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From fair price to fair volatility: Towards an Efficiency-Consistent Definition of Financial Risk
Augusto Pianese / Daniele Angelini / Massimiliano Frezza / Sergio Bianchi
brownian motion / stochastic processesResource overview

From fair price to fair volatility: Towards an Efficiency-Consistent Definition of Financial Risk

Paper2025

by Augusto Pianese, Daniele Angelini, Massimiliano Frezza, Sergio Bianchi

Tags
brownian motionstochastic 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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