for measuring and hedging directional exposure of the whole portfolio.

An Option’s Delta Is Not Constant

You might have noticed the frequent use of the words approximately and estimate in this article. The delta as a price change estimate is not precise. The reason is that the delta itself is not stable and it does change under the influence of several factors:

Delta changes with the underlying stock’s price. We have said that delta is different for in the money and out of the money options – it changes with the option’s moneyness. This relationship between the underlying’s price and delta is measured by another Greek letter, gamma.

Delta changes with passing time. In the money options become more sensitive to underlying price changes as they approach expiration and their delta gets closer to +1 for calls or -1 for puts. Out of the money options become less sensitive to the underlying price moves and their delta gets closer to zero near expiration. Delta can also change with volatility.

Related pages

intrinsic value of call optioncall option payoffwww yahoo finance com symbolsvix index yahooannualized standard deviation of monthly returnsgarman kohlhagen modelblack scholes valuationvariance function excelyahoo finance dow futuresvxx indexdelta for put optionvix contracthedging with vixcumulative probability excelfinding standard deviation calculatorwhat is the wacc formulaacceptable skewness and kurtosis valuesdow jones price weighteds&p 500 vix mid term futures indexformula for standard deviation on excelinterpreting variance and standard deviationhow to calculate relative strength indexvix optionvix future pricesweighted average inventory methodhistorical vix chartdirectional hedge fundhow to calculate formula in excelblack scholes greekmoments skewness and kurtosisoption greek deltalong term vix chartstandard error of skewnesshow to create an equation in excels&p 500 csvtechnical trading bookswhat is the wacc formulaleveraged volatility etfvix cboe volatility indexcontango forward curveblack scholes priceroptions futures and other derivatives global editioncalculating sample covariancehow to calculate 95th percentile in excelpayoff graphs&p500 vixnotepad _population standard deviation calculatorvariance deffixed income arbitrage examplesample variance formula excelput and calls for dummiesshort straddle strategyvelocityshares daily inverse vixoption greek calculatormeasures of dispersion calculatoravco inventoryblack scholes calculator onlinehistorical implied volatility chartoption payoff diagramvxx prospectusticker vxxwhat is macd indicatorkurtosis formulablack scholes original papermean average deviation calculatorhow to calculate skewness and kurtosissoros 13fblack scholes formulasmeaning of hedge fundsmacd histogram indicatorcompute weighted average cost of capitalrsi 2 periodstandard deviation calculator frequencyvix futures quotescalculating sharpe ratio