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Quantitative Finance · Glosario

¿Qué es Delta hedging and gamma?

También llamado: delta · delta hedging · gamma

Definition 26.2 Markets I: The Ecosystem and Exchange-Traded Markets · Capítulo 26 — Zero-Day Options, Weeklies and Retail Options Flow

The delta of an option is the change of its value per unit change of the underlying; delta hedging is holding the opposite quantity of the underlying so that the combined position is insensitive to small moves. Gamma is the change of delta per unit change of the underlying: the rate at which the hedge must be adjusted. A position that is long options is long gamma: its hedger sells as the price rises and buys as it falls. A short-option position’s hedger does the opposite.

At-the-money gamma at 16% volatility, as the change of delta, in delta points, that a linear extrapolation gives for a 1% move. It passes 100, the whole position, with about an hour to go: from then on a 1% move is more than the option’s entire remaining uncertainty. Data: the chapter’s build.
Figure 26.2. At-the-money gamma at 16% volatility, as the change of delta, in delta points, that a linear extrapolation gives for a 1% move. It passes 100, the whole position, with about an hour to go: from then on a 1% move is more than the option’s entire remaining uncertainty. Data: the chapter’s build.
Gamma of a 100-strike option at 16% volatility, expressed as the change of delta for a 1% move of the underlying (linear extrapolation: a delta cannot change by more than one). With a month to go the hedge changes by 0.09 per 1%, whatever the price; with an hour to go, by the whole position if the price is at the strike and by nothing if it is 1% away. Data: the chapter’s build.
Figure 26.3. Gamma of a 100-strike option at 16% volatility, expressed as the change of delta for a 1% move of the underlying (linear extrapolation: a delta cannot change by more than one). With a month to go the hedge changes by 0.09 per 1%, whatever the price; with an hour to go, by the whole position if the price is at the strike and by nothing if it is 1% away. Data: the chapter’s build.
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