Paper: arXiv 2503.14997

Authors: Benedict Burnett, Ryan McCrickerd, Benjamin Piau

Abstract

This article consolidates and extends past work on derivative pricing adjustments, including XVA, by providing an encapsulating representation of the adjustment between any two derivative pricing functions, within an Ito SDE/parabolic PDE framework. We give examples of this representation encapsulating others from the past 20 years, ranging from a well known option pricing adjustment introduced by Gatheral, to the collection of semi-replication XVA originating from Burgard & Kjaer. To highlight extensions, we discuss certain meta-adjustments beyond XVA, designed to help signal and mitigate XVA model risk.

Complexity vs Empirical Score

  • Math Complexity: 7.5/10
  • Empirical Rigor: 2.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents a rigorous theoretical unification of derivative pricing adjustments (XVA) and meta-adjustments within an Ito SDE/parabolic PDE framework. However, it is purely theoretical and mathematical, lacking empirical backtests, market data validation, or quantitative experiments.

Research Flowchart

  flowchart TD
    A[Research Goal: Unify & extend derivative pricing adjustments within Ito SDE/PDE framework] --> B[Inputs: Derivative pricing functions, XVA models & Gatheral option adjustments]
    B --> C[Methodology: Formulate encapsulating representation using Ito SDE / Parabolic PDE]
    C --> D[Computational Analysis: Map historical XVA models & semi-replication frameworks to unified model]
    D --> E[Extension Phase: Develop meta-adjustments to signal & mitigate XVA model risk]
    E --> F[Key Outcomes: Unified mathematical framework & novel model risk mitigation tools]

Cited References (26)

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  2. Interest rate modelling (2010)
  3. Handling model risk with XVAs (2024)
  4. Stochastic Volatility Modeling (2016)
  5. Model misspecification analysis for bond options and Markovian hedging strategies (2006)
  6. Funding strategies, funding costs (2013)
  7. Hedging Valuation Adjustment: Fact and friction (2021)
  8. The Cost of Hedging XVA (2021)
and 18 more
  1. Dynamic Asset Pricing Theory (2001)
  2. Functional It^o calculus (2019)
  3. The Fundamental Theorem of Derivative Trading - exposition, extensions and experiments (2017)
  4. The funding invariance principle (2016)
  5. Lecture 2: Fitting the Volatility Skew (2001)
  6. The Volatility Surface: A Practitioner’s Guide (2006)
  7. KVA: Capital Valuation Adjustment (2014)
  8. The smile of stochastic volatility: Revisiting the Bergomi-Guyon expansion (2021)
  9. Brownian Motion and Stochastic Calculus (1998)
  10. Fast Calculation of Cheapest-to-Deliver Curves (2025)
  11. Data-driven WWR for CVA and FVA (2022)
  12. CO2eVA: pricing the transition of Scope 3 emissions (2023)
  13. Implied Volatility: Statics, Dynamics and Probabilistic Interpretation (2005)
  14. Robustness of the Black and Scholes Formula (1998)
  15. Funding beyond discounting: collateral agreements and derivatives pricing (2010)
  16. Cooking with collateral (2012)
  17. Stochastic Calculus for Finance II: Continuous-Time Models (2004)
  18. XVA modelling: validation, performance and model risk management (2024)

0 of 26 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.