Fast calculation of Counterparty Credit exposures and associated sensitivities using fourier series expansion

ArXiv ID: 2311.12575 “View on arXiv”

Authors: Unknown

Abstract

This paper introduces a novel approach for computing netting–set level and counterparty level exposures, such as Potential Future Exposure (PFE) and Expected Exposure (EE), along with associated sensitivities. The method is essentially an extension of the Fourier-cosine series expansion (COS) method, originally proposed for option pricing. This method can accommodate a broad range of models where the joint distribution of involved risk factors is analytically or semi-analytically tractable. This inclusivity encompasses nearly all CCR models commonly employed in practice. A notable advantage of the COS method is its sustained efficiency, particularly when handling large portfolios. A theoretical error analysis is also provided to justify the method’s theoretical stability and accuracy. Various numerical tests are conducted using real-sized portfolios, and the results underscore its potential as a significantly more efficient alternative to the Monte Carlo method for practical usage, particularly applicable to portfolios involving a relatively modest number of risk factors. Furthermore, the observed error convergence rates align closely with the theoretical error analysis.

Keywords: Counterparty Credit Risk (CCR), Potential Future Exposure (PFE), Expected Exposure (EE), Fourier-Cosine Series, Risk Management

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 7.0/10
  • Quadrant: Holy Grail
  • Why: The paper uses advanced Fourier analysis and spectral methods with complex error analysis (high math), and validates the approach with large-scale numerical tests on real-sized portfolios, showing direct performance comparisons and convergence rates (high empirical rigor).
  flowchart TD
    A["Research Goal<br>Develop faster exposure calculation<br>method for CCR"] --> B["Methodology<br>Extend COS method to exposures"]
    B --> C["Data/Inputs<br>Real-sized portfolios<br>Risk factor distributions"]
    C --> D["Computational Process<br>Fourier series expansion<br>vs Monte Carlo simulation"]
    D --> E["Key Findings<br>Significant efficiency gain<br>vs Monte Carlo<br>Consistent error convergence"]