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Counterparty risk pricing: impact of closeout and first-to-default times

Research output: Contribution to journalArticle

Damiano Brigo, Cristin Buescu, Massimo Morini

Original languageEnglish
Article number1250039
JournalInternational Journal of Theoretical and Applied Finance
Volume15
Issue number6
Publication statusPublished - Sep 2012

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  • pdf

    1106.3496v1, 198 KB, application/pdf

    21/07/2015

    Submitted manuscript

    Preprint in ArXiv

King's Authors

Abstract

We compare two different bilateral counterparty valuation adjustment (BVA) formulas. The first formula is an approximation and is based on subtracting the two unilateral Credit Valuation Adjustment (CVA)'s formulas as seen from the two different parties in the transaction. This formula is only a simplified representation of bilateral risk and ignores that upon the first default closeout proceedings are ignited. As such, it involves double counting. We compare this formula with the fully specified bilateral risk formula, where the first to default time is taken into account. The latter correct formula depends on default dependence between the two parties, whereas the simplified one does not. We also analyze a candidate simplified formula in case the replacement closeout is used upon default, following ISDA's recommendations, and we find the simplified formula to be the same as in the risk free closeout case. We analyze the error that is encountered when using the simplified formula in a couple of simple products: a zero coupon bond, where the exposure is unidirectional, and an equity forward contract where exposure can go both ways. For the latter case we adopt a bivariate exponential distribution due to Gumbel to model the joint default risk of the two parties in the deal. We present a number of realistic cases where the simplified formula differs considerably from the correct one.

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