Credit valuation adjustment

Monte Carlo methods in finance | Actuarial science | Mathematical finance

Credit valuation adjustments (CVAs) are accounting adjustments made to reserve a portion of profits on uncollateralized financial derivatives. They are charged by a bank to a risky (capable of default) counterparty to compensate the bank for taking on the credit risk of the counterparty during the life of the transaction. These most common transaction types are interest rate derivatives, foreign exchange derivatives, and combinations thereof. The reserved profits can be viewed mathematically as the net present value of the credit risk embedded in the transaction. In financial mathematics one defines CVA as 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. This price depends on counterparty credit spreads as well as on the market risk factors that drive derivatives' values and, therefore, exposure. CVA is one of a family of related valuation adjustments, collectively xVA; for further context here see Financial economics § Derivative pricing. Unilateral CVA is given by the risk-neutral expectation of the discounted loss. The risk-neutral expectation can be written as where is the maturity of the longest transaction in the portfolio, is the future value of one unit of the base currency invested today at the prevailing interest rate for maturity , is the loss given default, is the time of default, is the exposure at time , and is the risk neutral probability of counterparty default between times and . 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". According to the Basel Committee on Banking Supervision's July 2015 consultation document regarding CVA calculations, if CVA is calculated using 100 timesteps with 10,000 scenarios per timestep, 1 million simulations are required to compute the value of CVA. Calculating CVA risk would require 250 daily market risk scenarios over the 12-month stress period. CVA has to be calculated for each market risk scenario, resulting in 250 million simulations. These calculations have to be repeated across 6 risk types and 5 liquidity horizons, resulting in potentially 8.75 billion simulations. (Wikipedia).

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Credit valuation adjustment

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