I've read that delta is a probability of option assignment. For example, if you have a put with a delta of -.70, there is a 70% chance the option will be assigned. If the delta is -.04, there is only a 4% chance the option will be assigned.

I can't remember where I read that reference. But everything I've read lately on delta simply regurgitates the standard definition. Can anyone confirm the above definition (with a reference)?


Googling "delta probability expiration" will offer lots of references on the web that discuss delta as a proxy for the probability of expiring in-the-money.

Delta is an approximation of the likelihood that the option will expire ITM. Since delta is affected by the various pricing variables, it will vary during the life of the option. Dramatic change in implied volatility can change delta significantly on a day to day basis so it's an estimate of probability rather than a guarantee.

Also, in a bull market such as we've had since 2009, calls expiring ITM exceeded the probability forecast by delta whereas puts under performed.

I consider Sheldon Natenberg to be an authority on options. In "Option Pricing And Volatility Strategies", he wrote:

There is one other definition of the delta which is of less practical value to the trader but which may be of interest from a theoretical standpoint. If we assume that futures prices are lognormally distributed, then the delta of an option is approximately the probability that the option will finish in-the-money ...

Since most option strategies depend not on the probability of an option finishing in-the-money but rather on the total expected return, this definition will not be of much use to the serious trader. A trader who is courageous enough (or foolish enough) to simply sell naked options might perhaps use this probability concept to help assess risk.

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