Closed Form Solutions for Contingent CDS on Cross Currency Swaps

17 Pages Posted: 18 Nov 2019

Date Written: November 7, 2019


In the simplest possible model that includes vols and correlations for interest rates in both currencies, the FX rate and the default intensity, a closed form solution is presented for the PV of a contingent credit default swap (CCDS) that pays in default the outstanding mark to market of a cross currency swap provided the latter is positive. Then some conditions are given that determine the direction of the sensitivities of this PV with respect to changes in the correlations. The three correlations involving only interest rates and FX determine the market risk of the underlying CCY swap. The other three correlations that involve the default intensity determine the right and wrong way risk of the CCDS. When some extra natural assumptions are made that prevent intensities, resp. PVs, from becoming negative then the sensitivities against the market risk correlations are uniform in the sense that their sign does not depend on the maturity, or the moneyness, of the underlying CCY swap, or whether the domestic rate is paid or received. This is quite clear intuitively because it is similar to the vega of a call and put being the same. In contrast, the paper derives necessary and sufficient conditions for the sensitivity directions against the credit related correlations. These conditions show a strong dependence on the characteristics of the CCY swap. In other words, right way risk can become wrong way risk when for example the maturity changes.

Keywords: contingent credit default swap, CCDS, wrong way risk, cross currency swap

JEL Classification: C02, G13

Suggested Citation

Hoehnle, Rainer, Closed Form Solutions for Contingent CDS on Cross Currency Swaps (November 7, 2019). Available at SSRN: or

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