CVA
FinPricing offers:
Four user interfaces:
- Data API.
- Excel Add-ins.
- Model Analytic API.
- GUI APP.
Credit Valuation Adjustment (CVA) Introduction
| 1. CVA Introduction |
Credit Valuation Adjustment (CVA) is an adjustment to the valuation of a portfolio to explicitly account for the credit worthiness of counterparties. The CVA of an over-the-counter (OTC) derivatives portfolio with a given counterparty is the market value of the credit risk of any failure by that counterparty to perform on agreements. It is applied to all OTC capital market trading products, including IR, FX, commodity, equity and credit derivatives.
One way to compute CVA was based on the difference in the expected loss (EL) for the counterparty and yourself, and was calculated as the expected exposure to yourself or the counterparty due to its default conditional on no previous default for the other side, assuming the independence of default times of yourself and the counterparty.
The other way to calculate the default rate of yourself or the counterparty conditional on no previous default for the other side now incorporates the default correlation between yourself and the counterparty. The Pearson correlation is used when considering the joint default. This enhancement will be applied to the CVA calculation of all of the products to incorporate the default correlation between yourself and the counterparty.
Credit valuation adjustment is first computed based on counterparty. A counterparty portfolio may consist of interest rate, foreign, equity, commodity, and credit derivatives. Therefore, a counterparty CVA amount is further required to be allocated into the sub-portfolio associated with different asset classes.
CVA allocation is based on the sum of the asset class stand-alone CVAs, rather than the CVA of the counterparty. Without netting, the CVA of a counterparty is equal to the sum of the asset-class stand-alome CVAs. However, this is not the case when netting and margin agreements are in place.
| 2. CVA Calculation |
We use a single example to elaborate CVA concept and calculation. Assume that an instrument that promises to pay a X from party B to party A at maturity date T, and nothing before date T.
By definition, CVA = Risk-free value – True (risky value)
Risk-Free Value
Risk-free values should be easily obtained as they are what brokers quote or what derivative trading systems or valuation models normally report.
The risk-free value of the instrument is given by
Risk or True Value
There are two primary types of models that attempt to describe default processes in the literature: structural models and reduced-form (or intensity) models. The structural models regard default as an endogenous event, focusing on the capital structure of a firm. The reduced-form models do not explain the event of default endogenously, but instead characterize it exogenously as a jump process. Many practitioners in the credit trading arena have tended to gravitate toward the reduced-from models given their mathematical tractability.
The risky or true value of the instrument is given by
CVA Amount
By definition, the CVA amount is given by
The above example is simple and intuitive but unrealistic as CVA in real world is calculated at a portfolio level. We provide a deeper and more realistic discussion.
CVA can be also caclulated based on the difference between theexpected loss of the counterparty and yourself:
CVA = EL_counterparty - EL_yourself
The survival probability curves for both the counterparty and yourself are obtained by bootstrapping the credit spreads of them assuming a constant recovery rate. The model simply states that, in a CDS contract, the expected premium payments from the protection buyer and the expected default payment from the protection seller in case of default should be equal; and therefore, employs an iterative one dimensional root finding mechanism to solve, in each CDS term, for the proper constant hazard rate.
In this approach, the joint default is considered when calculating the expected loss (EL) for the counterparty and yourself; however, the default times of the counterparty and Bank are assumed independent when considering the joint default. Therefore, one condition is set because of this assumption.
| Related Topics |