
How is cva calculated?
Credit valuation adjustment  Wikipedia, the free encyclopedia

** Credit valuation adjustment **
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*Credit valuation adjustment* (CVA) is the difference between the riskfree
portfolio value and the true portfolio value that takes into account the
possibility of a counterpartyâs default. In other words, CVA is the
market value of counterparty credit risk.
Unilateral CVA is given by the riskneutral expectation of the discounted
loss. The riskneutral expectation can be written as
\mathrm{CVA} = E^Q[L^*] = (1R)\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)
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