Fast calculation of counterparty credit exposures and associated sensitivities using fourier series expansion

Abstract

This paper presents a novel approach for computing portfolio-level counterparty exposures, such as Potential Future Exposure (PFE) and Expected Exposure (EE), along with the associated sensitivities. The method is based on Fourier-cosine series expansion (COS) and 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. An evident advantage of the COS method is its sustained efficiency, particularly when handling large portfolios.
Numerical test results underscore its potential as a significantly more efficient alternative to the Monte Carlo method, 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, reinforcing the method's efficiency and stability in practical applications.