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CVA under Bates Model with Stochastic Default Intensity

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Document pages: 18 pages

Abstract: Counterparty credit risk has received increasing attention and become a topical issue since 2007 credit crisis, particularly for its impact on the valuation of the OTC derivatives. Credit Value Adjustment (CVA) has become an import field and it is required in Basel III. This paper studies CVA for European options under Bates model with stochastic default intensity. We develop a Monte Carlo and finite difference method framework for assessing exposure profiles and impact of counterparty credit risk in pricing. The exposures are computed by solving a partial integro-differential Equation (PIDE) using implicit-explicit (IMEX) time discretization schemes. CVA in presence of wrong way risk (WWR) is embedded in the correlation between risk factor and default intensity. Meanwhile, the jump-at-default feature of the models offers an effective means to assess WWR. Our results show that both jump and WWR play an important role in evaluating CVA and exposures. The impact is significant and it is crucial for risk management purpose.

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