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Thread: delta gamma hedging

  1. #1
    Actuary.com - Level I Poster
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    delta gamma hedging

    a bit confused on delta gamma hedging
    When you set up first you do your gamma, set it equal to 0. you solve for # of options to buy/sell,right? it positive is it buy or is it sell.

    When setting Deltas = 0 you solve for number of stock to buy/sell. If that is positive is that buy or is it sell.

    Ive seen it two different ways with two different answers.
    IM CONFUSED!!!!!!!

  2. #2
    Actuary.com - Level III Poster
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    Ok - let's say you are a market maker and sell a put option. You wish to delta-gamma hedge your position.

    We begin by calculating the gamma for our position. Hypothetically, let's say that gamma_put = 0.5988 . Since we sold the put option, gamma for the position is (-1)(0.5988) = -0.5998. In order to make the gamma of our total position zero, we must have another position with a gamma value of +0.5998. Since gamma is always positive for both calls and puts, we can purchase X options so that their gamma is +0.5998. Let's say we want to put a call option to do this, with and the gamma of the call is 0.3277. We must purchase (0.5998)/(0.3277) call options. Now the portfolio has a gamma of 0 and is gamma-hedged.

    Follow the same process for delta, but instead, purchase/sell the appropriate values of stock. To start off, remember that we sold the put, so the value of delta for the position will be (-1)(delta_put) where the delta_put has a negative value. Since we bought calls to gamma hedge, we will be adding the delta of the X call options (which will produce a larger, positive value for delta). To offset this positive delta, we must short sell the stock, since stocks have a delta of +1 and selling stock creates a negative delta.

    Hope this helps.

  3. #3
    Actuary.com - Level III Poster
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    It really helps to think everything out step-by-step. Say you're only delta-hedging and sold a call. The holder of the call benefits from an increase in the stock price (this hurts you). To offset this risk, you want to purchase the stock, so if the price of it rises, you offset your written call risk.

    Mathematically, by selling a call, you have a (-1)(delta_call) value of delta and offset it by purchasing delta_call shares of the stock.

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