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TL;DR

The rate of change of option price with respect to underlying price: \( \Delta = \frac{\partial V}{\partial S} \). For a Black-Scholes call, \( \Delta = N(d_1) \in [0,1] \).

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

Delta (Greek)

The rate of change of option price with respect to underlying price: \( \Delta = \frac{\partial V}{\partial S} \). For a Black-Scholes call, \( \Delta = N(d_1) \in [0,1] \).

Why it matters for interviews

Delta is the primary hedging ratio -- the number of shares needed to hedge one option. Delta-hedging is the foundation of options market making. Interviewers expect candidates to derive and interpret all Greeks.

Definition and Mathematical Foundation

The rate of change of option price with respect to underlying price: \( \Delta = \frac{\partial V}{\partial S} \). For a Black-Scholes call, \( \Delta = N(d_1) \in [0,1] \).

Application in Quantitative Finance

Delta is the primary hedging ratio -- the number of shares needed to hedge one option. Delta-hedging is the foundation of options market making. Interviewers expect candidates to derive and interpret all Greeks.

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Frequently Asked Questions

What is delta-hedging?
Holding \( -\Delta \) shares per option to eliminate first-order price risk. The portfolio becomes locally insensitive to small stock moves. Gamma exposure means the hedge must be continuously rebalanced.
What is delta as a probability approximation?
Delta approximately equals the risk-neutral probability that the option expires in-the-money. A call with \( \Delta = 0.7 \) has roughly a 70% chance of expiring ITM under the risk-neutral measure.
What is delta-gamma hedging?
Adding a second option to eliminate both delta and gamma exposure. This creates a portfolio insensitive to both small and moderate stock moves, reducing rebalancing frequency.