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TL;DR

The rate of change of delta with respect to underlying price: \( \Gamma = \frac{\partial^2 V}{\partial S^2} = \frac{\partial \Delta}{\partial S} \). It measures the curvature of the option price function.

By Valenke Exam Prep Team·Last updated 2026-06-03

Gamma (Greek)

The rate of change of delta with respect to underlying price: \( \Gamma = \frac{\partial^2 V}{\partial S^2} = \frac{\partial \Delta}{\partial S} \). It measures the curvature of the option price function.

Why it matters for interviews

Gamma determines how quickly a delta hedge becomes stale. High gamma near expiration means frequent rebalancing. Gamma P&L (from realized vs implied volatility) is a key concept in options trading.

Definition and Mathematical Foundation

The rate of change of delta with respect to underlying price: \( \Gamma = \frac{\partial^2 V}{\partial S^2} = \frac{\partial \Delta}{\partial S} \). It measures the curvature of the option price function.

Application in Quantitative Finance

Gamma determines how quickly a delta hedge becomes stale. High gamma near expiration means frequent rebalancing. Gamma P&L (from realized vs implied volatility) is a key concept in options trading.

Related Terms

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Frequently Asked Questions

What is gamma scalping?
A strategy that is long gamma (long options, delta-hedged). When the stock moves, the delta hedge profits from rebalancing. The P&L depends on realized volatility exceeding implied volatility.
Why is gamma highest near the strike at expiration?
Near expiration, ATM options have rapidly changing delta (0 to 1 over a small price range). This extreme sensitivity produces high gamma. Deep ITM/OTM options have near-zero gamma.
What is the relationship between gamma and theta?
For a delta-hedged portfolio: daily P&L \( \approx \frac{1}{2}\Gamma S^2(\sigma_{realized}^2 - \sigma_{implied}^2)dt \). Theta is the cost of carrying gamma exposure -- you pay theta to earn potential gamma profits.