Delta and Gamma

The hedge, and how fast the hedge goes stale

Delta is how much an option’s value moves for a one-unit move in the underlying, and it is therefore the size of the hedge. Gamma is how fast the delta itself changes, and it is therefore how often that hedge has to be redone. A delta-hedged option position is not a position in the underlying at all: it is a position in gamma against theta, which is the trade an options desk is actually running.

Open in the app · Risk & the Greeks · intermediate

Risk & the Greeks is part of the OTC Learn subscription. Everything the app shipped with — 36 products across six asset classes — stays free.

What the lesson covers

1. What delta is
2. What gamma is
3. Gamma against theta
4. Hedging in practice
5. Risks to watch

Key terms

• Delta — The change in an option’s value per unit change in the underlying, and so the size of the hedge.
• Gamma — The rate of change of delta, and so how fast an existing hedge becomes wrong.
• Theta — The value lost per day from the passage of time, which is what pays for gamma.
• Delta hedging — Holding an offsetting position in the underlying so the option position has no directional exposure.
• Break-even move — The daily move at which re-hedging profit exactly covers the position’s theta.
• Gap risk — The exposure left when the underlying jumps rather than moves smoothly, giving no chance to re-hedge.

In practice

Every options market maker runs this trade whether it wants to or not: quoting two-way prices leaves the desk long or short gamma, and the hedging programme is what turns that into P&L. The same arithmetic drives the “gamma squeeze” stories in equity markets, where dealers short a heavily traded strike have to buy into a rally to stay hedged.

Read next

• FX Option — The right to exchange currency at a strike
• OTC Equity Option — A custom, bilaterally negotiated option
• Vega and the Volatility Surface — What a book loses when volatility reprices

In the app, Delta and Gamma carries a five-step lesson, a worked example and a bank of twelve questions drawn differently every sitting.

Get OTC Learn on Google Play

Educational content only. Nothing here is financial advice, an offer to trade, or a recommendation to buy or sell any instrument.