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TL;DR

A pricing framework where derivatives are valued as discounted expected payoffs under a risk-neutral measure Q, where all assets earn the risk-free rate in expectation: \( V = e^{-rT}E^Q[\text{payoff}] \).

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

Risk-Neutral Pricing

A pricing framework where derivatives are valued as discounted expected payoffs under a risk-neutral measure Q, where all assets earn the risk-free rate in expectation: \( V = e^{-rT}E^Q[\text{payoff}] \).

Why it matters for interviews

The central concept in derivatives pricing. Understanding why risk preferences do not affect derivative prices (given no-arbitrage) is the deepest insight in mathematical finance and a core interview topic.

Definition and Mathematical Foundation

A pricing framework where derivatives are valued as discounted expected payoffs under a risk-neutral measure Q, where all assets earn the risk-free rate in expectation: \( V = e^{-rT}E^Q[\text{payoff}] \).

Application in Quantitative Finance

The central concept in derivatives pricing. Understanding why risk preferences do not affect derivative prices (given no-arbitrage) is the deepest insight in mathematical finance and a core interview topic.

Related Terms

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Frequently Asked Questions

Why can we assume risk-neutrality for pricing?▼
Because we can replicate the derivative with a self-financing portfolio. The replication argument shows that the price is independent of risk preferences -- only the probability measure changes, not the real-world probabilities.
What is the First Fundamental Theorem of Asset Pricing?▼
A market is arbitrage-free if and only if there exists an equivalent martingale measure (risk-neutral measure). This connects no-arbitrage to the existence of a pricing measure.
What is the Second Fundamental Theorem?▼
The market is complete (every contingent claim can be replicated) if and only if the equivalent martingale measure is unique. Incomplete markets have multiple valid pricing measures.