Abstract
We present a unified framework for computing CVA sensitivities, hedging the CVA, and assessing CVA risk, using probabilistic machine learning meant as refined regression tools on simulated data, validatable by low-cost companion Monte Carlo procedures. Various notions of sensitivities are introduced and benchmarked numerically. We identify the sensitivities representing the best practical trade-offs in downstream tasks including CVA hedging and risk assessment.
Summary
A purely regression/ML-based approach to CVA sensitivities, hedging, and risk assessment. No BSDE, HJB, or stochastic control formulation — methodologically orthogonal to the XVA HJB paper. The paper introduces a taxonomy of sensitivity types (benchmark bump, linear bump, smart bump, AAD bump, EC-optimized, PLE-optimized, LS run-on) and benchmarks them on a 500-swap portfolio with 10 economies and 8 counterparties. Key finding: optimized sensitivities (EC, PLE, LS) dramatically outperform classical bump sensitivities for hedging, especially in run-off mode where default risk dominates.
Key Contributions
- Taxonomy of 7+ CVA sensitivity types with systematic benchmarking
- Smart bump sensitivities: 90x faster than benchmark bumps with comparable accuracy
- EC and PLE sensitivities for optimized hedging — “deep hedging over one time step”
- Twin Monte Carlo validation without nested simulation
- Run-off vs. run-on CVA hedging comparison
Key Findings
- Naive AAD sensitivities are unreliable — differentiation is not continuous in sup-norm
- For run-off hedging (with defaults): bump sensitivities are counterproductive; EC/PLE sensitivities achieve 3.5-5x risk compression
- For run-on hedging (pure market risk): all sensitivities help; LS run-on is fastest and “excellent”
- Works under a P/Q blend measure (Albanese et al. 2021)
- No overlay structure — static hedging over single risk horizon