PDE models and numerical methods for total value adjustment in European and American options with counterparty risk

DOI10.1016/j.amc.2017.03.008zbMath1411.91613OpenAlexW2599446604MaRDI QIDQ1738076

Iñigo Arregui, Carlos Vázquez, Beatriz Salvador

Publication date: 29 March 2019

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2017.03.008

zbMATH Keywords

finite elementscounterparty riskcharacteristics methodaugmented Lagrangian active set method(non)linear PDEscredit value adjustments

Mathematics Subject Classification ID

Numerical methods (including Monte Carlo methods) (91G60) Derivative securities (option pricing, hedging, etc.) (91G20) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60)

Related Items (13)

A Monte Carlo approach to American options pricing including counterparty risk ⋮ Total value adjustment for a stochastic volatility model. A comparison with the Black-Scholes model ⋮ A computational approach to hedging credit valuation adjustment in a jump-diffusion setting ⋮ Mathematical analysis of a nonlinear PDE model for European options with counterparty risk ⋮ Modelling and Computing the Total Value Adjustment for European Derivatives in a Multi-Currency Setting ⋮ A Multi-Level Monte-Carlo with FEM for XVA in European Options ⋮ Analysis of non-linear approximated value equation under multiple risk factors and stochastic intensities ⋮ Boundary-safe PINNs extension: application to non-linear parabolic PDEs in counterparty credit risk ⋮ Models and numerical methods for XVA pricing under mean reversion spreads in a multicurrency framework ⋮ Corrigendum to ``Total value adjustment for a stochastic volatility model. A comparison with the Black-Scholes model ⋮ Total value adjustment for European options in a multi-currency setting ⋮ PDE models for American options with counterparty risk and two stochastic factors: mathematical analysis and numerical solution ⋮ Total value adjustment for European options with two stochastic factors. Mathematical model, analysis and numerical simulation

Cites Work

• Augmented Lagrangian active set methods for obstacle problems
• PDE and martingale methods in option pricing.
• An upwind approach for an American and European option pricing model
• Numerical methods to solve PDE models for pricing business companies in different regimes and implementation in GPUs
• Mathematical Analysis and Numerical Methods for Pricing Pension Plans Allowing Early Retirement
• Elementary Stochastic Calculus, with Finance in View
• BILATERAL COUNTERPARTY RISK UNDER FUNDING CONSTRAINTS—PART I: PRICING
• BILATERAL COUNTERPARTY RISK UNDER FUNDING CONSTRAINTS—PART II: CVA
• A Semi-Lagrangian Approach for American Asian Options under Jump Diffusion

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