Option Delta
The delta of an option is the sensitivity of an option price relative to changes in the price of the underlying asset. It tells option traders how fast the price of the option will change as the underlying stock/future moves.
The above graph illustrates the behaviour of both call and put option deltas as they shift from being out-of-the-money (OTM) to at-the-money (ATM) and finally in-the-money (ITM). Note that calls and puts have opposite deltas - call options are positive and put options are negative.
Option delta is represented as the price change given a 1 point move in the underlying asset and is usually displayed as a decimal value. Delta values range between 0 and 1 for call options and -1 to 0 for put options. Note - some traders refer to the delta as a whole number between 0 to 100 for call options and -100 to 0 for put options. However, I will use the decimal version of -1 to 0 (puts) and 0 to 1 (calls) throughout this site.
Call Options
Whenever you are long a call option, your delta will always be a positive number between 0 and 1. When the underlying stock or futures contract increases in price, the value of your call option will also increase by the call options delta value. Conversely, when the underlying market price decreases the value of your call option will also decrease by the amount of the delta.
The above graph shows how the delta of a call option changes as the underlying price changes.
When the call option is deep in-the-money and has a delta of 1, then the call will move point for point in the same direction as movements in the underlying asset.
Put Options
Put options have negative deltas, which will range between -1 and 0. When the underlying market price increases the value of your put option will decreases by the amount of the delta value. Conversely, when the price of the underlying asset decreases, the value of the put option will increase by the amount of the delta value.
The above graph shows how the delta of a put option changes as the underlying price changes. So, when the underlying price rallies, the price of the option will decrease by delta amount and the put delta will also decrease as the option moves further out-of-the-money.
Comments (19)
Peter
August 28th, 2010 at 12:52am
How do you mean...because it's negative?
juan
August 27th, 2010 at 11:55pm
the put graph seems to be wrong ?
Peter
August 1st, 2010 at 9:01pm
It's the relationship between volatility (probability of option expiring in the money) and time being non-linear - asset volatility follows a log-normal distribution.
Option Theta is highest for strikes at (close to) the money and tapers off either side in a non-linear fashion.
sam
July 31st, 2010 at 2:23pm
what is the financial intuition behind time value of option decreasing convexly for strikes away from asset price?
Peter
June 3rd, 2010 at 10:04pm
You'll have to calculate the Greek values. You can use the spreadsheet found under the pricing link. Or, you can go to;
www.option-price.com
Sundraa
June 3rd, 2010 at 12:47pm
Forget continuous or discrete compounding.. just take it this way. Long Call option profit is virtually unlimited... whereas with a long put, your profits has a cap (because stock prices cannot go below 0). So call option can give you more returns than a put option and hence delta of ATM call is greater than a put.
Ray
June 2nd, 2010 at 1:38pm
Gentlemen, where do I go to get current option delta values?
Peter
December 23rd, 2009 at 4:33pm
I disagree. It is the compounding of those factors that causes the curve to skew to the upside, hence becoming log normal. Without compounding the curve is symmetrical as the returns to the upside have no bias over those to the downside. When you begin to compound the returns, you will notice that a compounded negative rate of return yields a lower absolute change than a return that is positive.
For example, if you take $100 at a 5% return and compound it for 10 years you end up with a profit of $62. If you take -5% you will lose only $40, hence the skew to the upside.
Marc
December 18th, 2009 at 2:35pm
Your explanation of the log normal distribution (LGD) is wrong. The LGD is not used over a normal because option models are "continuous". Both normal and lognormal are continuous. Lognormal is used for the simple fact that is a natural way to enforce positive asset prices. This in turn introduces a skew that does not exist in the normal distribution. Continuous compounding rates, dividends, and volatility, have absolutely nothing to do with it.
Alan
December 17th, 2009 at 11:53pm
Thank you very much Peter. Really appreciate your help.
Peter
December 15th, 2009 at 6:40pm
Hi Alan,
Yes, this is due to the Log Normal Distribution curve that is used by the Black and Scholes model to estimate the "rate of return" (interest and volatility). The Log Normal curve is used over a Normal Distribution because option models are considered continuous, where volatility, interest and dividends are taken to be continuously compounded and hence produce and upward bias in returns.
Alan
December 15th, 2009 at 8:19am
Hi Peter, i have a question regarding ATM call and put. ATM calls seems to be like 52 delta and ATM put seems to be around 48 delta. there were some comments made saying its due to Black Scholes model preference for puts over call. Would appreciate if you can help to explain.
Peter
November 10th, 2009 at 4:21am
Hi Ashi, a Box Spread is a combination of two opposing vertical spreads i.e. a long call spread and a short put spread. Both spreads would have the same strikes and expiration date.
The idea is that the credit received for the short spread is more than what is required to be paid for the long spread and hence a risk-free profit is locked in.
Regarding Collars vs Bull Spread...this depends on your capital requirements and the prices for the option components. A Collar consists of a long stock meaning a much greater burden on your trading account.
Ashi
November 9th, 2009 at 5:10pm
Hiya
I stumbled upon your page while preparing for an exam :) and I found your material really useful.
what is a BOX SPREAD by the way? And I am always confused between choosing a Collar options verus a call Bull spread...both profiles look the same... when do you choose one or the other?
Jo Jack
July 7th, 2009 at 2:04am
Peter,
Your graph is correct. Thank you for all the information on this site.
Peter
May 22nd, 2009 at 3:14am
Hi Steve,
Actually, I think it is correct. The graph is showing the delta of a 50 strike put option, which has a negative delta. As the stock price declines, the option becomes shorter hence the delta approaches -1. When the put option is deep in the money the delta will reach -1 and behave like a short underlying position.
As the stock price increases and becomes out of the money the delta will approach zero and eventually become worthless.
Let me know if you dissagree.
Steve
May 22nd, 2009 at 1:15am
Your put option graph is reversed. The red line in the bottom graph should has the wrong slope.
aranjan
April 9th, 2009 at 3:59am
Very good explanation
Pratap
January 21st, 2009 at 11:42pm
Very Useful......
Rating - 5 out of 5
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