Application of Chebyshev approximation techniques applied to banking risk calculations

Abstract

Risk management in banking necessitates computationally intensive risk metric calculations, particularly through scenario analysis. This process is often time-consuming and costly. Numerical techniques, such as Chebyshev methods, can mitigate these burdens by enhancing calculation efficiency and reducing complexity. This study evaluates the application of Chebyshev numerical techniques in risk calculations, specifically focusing on counterparty credit risk due to its relevance and increased importance post the 2007-08 financial crisis. Using adaptations from open-source libraries such as MOCAX Intelligence, trials were conducted on representative instruments and portfolios. Key metrics, including credit value adjustment and potential future exposures, were computed. The findings reveal that Chebyshev techniques significantly reduce computation costs (1%-10% of current costs) and enhance calculation speeds while maintaining acceptable accuracy for risk management. Thus, Chebyshev numerical methods substantially improve the efficiency of risk metric calculations within the banking sector.