Efficient Risk Estimation for the Credit Valuation Adjustment
Michael B. Giles, Abdul-Lateef Haji-Ali, Jonathan Spence
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 3 orders of magnitude
compared to standard Monte Carlo.