Hierarchical and Adaptive Methods for Efficient Risk Estimation

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This project aims to expand upon existing adaptive schemes to efficiently compute important measures of risk with applications to finance. In particular, we aim to apply these methods to the Credit Value Adjustment (CVA) Capital Charge - which requires banks to reserve money to protect against losses resulting from a party who is owe money to the bank defaulting and not repaying money owed. The CVA charge is a key component in the Basel III accord which aims to mitigate the risks which played a key role in the 2008 financial crash. The nature of the explicit formula for the CVA charge and the variety of variables influencing the charge render standard computational methods infeasible. Banks often resort to using cheap, inaccurate approximations instead. It is our goal to improve upon the complexity of accurate computational methods to provide an efficient, accurate alternative to these cheap approximations. We also plan to expand the research for use in other (so-called xVA) financial risk-measures. It is also our goal to generalize the same approach to incorporate various financial contracts with computationally difficult structure.