Dynamic Delta Hedging & Gamma Related Issues

  • Traders and securities dealers can use an option's delta to create hedges for the price risk exposure that they have in other option or underlying asset positions.

Example, assume that a securities dealer has sold (short position) 100 call options on Ford Motors (NYSE: F) and that each option represents 100 shares. Thus, the dealer's net stock exposure is 10,000 shares. If the options on F have a delta of 0.8, then the dealer can counter his short call position by buying 8,000 shares of F. Thus if the stock increases by $1, the increase in the value of the long stock position should offset the loss on the short call option position.

  • Delta is dynamic, though, and will change as the underlying asset price changes. Therefore delta hedging requires constant readjustment.

  • Because of this, delta hedging is also called dynamic hedging.

  • Delta hedging loses its effectiveness when an underlying asset has large price moves, either up or down.

  • As previously discussed, gamma represents the sensitivity of delta to a change in the underlying asset's price.

  • When an option is either deep in or deep out of the money, gamma will be close to zero as it will take a large price move to impact the value of delta; an option's gamma is comparable to a bond's convexity.

  • When an option is at the money and expiration is close, then gamma tends to be high.

  • When gamma is high, delta becomes a less accurate measure of option price sensitivity to the underlying asset and delta hedging loses accuracy as a hedging technique.

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