option gamma question

Discussion in 'Options' started by buybig, Mar 23, 2008.

  1. buybig


    what causes an option to have a high or low gamma?
  2. MTE


    Here's just one of hundreds of links you can find using Google, for example, that explain Gamma.
  3. buybig


    thanks but that didnt explain my question.

    example: NM jun08 10 call @ 10 gamma

    vs XYZ @ 2 gamma

    NM is no more subject to large swings than others w/ lower gamma

    the smaller gamma seems be more common

    confused and curious
  4. paden


    Gamma is highest for ATM options, and is progressively lower as options are ITM and OTM
  5. Highest for the shortest term closest to the money option. Gamma can also change quickly. Google it
  6. MTE


    From the link:

    "If you were to look at a graph of gamma versus the strike prices of the options, it would look like a hill, the top of which is very near the ATM strike. Gamma is highest for ATM options, and is progressively lower as options are ITM and OTM...

    ...Judging how gamma changes as time passes and volatility changes depends on whether the option is ITM, ATM or OTM. Time passing or a decrease in volatility acts as if it's "pulling up" the top of the hill on the graph of gamma, and making the slope away from the top steeper. What happens is that the ATM gamma increases, but the ITM and OTM gamma decreases. The gamma of ATM options is higher when either volatility is lower or there are fewer days to expiration. But if an option is sufficiently OTM or ITM, the gamma is also lower when volatility is lower or there are fewer days to expiration."

    I'd say it explains Gamma pretty well!
  7. nitro


    That explains how, not why.

    To the original poster. In this case, you need to think in the mathematical domain and not the trader domain.

    1) The delta is the first partial derivative with respect to price.

    2) The gamma is the second partial derivative with respect to price, or the first partial derivative of delta. Once you understand delta and it's graph as the underlying moves, understanding gamma is simple.

    The hard part is that gamma is affected non-trivially by other partial derivatives (other "greeks"), because the delta is sensitive to them.

    A little math can make things clearer. I offer this simple link:



  8. Math doesn't usually make these things clearer. If anything, math confuses the issue for people who are non-mathy enough that they didn't do the math for themselves in the first place. Here's how you do calculus without any calculus:

    Start with a very basic definition. Gamma is how quickly delta changes when the stock moves.

    Let's take an option that has a lot of time left. You know that if you go really deep OTM the delta is zero. If you move around a buck or two while staying DOTM, the delta doesn't really change - low gamma.

    Take that same option, now DITM. You know the delta there is basically 1, and if you move around a couple bucks it will still be 1. Again, delta not changing much equals low gamma.

    So where is gamma not zero? Right in between DITM and DOTM - right at the money. Intuitively, gamma gradually increases from zero DOTM to some maximum value ATM and gradually decreases back to zero as you go DITM. that gives you a broad region where gamma is nonzero.

    Now, look at the case near expiration. Like, expiration day. What's delta in that situation? Delta is zero anywhere OTM and 1 anywhere ITM. As you cross the strike price, delta jumps straight from zero to 1 and that's the only place it changes. That means gamma is basically an infinite spike right at the money and zero everywhere else.

    Let your mind generalize that a bit, and you see that having less time to expiration means you have more gamma at the money and it drops off faster as you move away from the strike price in either direction.

    Lower IV behaves more or less like having less time to expiration. High IV behaves like having more time to expiration.
  9. buybig


    thank you..

    so if im thinking right.. the potential for an ATM option to move ITM w/ high probability would generate a high gamma?

    thanks for your help..

    thanks to all who contributed constructively

  10. Thanks for that explanation. I am one of those non-mathy types you referred to.

    That really helped. Thanks.
    #10     Mar 26, 2008