Calculating sensitivities of xVAs

Specialeforsvar ved Simon Boe Pedersen

Titel: Calculating sensitivities of xVAs

Abstract: In this thesis an algorithm for efficient calculation of credit value adjustments (CVA) is considered and differentiated with automatic differentiation. The algorithm is based on the application of a least squares regression in order to produce an approximation of the future portfolio values. The thesis is divided into three parts. In the first part we specify the Vasicek and Hull-White model used for the simulation of interest rates and derive an expression for CVA. In the second part we derive the Proxies Only in Indicators (POI) algorithm and show how the algorithm's low reliance on the regression proxy still has desirable accuracy, even when the approximation is poor. Thirdly, we derive the technique of Automatic Adjoint Differentiation (AAD), give a sample implementation and apply it to the POI algorithm to calculate sensitivities for CVA. It is shown that AAD has constant computational complexity and the computational cost are compared to finite differencing. We consider uncollateralized portfolios of interest rate swaps and assume independence of default probability and interest rates.

Vejleder: Rolf Poulsen
Censor: Thomas Kokholm