Fast and Stable Credit Gamma of CVA

ArXiv ID: 2311.11672 “View on arXiv”

Authors: Unknown

Abstract

Credit Valuation Adjustment is a balance sheet item which is nowadays subject to active risk management by specialized traders. However, one of the most important risk factors, which is the vector of default intensities of the counterparty, affects in a non-differentiable way the most general Monte Carlo estimator of the adjustment, through simulation of default times. Thus the computation of first and second order (pure and mixed) sensitivities involving these inputs cannot rely on direct path-wise differentiation, while any approach involving finite differences shows very high statistical noise. We present ad hoc analytical estimators which overcome these issues while offering very low runtime overheads over the baseline computation of the price adjustment. We also discuss the conversion of the so-obtained sensitivities to model parameters (e.g. default intensities) into sensitivities to market quotes (e.g. Credit Default Swap spreads).

Keywords: Credit Valuation Adjustment (CVA), Sensitivities, Monte Carlo estimation, Default intensities, Credit Default Swaps, Fixed Income (Credit)

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 3.0/10
• Quadrant: Lab Rats
• Why: The paper introduces advanced mathematical techniques, including adjoint algorithmic differentiation for discontinuous payoffs and distributional derivatives using Dirac deltas, with heavy analytical derivations. However, it focuses on theoretical estimators and methodological development without presenting backtest results, datasets, or extensive statistical metrics.

  flowchart TD
    Start["Research Goal<br>Compute stable CVA gamma<br>with low computational overhead"] --> Problem["Problem<br>Default intensity vectors cause<br>non-differentiability in Monte Carlo"]

    Problem --> Methodology["Methodology<br>Derive ad-hoc analytical estimators<br>for first & second order sensitivities"]

    Methodology --> Data["Data & Inputs<br>Counterparty default intensities<br>CDS market quotes"]

    Data --> Computation["Computational Process<br>1. Baseline CVA calculation<br>2. Analytical sensitivity estimation<br>3. Model-to-market conversion"]

    Computation --> Findings["Key Findings<br>• Eliminates path-wise differentiation issues<br>• Reduces statistical noise<br>• Low runtime overhead<br>• Enables active CVA risk management"]

    Findings --> End["Outcome<br>Fast & stable credit gamma<br>ready for trading desks"]