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TL;DR

Approximating definite integrals using discrete summations. Methods include the trapezoidal rule, Simpson's rule, and Gaussian quadrature, each with different accuracy-cost tradeoffs.

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

Numerical Integration

Approximating definite integrals using discrete summations. Methods include the trapezoidal rule, Simpson's rule, and Gaussian quadrature, each with different accuracy-cost tradeoffs.

Why it matters for interviews

Option prices, risk measures, and posterior distributions often require integration that cannot be done analytically. Choosing the right quadrature method affects both accuracy and computational speed.

Definition and Mathematical Foundation

Approximating definite integrals using discrete summations. Methods include the trapezoidal rule, Simpson's rule, and Gaussian quadrature, each with different accuracy-cost tradeoffs.

Application in Quantitative Finance

Option prices, risk measures, and posterior distributions often require integration that cannot be done analytically. Choosing the right quadrature method affects both accuracy and computational speed.

Related Terms

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Frequently Asked Questions

When should you use quadrature vs Monte Carlo?▼
Quadrature is faster and more accurate in low dimensions (1-3). Monte Carlo is superior in high dimensions because its convergence rate \( O(1/\sqrt{n}) \) does not depend on dimension, while quadrature costs grow exponentially.
What is Gaussian quadrature?▼
An integration method that chooses optimal evaluation points and weights. With n points, it exactly integrates polynomials up to degree 2n-1. Much more efficient than equally-spaced rules for smooth functions.
How is numerical integration used in option pricing?▼
The Black-Scholes formula involves a normal CDF (integrated analytically), but more complex models (stochastic volatility, jumps) require numerical integration of the characteristic function via Fourier inversion.