Efficient risk estimation for the credit valuation adjustment

Journal article

The valuation of over-the-counter derivatives is subject to a series of valuation adjustments known as xVA, which pose additional risks for financial institutions. Associated risk measures, such as the value-at-risk of an underlying valuation adjustment, play an important role in managing these risks. Monte Carlo methods are often regarded as inefficient for computing such measures. As an example, we consider the value-at-risk of the Credit Valuation Adjustment (CVA-VaR), which can be expressed using a triple nested expectation. Traditional Monte Carlo methods are often inefficient at handling several nested expectations. Utilising recent developments in multilevel nested simulation for probabilities, we construct a hierarchical estimator of the CVA-VaR which reduces the computational complexity by several orders of magnitude compared to standard Monte Carlo.

Authors: Giles, MB; Haji-Ali, A-L; Spence, J

• Publication status: Accepted
• Peer review status: Peer reviewed
• Publisher: Springer
• Journal: Finance and Stochastics
• Acceptance date: 2025-10-02
• EISSN: 1432-1122
• ISSN: 0949-2984
• Language: English
• Keywords: multilevel Monte Carlo; nested simulation; risk estimation