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Bilateral Credit Valuation Adjustment of an Optional Early Termination Clause

by Claudio Nordio of Banco Popolare, and
Lorenzo Giada of Banco Popolare

January 24, 2013

Abstract: Is an option to early terminate a swap at its market value worth zero? At first sight it seems so, but in presence of counterparty risk it depends on the criteria used to determine such market value. In case of a single uncollateralised swap transaction between two defaultable counterparties, the additional unilateral option to early terminate the swap at predefined dates requires the evaluation of a Bermudan option. We give a general pricing formula assuming a default-free close-out amount, and apply it to different kinds of derivatives in a setting with deterministic default intensity, showing that the impact on the fair value at inception and on the counterparty risk of the transaction might be non negligible.

JEL Classification: G12, G13.

AMS Classification: 62H20, 62L15, 91B25, 91B70.

Keywords: Counterparty risk, Credit Valuation Adjustment, Unilateral CVA, Bilateral CVA, Debit Valuation Adjustment, Closeout, ISDA, Bermudan option, Equity Forward Contract, Break clause, Optional Early Termination clause, Additional Early Termination clause, Bivariate exponential distributions, Gumbel bivariate exponential distributions.

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