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

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.