"Can Options Delta Move Over 1?"

"Can Options Delta Move Over 1?"

"Can delta surpass 1.0 due to gamma and for $1 move in the underlying can the option move $1.25 due to delta being over 1.0 overtime?"
- Asked By Tony Guzman 13 March 2010

Answered by Mr. OppiE

Hi Tony,

The short answer is, No. There is no way the delta value of an option can ever exceed 1 (or -1 for put options) in options trading. I don't think this comes as a surprise to you at all and I suppose what you really want to know is "Why", right?

All long options positions, no matter call option or put option, comes with positive gamma value. Gamma value is the options greek that measures the rate of change of an option's delta value to a change in the price of the underlying stock. Positive gamma value increases the delta value of call options towards 1 and decreases the delta value of put options towards -1 when these options goes more and more in the money.

Since positive delta increases the delta value of options when they go more and more in the money, surely there will come a point where the delta value exceeds 1 or -1, right? Well, this would be true IF gamma value remains unchanged no matter how the price of the underlying stock changes. However, gamma value also changes with the moneyness of an option.

When an option goes more and more in the money or out of the money, gamma value also decreases. By the time the delta value of an option reaches 1 or -1, the gamma value of the option would also have decreased to zero. When gamma is zero, the delta value of an option would cease to change with any change in the price of the underlying stock, that is why delta value would never move beyond 1 or -1 no matter how much more they move in the money after that. Below is the call options pricer for QQQQ call options on June2009.

gamma values of an option

As you can see from the picture above, gamma value decreases as the call options goes more and more in the money. Finally, when the delta value reaches 1.0 at the $25 strike price, gamma value turns to zero as well. This is why you can never have delta of more than 1.

The Delta value of an option is also an indication of the probability that an option will end up in the money by expiration and there is no greater probability than 100%, right?

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