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.
Highlights
Counterparty credit risk (CCR) refers to the risk that a counterparty of a financial contract will default prior to the expiration of the contract, and cannot make the required contractual payments
This paper contributes as follows: first we expand Bates model by modeling the intensity of jump to default with the stochastic process, i.e., the CIR++ process which provides a natural and effective framework to handle the correlation between the underlying asset and the default, evaluate the impact on exposure and Credit Value Adjustment (CVA) and assess wrong way risk (WWR); second we develop an efficient PDE based Monte Carlo framework for pricing CVA and assessing exposure profile under Bates model with stochastic intensity of the jump to default which combines advantages of Monte Carlo simulation and efficiency of PDE pricing
In order to study the impact of WWR, we show the EE and CVA for vanilla European option
Summary
Counterparty credit risk (CCR) refers to the risk that a counterparty of a financial contract will default prior to the expiration of the contract, and cannot make the required contractual payments. The other difficulty in pricing CVA concerns the dependency between exposure and counterparty credit quality, which is known as wrong/right way risk (WWR). Jumps modeling the sudden changes in the risk factors and it could be related to counterparty’s default. In this paper we model CVA for European options under Bates model with stochastic default intensity which presents several attractive features. Option values in the model are computed by finite difference method of the corresponding PIDE Both Heston model and jump diffusion models are nested by Bates model. WWR is formulated by introducing a kind of model-to market survival rate change ratio Under this framework, CVA for both single trade and portfolios can be treated.
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