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Paper / 2026SMQ / 86110162493120
Local Stochastic Rough Volatility: Pathwise Filtering and the Conditional Density Equation
Damiano Brigo / Vladimir Lucic
partial differential equations / rough volatilityResource overview

Local Stochastic Rough Volatility: Pathwise Filtering and the Conditional Density Equation

Paper2026

by Damiano Brigo, Vladimir Lucic

Tags
partial differential equationsrough volatilitystochastic calculusstochastic differential equationsstochastic processes

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Suggested foundations for volatility models and surfaces and stochastic processes and pricing. Specialist prerequisites vary by paper.

Before you read

  1. Stochastic Processes, Brownian Motion and Itô's Lemma

    Follow Brownian dynamics and the second-order term in Itô calculus.

  2. ARCH and GARCH

    Separate conditional volatility from observed returns.

  3. Conditional Expectation

    Understand what it means to condition on current information.

Go further

  1. Stochastic Volatility and the Heston Model

    Study a correlated stochastic-variance model.

  2. Reading the Implied Vol Surface — Moneyness, Term Structure, and Quoting Conventions

    Interpret prices across strikes and expiries.

  3. Market Model and Risk-Neutral Valuation

    Connect stochastic dynamics to no-arbitrage prices.

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