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# Credit Valuation Adjustment

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

$CVA = E^Q[L^*] = (1-R)\int_0^T E^Q[\frac{B_0}{B_t} E(t)|\tau=t] dPD(0,t)$

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, R is the fraction of the portfolio value that can be recovered in case of a default, τ is the time of default, 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

$CVA = (1-R) \int_0^T EE^*(t) dPD(0,t)$

where EE* = 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 both finance and a trading desk in the Front Office. Tier 1 banks either already generate counterparty EPE and ENE (expected positive/negative exposure) 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.

A good introduction can be found in a paper by Michael Pykhtin and Steven Zhu.[1]

## References

1. ^ A Guide to Modeling Counterparty Credit Risk, GARP Risk Review,July-August 2007 Related SSRN Research Paper

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