Delta Gamma risks in financial derivatives, particularly in crypto options trading, refer to the combined exposure arising from both the first and second derivatives of an option’s price with respect to the underlying asset’s price. Delta quantifies the linear sensitivity, while Gamma measures the rate of change of Delta. The purpose of analyzing these risks is to quantify the potential for non-linear price movements and hedging effectiveness, especially under significant market volatility or large underlying price shifts.
Mechanism
Delta measures the change in option price for a one-unit change in the underlying asset. Gamma measures the change in Delta for a one-unit change in the underlying asset, thus indicating how quickly a position’s Delta will shift. A high Gamma position implies that Delta will change substantially with small movements in the underlying asset, necessitating frequent rebalancing of hedges. This dynamic relationship dictates how a portfolio’s market value responds to asset price fluctuations.
Methodology
Risk management methodology involves calculating and monitoring a portfolio’s aggregate Delta and Gamma exposure across all derivative instruments. Traders employ strategies such as dynamic hedging, where positions are adjusted continually to maintain a desired Delta, often aiming for Delta neutrality. However, Gamma exposure introduces a second-order risk, as rebalancing becomes more frequent and costly when Gamma is high, highlighting the cost of maintaining a Delta-neutral position as the underlying price moves.
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