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 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


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