Delta-Gamma Neutral Self Financing

Discussion in 'Options' started by eagertolearn, May 12, 2007.

  1. I'm trying to design a position for an investor who would like to benefit from an increase in volatility by
    5% percentage points in the amount of $1000 but would like to be delta and gamma neutral, and have
    the portfolio designed be self financing.

    The spot price on the underlying asset is $100 with a continuously compounded interest rate
    of 6% and a dividend yield of 2%, also continuously compounded. A three month put struck at 80 and
    a six month call struck at 120 have the following information:

    80Put maturity=0.25 120Call maturity=.5
    Price 2.0836 7.9372
    Delta -0.1444 0.3849
    Gamma 0.008929 0.01376
    Vega 11.3458 16.9264

    Any ideas on how to start/go about this. I know it is relatively simple, but I am still learning:confused:
  2. You also want to be theta neutral if you're holding long options for a while.
  3. cvds16


    I can't help asking: "is this your homework ? "
    The answer is just a simple set of equations and solving them
  4. what is the rate of speed in vols increase ? IOW , when your investor expecting volatility to become X+5 ?
  5. cvds16


    There is a lot of information too much here
    I would need to do the detailed job myself, but from what I think (i'm better at the real thing than these artificial made up examples)
    you would need to solve three equations
    with x number of puts, y number of calls and z number of stock
    x*-0.1444 + y*0.3849 + z = 0 for deltaneutrality
    x*0.008929+ y* 0.01376 = 0 for gammaneutrality
    (x*11.3458+y*16.9264)*5 = 1000 for the increase in vol
    the rest is basic math
  6. cvds16


    I did this a bit too fast and forgot to multiply the delta's and gamma's en the vega by 100, so the equations need some (minor) adjustments
  7. Thanks so much....just curious though how the maturity, strikes, and dividend yield play into designing the position.
  8. cvds16


    they all influence the delta, gamma and vega figures through the option model used.
  9. A long time fly or a long ratio calendar would be the position of choice in limiting your greek mag and drift. Regardless, it would require fairly discrete hedging.
  10. The only position I can think of that's both delta neutral and gamma neutral is a box spread. But unfortunately it's also vega neutral so you wouldn't benefit from rising IV.

    Perhaps the easiest way would be to do something with VIX futures or options ?
    #10     May 13, 2007