Skip to main content

TL;DR

Continuously adjusting a portfolio of the underlying asset to maintain a delta-neutral position, eliminating first-order price risk from an options position.

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

Delta Hedging

Continuously adjusting a portfolio of the underlying asset to maintain a delta-neutral position, eliminating first-order price risk from an options position.

Why it matters for interviews

Delta hedging is the practical implementation of the Black-Scholes replication argument. Understanding hedging frequency, transaction costs, and gamma exposure is essential for options trading roles.

Definition and Mathematical Foundation

Continuously adjusting a portfolio of the underlying asset to maintain a delta-neutral position, eliminating first-order price risk from an options position.

Application in Quantitative Finance

Delta hedging is the practical implementation of the Black-Scholes replication argument. Understanding hedging frequency, transaction costs, and gamma exposure is essential for options trading roles.

Related Terms

Ready to practice for the Quant Trading Interview?

Adaptive practice powered by Item Response Theory targets your weak areas. Start with 3 free sessions.

Start free practice →

Frequently Asked Questions

Why is continuous delta hedging impossible in practice?▼
Markets have discrete prices and transaction costs. Hedging every tick is prohibitively expensive. Practitioners hedge at discrete intervals, accepting gamma risk in exchange for lower costs.
What determines the P&L of a delta-hedged option?▼
The P&L is approximately \( \frac{1}{2}\Gamma S^2 (\sigma_{realized}^2 - \sigma_{implied}^2) \Delta t \). If realized volatility exceeds implied, the delta-hedger profits (long gamma). If not, they lose.
What is the hedging error?▼
The difference between the option payoff and the terminal value of the replicating portfolio. With discrete hedging, the error has zero mean but positive variance proportional to \( 1/n \) where n is the number of rebalancing periods.