Function approximations for counterparty credit exposure calculations

2025/07/11 by Domagoj Demeterfi, Demeterfi, Domagoj, Kathrin Glau +3
Economics, Econometrics and Finance · #Computational Finance (q-fin.CP) #Credit Risk and Financial Regulations #FOS: Economics and business

paper · pdf · doi:10.48550/arxiv.2507.09004

openalex publication_date 2025/07/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The challenge to measure exposures regularly forces financial institutions into a choice between an overwhelming computational burden or oversimplification of risk. To resolve this unsettling dilemma, we systematically investigate replacing frequently called derivative pricers by function approximations covering all practically relevant exposure measures, including quantiles. We prove error bounds for exposure measures in terms of the L^p norm, 1 ≤ p < ∞, and for the uniform norm. To fully exploit these results, we employ the Chebyshev interpolation and show exponential convergence of the resulting exposure calculations. As our main result we derive probabilistic and finite sample error bounds under mild conditions including the natural case of unbounded risk factors. We derive an asymptotic efficiency gain scaling with n^1/2-ε for any ε>0 with n the number of simulations. Our numerical experiments cover callable, barrier, stochastic volatility and jump features. Using 10 000 simulations, we consistently observe significant run-time reductions in all cases with speed-up factors up to 230, and an average speed-up of 87. We also present an adaptive choice of the interpolation degree. Finally, numerical examples relying on the approximation of Greeks highlight the merit of the method beyond the presented theory.

Citations

• Multi-Layer Deep xVA: Structural Credit Models, Measure Changes and Convergence Analysis
• Sparse Grid Method for Highly Efficient Computation of Exposures for xVA
• Deep xVA solver -- A neural network based counterparty credit risk\n management framework
• Speed-up credit exposure calculations for pricing and risk management
• Low-rank tensor approximation for Chebyshev interpolation in parametric\n option pricing
• A new approach for American option pricing: The Dynamic Chebyshev method
• Counterparty Trading Limits Revisited:CSAs, IM, SwapAgent(r), from PFE\n to PFL
• The Chebyshev method for the implied volatility
• Improved error bound for multivariate Chebyshev polynomial interpolation
• Chebyshev Interpolation for Parametric Option Pricing
• Bilateral Credit Valuation Adjustment for Large Credit Derivatives Portfolios
• A Proof of the Smoothness of the Finite Time Horizon American Put Option for Jump Diffusions
• The Pricing of Options and Corporate Liabilities

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