Calculating the UL price in which delta equals zero

Discussion in 'Options' started by TskTsk, Feb 12, 2012.

  1. TskTsk


    How do you calculate the UL price in which your portfolio delta will be equal to zero? Is it as easy as current UL price +/- (delta/gamma)? I fear this wont work since gamma is nonlinear. Anyone care to confirm, or maybe have a better formula for me? Thanks
  2. It's very simple:

    UL price - UL price = portfolio delta will be equal to zero
  3. newwurldmn


    You are right. Use delta and fixed gamma to get you close to the answer, recalculate your Greeks and repeat. Do so until you get to some epislon away.
  4. TskTsk


    UL price - UL price? You mean UL price (at zero delta ) minus UL price (at current delta)? That wont work, since I dont have UL price at zero delta.

    So say I have +100 D and +200 G. So according to this my required UL movement is 0.5 to get back to delta neutral. Now, you mention greek recalculation as the next exactly do you go about this?

  5. 1. Take UL = UL - delta/gamma

    2. Calculate new delta and gamma by plugin UL in BS calculator.

    3. If |delta| > epsilon, where epsilon is a small positive number, goto 1. Else UL is UL(delta=0).
  6. newwurldmn


    Correct. I think. I have always looked at delta and gamma in dollar terms. But of you did your way you would be close to the right answer. Probably close to within reasonable rounding error to the size of your book. The recalc would be of you had some really convex options levered skew (where dgamma/dspot is high) or were really anal.