Formula for gamma change wrt time?

Discussion in 'Options' started by TskTsk, Feb 10, 2012.

  1. TskTsk

    TskTsk

    Im curious if anyone has any formula / paper / etc. that shows how gamma changes with time? I'm trying to run some simple simulations. Say I have 10 options with 0.03 gamma. How will that gamma look in 10 days from now? It will have increased, but how much?
     
  2. why not just remodel the option with a new time to expiry?
     
  3. 0.03 gamma x 10 days = 0.30
     
  4. WRONG.
     
  5. TskTsk

    TskTsk

    Please help, I looked at the Wikipedia article for "Greeks (finance)", but the formula for Color (gamma decay) doesnt make sense to me. It looks like this :
    [​IMG]

    Anyone care to explain the formula a bit would be much appreciated.

    EDIT: Just saw this post, yes that is probably the best idea. Only problem is I can only remodel things down to day by day, I need to know spesifically how gamma changes from minute to minute, this is especially important the last couple hours on friday.
     
  6. TskTsk

    TskTsk

    Ah yes I see it now:
    [​IMG]

    Only problem is I neither have a financial or mathematical background. Could anyone perhaps give me an example of its use? Also, can it give me predictions of intraday changes in gamma? (which is what I need)
     
  7. A simplified version of the formula, good for "in your head" or back of the envelope calcs is:

    -(1-d1*d2)*n(d1)/(2*S*vol)

    This assumes zero interest rate, zero dividends, and vol is time adjusted (vol = annualized_vol * sqrt(time)).

    The full formula is available in most options texts. However the above is a pretty good approximation for stocks that do not pay dividends.

    Edit: for a slightly better approximation substitute the forward price for S
     
  8. TskTsk

    TskTsk

    Nice, thanks for this

    In the formula above, is time option life as percentage of year?
    Also is there any spreadsheet or something that will calculate d1, d2, n(d1) and n(d2) for me?
    Apologize if this sounds stupid but I have never touched on any of this before.
     
  9. #10     Feb 10, 2012