Bilateral Credit Value Adjustment With Default Correlation

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Credit value adjustment (CVA) is a financial concept used to account for the potential loss in value of a portfolio due to counterparty credit risk. Essentially, CVA reflects the difference between the risk-free portfolio value and the true portfolio value, considering the possibility of counterparty default. It’s a critical component in derivative pricing, especially in over-the-counter transactions, where parties are exposed to credit risk.

Reference [1] generalized the CVA concept and developed a bilateral CVA. It also extended the Hull and White hazard rate model to incorporate default correlation. The authors pointed out,

This paper has developed a counterparty credit risk adjustment model to value OTC financial derivatives. The proposal comprises a bilateral CVA with WWR and dependency between the defaults of the entities involved, based on the Hull-White model (2012) which incorporates the hazard rate as an exponential function dependent on the value of the portfolio.

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When applying the model to obtain the fair value of an IRS, the results demonstrate that the bilateral CVA with WWR increases and, as a consequence, the fair value of the swap decreases when the dependency between the entities’ de-faults is considered. Here, Monte Carlo simulation has been used to determine the CVA and the fair value of the swap. The relationship between these magnitudes for the two models analyzed was found to be the same for the ten sets of simulations performed.

In short, the paper developed a bilateral CVA and applied it to price an interest-rate swap. Its important finding is that the default correlation increases the CVA value.

Does it intuitively make sense?

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References

[1] Merche Galisteoa, Isabel Morilloa and Teresa Preixensa, CVA with wrong-way risk and correlation between defaults: An application to an interest rate swap, 2023 – Vol. 1 – n.º 3 – Artículo 2

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