Using a Delta-Gamma Hedge
With delta hedging alone, a position has protection from small changes in the underlying asset. However, large changes will change the hedge (change delta), leaving the position vulnerable. By adding a gamma hedge, the delta hedge remains intact.
Using a gamma hedge in conjunction with a delta hedge requires an investor to create new hedges when the underlying asset’s delta changes. The number of underlying shares that are bought or sold under a delta-gamma hedge depends on whether the underlying asset price is increasing or decreasing, and by how much.
Large hedges that involve buying or selling significant quantities of shares and options may have the effect of changing the price of the underlying asset on the market, requiring the investor to constantly and dynamically create hedges for a portfolio to take into account greater fluctuations in prices.
Example of Delta-Gamma Hedging Using the Underlying Stock
Assume a trader is long one call of a stock, and the option has a delta of 0.6. That means that for each $1 the stock price moves up or down, the option premium will increase or decrease by $0.60, respectively. To hedge the delta, the trader needs to short 60 shares of stock (one contract x 100 shares x 0.6 delta). Being short 60 shares neutralizes the effect of the positive 0.6 delta.
As the price of the stock changes, so will the delta. At-the-money (ATM) options have a delta near 0.5. The deeper ITM an option goes, the closer delta gets to one. The deeper OTM an option goes, the closer it gets to zero.1
Assume that the gamma on this position is 0.2. That means that for each dollar change in the stock, the delta changes by 0.2. To offset the change in delta (gamma), the prior delta hedge needs to be adjusted.
If delta increases by 0.2, then delta is now 0.8. That means the trader needs 80 short shares to offset delta. They already shorted 60, so they need to short 20 more. Conversely, if delta decreased by 0.2, the delta is now 0.4, so the trader only needs 40 shares short. They have 60, so they can buy 20 shares back.
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PS Gamma hedging is usually done via options (you hedge your calls with puts). That of course gets delta hedged via selling/buying the underlying by whoever is selling the gamma hedge. But as I said, I don't know zip about options. |
