Valuation of kth-to-default credit-linked notes with counterparty risk in a reduced-form model

In this paper we analyze the kth-to-default credit-linked notes (CLN) with counterparty risk by the reduced-form model. We study the structure of the kth-to-default CLN and present a general valuation framework for CLN values and counterparty valuation adjustments (CVA) under the conditional independence assumption. Explicit formulas of the kth-to-default CLN values and their CVAs are obtained by the PDE approach. Numerical simulations are conducted to show the effects of the correlated default risk on the kth-to-default CLN values and their CVAs.