Modelling Credit Valuation Adjustment for Interest Rate Derivatives under Wrong Way Risk

Specialeforsvar ved Stine Qvistgaard Ludwig

Titel: Modelling Credit Valuation Adjustment for Interest Rate Derivatives under Wrong Way Risk

Abstract: In this thesis, we investigate credit valuation adjustment (CVA) for interest rate derivatives under correlation between exposure and the credit quality of the counterparty. When correlation is negative, derivatives exhibit wrong-way risk, whereas right-way risk occurs when correlation is positive. We examine different ways of jointly modelling the interest rate and the default time of the counterparty. First, we consider exposure measures and CVA when modelling the short rate using the Vasicek model, while the default intensity is modelled using the extension of the Cox-Ingersoll-Ross (CIR++) model. Wrong- and right-way risk are incorporated through dependence between the driving Brownian motions from each of the models. We then examine the impact on CVA of replacing the CIR++ model with the simpler CIR model. Moreover, we investigate in detail the effect of modelling the short rate using either the Two-Additive-Factor Gaussian (G2++) model or the Vasicek model with deterministic jumps at the default time of the counterparty. In the latter model, wrong- and right-way risk are captured through jumps only. We find that both CVA and percentage deviation from independent CVA are remark-ably dependent on the choice of derivative contract, counterparty, short rate and intensity model, and the associated parameter values. The nature of the dependence structure between exposure and the default time of the counterparty differs considerably acrossthe short rate models and hence, wrong- and right-way risk are captured in qualitatively different ways. Common to all joint models of the short rate and the intensity process is that dependence between the factors has a relevant impact on CVA.

Vejleder: David Glavind Skovmand
Censor: Bjarne Astrup Jensen, CBS