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Recovering Risk-Neutral Moments from Options
Tjeerd De Vries
foreign exchange / mathematical financeResource overview

Recovering Risk-Neutral Moments from Options

Paper2026

by Tjeerd De Vries

Tags
foreign exchangemathematical financeoption pricingtail risk

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Understand this paper

Suggested foundations for options and derivatives pricing and risk measurement and stress. Specialist prerequisites vary by paper.

Before you read

  1. The Binomial Model

    Build replication and risk-neutral probabilities in a tractable model.

  2. Market Model and Risk-Neutral Valuation

    Distinguish pricing probabilities from physical forecasts.

  3. Random Variables and Distributions

    Represent losses as a distribution rather than one forecast.

  4. Expected Shortfall and Other Tail Risk Measures

    Distinguish a loss quantile from the average loss in the tail.

Go further

  1. The Black-Scholes PDE, Formula and Implied Volatility

    Connect the pricing equation, closed-form value and implied volatility.

  2. VaR Estimation in Practice: Variance-Covariance, Historical Simulation, Monte Carlo

    Compare risk estimators and their assumptions.

  3. Backtesting VaR and ES: Coverage Tests and Model Validation

    Check forecasts against realised losses.

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Lesson links open public previews. Access to full lessons depends on the topic and your membership.

Explore Derivatives Pricing and Computational Finance Explore Quantitative Risk Management

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