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

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.