Thursday, March 18, 2010

Dangerous Knowledge: Credit value adjustment with credit triggers

By Chuang Yi of the Royal Bank of Canada:

Abstract: We generalize the arbitrage-free valuation framework for counterparty credit risk (CCR) adjustments when credit triggers are allowed in the contract. The settlement of the deal for the investor could be either obliged or optional to execute when the counterparty hits its credit trigger before any default events. General formulas for credit value adjustment (CVA) are given for all four cases: obliged unilateral, obliged bilateral, optional unilateral and optional bilateral. We show that adding credit triggers will decrease the unilateral CVA for both obliged and optional cases, which are in line with the motivation of investors to reduce CCR. However, adding credit triggers may not necessarily reduce bilateral CVA. Counter-intuitively, we show that the bilateral CVA may actually increase by adding credit triggers. Moreover, the increased amount of bilateral CVA due to credit triggers for one party is exactly the same amount of bilateral CVA reduced for the other party. The CVA calculation is subjected to large uncertainty of model risks, mostly due to the lack of data for calibrating jump-to-default probabilities. Some explicit models for obliged unilateral CVA are discussed with special caveats on the model assumptions. Numerical examples are also given to illustrate the model risk of CVA calculation due to the uncertainty of jump sizes, even though pure jump models are assumed.

Download paper here: http://www.math.mcmaster.ca/~yichuang/CVA_Doc.pdf

No comments: