Abstract/Summary

The interdependency between the evolution of counterparty credit quality and the underlying risk factor(s) driving the value of a derivative contract has led to wrong way/right way risk, which could have a significant impact on the exposure and CVA profiles of OTC derivatives portfolios. Traditional approaches in modelling counterparty credit risk are mainly classified into Merton-type structural models and reduced form models. However, the former suffers from the drawback that the default probabilities generated from the model are not consistent with the market implied ones while the latter fails to offer a reasonable economic rationale and is of limited asset-credit correlation structures. This thesis is dedicated to the modelling of wrong way/right way risk of fixed income derivatives based on the Bessel bridge approach proposed by Davis and Pistorius (2010). I begin with a brief review of the existing literature on counterparty credit risk modelling with a focus on structural and reduced-form approaches and pointing out the advantages and disadvantages of both methods. Then in the second part of the thesis, we go through the technical details of inverse first-passage time problem of the credit index process and Bessel bridge approach. We apply the unilateral version of the default framework to an FX-Hull-White hybrid setting for the exchange rate and correlated interest rates to establish a joint FX-credit unilateral default model. An extension to the bilateral version of the joint FX-credit default model without identifying the joint distribution density function of the two credit index processes conditional on default is presented in the third part of the thesis and extensive numerical analysis are conducted in the expected positive exposure profiles of a cross currency swap contract for various sets of FX-credit and default correlation scenarios. The impact of wrong way/right way risk illustrated are plausible. For the final main topic of thesis, we work on CVA of Bermudan swaptions. A multi-curve interest rate framework with stochastic basis spreads are developed, into which the unilateral Bessel bridge approach based joint interest rate-credit model is integrated and least-square Monte-Carlo simulation is applied to compute CVA with the presence of wrong way/right way risk.