Abstract
Recently, financial institutions were required to provide the financial derivatives instrument level credit valuation adjustment (CVA) by the new accounting standard. CVA trading desks are facing difficulties to calculate a netting-set level CVA with wrong-way risk (WWR) since the dynamics of the exposures and probability of default (PD) are separated and calculated by different counterparty credit risk (CCR) computing systems. Another difficult work is that the netting-set level CVA mixed the pricing models for all trades under a netting-set. It is significant to develop a new CVA model that is based on the credit adjustment to the existing pricing model under one risk-neutral framework. This paper presents the work on CVA with WWR under the credit deterioration dynamics in both normal and stressed economic conditions. In terms of the double-correlation structure that is constructed based on the Gaussian latent variable models we propose an analytical expression of CVA for the fundamental financial derivatives such as futures or forwards contracts. The double-correlation structure captures the market- and asset-credit correlations. The proposed CVA pricing framework is based on the credit deterioration dynamics rather than default dynamics. The credit deterioration index (CDI) is defined as the limit of the credit deterioration variable and calculated using the rating agency credit rating transition data. The proposed CVA with WWR model is a function of the correlations, CDI, counterparty probability of default, loss given default, interest rate and volatility of the traded derivatives. The market- and asset-credit correlation parameters are calibrated to either the normal or stressed market. Under the stressed market, the scenario design, shock variable selection and shock magnitude are discussed. The numerical results show that the CVA is an increasing function of the market-credit correlation and a decreasing function of the credit rating. The stressed CVA is about four times higher than the normal CVA.
Highlights
Counterparty credit risk (CCR) has received a lot of attention from financial institutions since the 2007-2009 Global Financial Crisis (GFC)
The major reforms introduced by Basel Committee on Banking Supervision (BCBS) are (a) "Going forward, banks must determine their capital requirement for counterparty credit risk using stressed inputs". (b) "Banks will be subject to a capital charge for potential mark-to-market losses associated with a deterioration in the credit worthiness of a counterparty" (Reference [1], paragraph 14)
[12] Pan, Pan and Khandrika derived an analytical expression for credit valuation adjustment (CVA) with wrong-way risk (WWR) using the Gaussian copula model and calculated CVA for commodity futures and equity forwards. [13, 14] It is hard to list all of the studies on CVA with WWR models
Summary
Counterparty credit risk (CCR) has received a lot of attention from financial institutions since the 2007-2009 Global Financial Crisis (GFC). [1] Basel III addressed CCR under financial and economic stress. As Basel III addressed, the major credit losses during the GFC were from the counterparty credit downgrade or deterioration rather than the actual default. The major reforms introduced by Basel Committee on Banking Supervision (BCBS) are (a) "Going forward, banks must determine their capital requirement for counterparty credit risk using stressed inputs". (b) "Banks will be subject to a capital charge for potential mark-to-market losses (ie credit valuation adjustment - CVA - risk) associated with a deterioration in the credit worthiness of a counterparty" (Reference [1], paragraph 14) The major reforms introduced by Basel Committee on Banking Supervision (BCBS) are (a) "Going forward, banks must determine their capital requirement for counterparty credit risk using stressed inputs". (b) "Banks will be subject to a capital charge for potential mark-to-market losses (ie credit valuation adjustment - CVA - risk) associated with a deterioration in the credit worthiness of a counterparty" (Reference [1], paragraph 14)
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