Credit valuation adjustment

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Credit valuation adjustment (CVA) is 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

 \mathrm{CVA} = E^Q[L^*] = (1-R)\int_0^T E^Q\left[\frac{B_0}{B_t} E(t)|\tau=t\right] d\mathrm{PD}(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, \tau is the time of default, E(t) is the exposure at time t, and  \mathrm{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.

More generally CVA can refer to a few different concepts:

  • The mathematical concept as defined above;
  • A part of the regulatory Capital and RWA (Risk weighted asset) calculation introduced under Basel 3;
  • The CVA desk of an investment bank, whose purpose is to:
    • hedge for possible losses due to counterparty default;
    • hedge to reduce the amount of capital required under the CVA calculation of Basel 3;
  • The "CVA charge". The hedging of the CVA desk has a cost associated to it, i.e. the bank has to buy the hedging instrument. This cost is then allocated to each business line of an investment bank (usually as a contra revenue). This allocated cost is called the "CVA Charge".

Exposure, independent of counterparty default[edit]

Assuming independence between exposure and counterparty’s credit quality greatly simplifies the analysis. Under this assumption this simplifies to

 \mathrm{CVA} = (1-R) \int_0^T \mathrm{EE}^*(t)~d\mathrm{PD}(0,t)

where \mathrm{EE}^* is the risk-neutral discounted expected exposure (EE)

The function of the CVA desk and implications for technology solution[edit]

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 requirements of an active CVA desk differ from those of a Risk Control group and it is not uncommon to see institutions use different systems for risk exposure management on one hand and CVA pricing and hedging on the other.

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

References[edit]

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