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Paper / 2026SMQ / 75371950139728
On Prudence of Risk Measures
Denny H. Leung / Foivos Xanthos / Niushan Gao
mathematical financeResource overview

On Prudence of Risk Measures

Paper2026

by Denny H. Leung, Foivos Xanthos, Niushan Gao

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mathematical finance

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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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