An Adaptive Importance Sampling Approach for Variance Reduction in Jump-Diffusion CVA Calculations

Yutong Huang

doi:10.54254/2755-2721/2025.GL27136

Applied and Computational EngineeringOpen access

An Adaptive Importance Sampling Approach for Variance Reduction in Jump-Diffusion CVA Calculations

Research Article

Open Access

An Adaptive Importance Sampling Approach for Variance Reduction in Jump-Diffusion CVA Calculations

Yutong Huang ^1*

¹ Rutgers University

^*Corresponding author: moon225@gmail.com

Published on 24 September 2025

ACE Vol.186

ISSN (Print): 2755-273X

ISSN (Online): 2755-2721

ISBN (Print): 978-1-80590-383-3

ISBN (Online): 978-1-80590-384-0

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Abstract

Credit Valuation Adjustment computation encounters substantial computational challenges under jump-diffusion asset dynamics, particularly regarding convergence rates in Monte Carlo simulations. Traditional sampling methods require excessive simulation paths for acceptable confidence intervals, creating operational bottlenecks in real-time risk management systems. This research develops an adaptive importance sampling framework specifically designed for high-dimensional jump-diffusion processes in CVA calculations. The methodology dynamically adjusts sampling densities to account for jump risk while maintaining unbiased estimation properties. A self-adaptive algorithm identifies and oversamples critical paths contributing disproportionately to CVA variance. Experimental results demonstrate variance reduction ratios exceeding 85% compared to standard Monte Carlo methods, with computational efficiency improvements of approximately 400% for portfolios containing European and barrier options under Merton jump-diffusion dynamics. The framework achieves significant variance reduction without sacrificing numerical accuracy, enabling faster risk reporting and more responsive counterparty risk management.

Keywords:

Credit Valuation Adjustment, Importance Sampling, Variance Reduction, Jump-Diffusion Process

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References

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References

[2]. Deo, A., & Murthy, K. Efficient black-box importance sampling for VaR and CVaR estimation. In 2021 Winter Simulation Conference (WSC) (pp. 1-12). IEEE.

[3]. Xing, Y., Sit, T., & Ying Wong, H. (2022). Variance reduction for risk measures with importance sampling in nested simulation. Quantitative Finance, 22(4), 657-673.

[5]. Castellano, R., Corallo, V., & Morelli, G. (2022). Structural estimation of counterparty credit risk under recovery risk. Journal of Banking & Finance, 140, 106512.

[7]. Mies, F., Sadr, M., & Torrilhon, M. (2023). An efficient jump-diffusion approximation of the Boltzmann equation. Journal of Computational Physics, 490, 112308.

[9]. Fantazzini, D. (2024). Adaptive Conformal Inference for Computing Market Risk Measures: An Analysis with Four Thousand Crypto-Assets. Journal of Risk and Financial Management, 17(6), 248.

[11]. Cong, W., Ramezani, M., & Mahdavi, M. (2021). On the Importance of Sampling in Training GCNs: Tighter Analysis and Variance Reduction. arXiv preprint arXiv: 2103.02696.

Cite this article

Huang,Y. (2025). An Adaptive Importance Sampling Approach for Variance Reduction in Jump-Diffusion CVA Calculations. Applied and Computational Engineering,186,59-70.

Data availability

The datasets used and/or analyzed during the current study will be available from the authors upon reasonable request.

About volume

Volume title: Proceedings of CONF-FMCE 2025 Symposium: Semantic Communication for Media Compression and Transmission

ISBN: 978-1-80590-383-3(Print) / 978-1-80590-384-0(Online)

Editor: Anil Fernando

Conference website: https://2025.conffmce.org/glasgow.html

Conference date: 24 October 2025

Series: Applied and Computational Engineering

Volume number: Vol.186

ISSN: 2755-2721(Print) / 2755-273X(Online)

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