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Change in Delta - Option Gamma
The gamma effect means that position deltas move as the asset price moves and predictions of revaluation profit and
loss based on position deltas are therefore not accurate, except for small moves.
Gamma (G) measures the response of an option's Delta to
changes in rates.
Gamma = Change in Delta / Change in Underlying Asset
Bought options have positive gamma while sold options
have negative gamma. A portfolio's gamma will be the weighted sum of its option's gammas and the resulting gamma will be determined by the dominant options in the portfolio. In this regard, options close to the money with short time to expiry have a dominant influence on the portfolio's gamma. The Gamma of an option increases as the option matures and decreases with volatility.
A portfolio with a positive gamma gets longer as the
market goes up and shorter as the market goes down, which is ideal. A portfolio with negative gamma gets shorter as the market goes up and longer as the market goes down.
A portfolio with a positive gamma is more attractive than a negative gamma portfolio with time decay being the mitigating factor. A negative gamma means the rate of losses increases as losses are sustained and the rate of profit falls as profits are experienced.
With delta neutral positions, the sign of Gamma is useful. If Gamma is negative, the portfolio profits so long as the spot rate remains stable. If Gamma is positive, the portfolio will only profit from large movements in spot rates in either direction.
To adjust the Gamma of a portfolio a trader must buy or sell additional option contracts as the Gamma of a cash position is zero.
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