TL;DR

Models where volatility is itself a random process, capturing the empirical observation that market volatility varies unpredictably over time. The Heston model is the canonical example.

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

Stochastic Volatility

Models where volatility is itself a random process, capturing the empirical observation that market volatility varies unpredictably over time. The Heston model is the canonical example.

Why it matters for interviews

Stochastic volatility models explain the volatility smile and produce more realistic option prices than Black-Scholes. Understanding Heston, SABR, and their calibration is essential for derivatives quants.

Definition and Mathematical Foundation

Models where volatility is itself a random process, capturing the empirical observation that market volatility varies unpredictably over time. The Heston model is the canonical example.

Application in Quantitative Finance

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

What is the Heston model?▼

Stock: \( dS = \mu S dt + \sqrt{v} S dW^S \). Variance: \( dv = \kappa(\bar{v}-v)dt + \xi\sqrt{v}dW^v \) with \( \text{Corr}(dW^S, dW^v) = \rho \). The correlation \( \rho < 0 \) produces the volatility skew.

What is the SABR model?▼

Stochastic Alpha Beta Rho model for interest rate derivatives: \( dF = \sigma F^\beta dW^1 \), \( d\sigma = \alpha\sigma dW^2 \). It provides an analytical approximation for implied volatility as a function of strike, widely used for swaption pricing.

How are stochastic volatility models calibrated?▼

Minimize the difference between model and market implied volatilities across strikes and expirations. For Heston, the characteristic function allows semi-analytical pricing, making calibration feasible via Fourier inversion.