Credit value adjustment (CVA) is by definition the difference between the risk-free portfolio value and the true portfolio value that takes into account the possibility of a counterparty’s default. In other words, CVA is the market value of counterparty credit risk.
Unilateral CVA is given by the risk-neutral expectation of the discounted loss. The risk-neutral expectation
can be written as
where T is the maturity of the longest transaction in the portfolio, B(t) is the future value of one unit of the base currency invested today at the prevailing interest rate for maturity t ,1{.} is the indicator function that takes value one if the argument is true (and zero otherwise) and PD(s,t) is the risk neutral probability of counterparty default between times s and t. These probabilities can be obtained from the term structure of credit-default swap
(CDS) spreads.
Exposure, Independent of Counterparty Default
Assuming independence between exposure and counterparty’s credit quality greatly simplifies the analysis. Under this assumption this simplifies to
where
which is the risk-neutral discounted expected exposure (EE)
The Function of the CVA Desk and Implications for Technology Solution
In the view of leading investment banks, CVA is essentially an activity carried out by a trading desk in the Front Office. Tier 1 banks either already generate counterparty EPE and ENE under the ownership of the CVA desk (although this often has another name) or plan to do so. Whilst a CVA platform is based on an exposure measurement platform, the solution drivers are very different and it is unwise to create dependencies between the Risk exposure management system and Front Office CVA system, even if they share similar intermediate outputs.
CVA Operating Model
The originating desks for the OTC trades essentially buy their credit protection from the CVA desk. The credit risk of these desks is thus consolidated into a single book, with the net risk of that book hedged by the CVA desk with the rest of the market.
- The key considerations for a Front Office CVA desk are:
- Charge Model
- Hedging Portfolio CVA
- Proxy Hedging
- Hedge Effectiveness
- P&L Attribution/Revaluation of Portfolio
References
1. A Guide to Modeling Counterparty Credit Risk, GARP Risk Review, July/August 200, Steven H. Zhu, Michael Pykhtin.
2. EM RISK, Risk Analytics (Credit Valuation Adjustment Solution Consultants)