Explicit formulas for pricing credit-linked notes with counterparty risk under reduced-form framework

Abstract

A credit-linked note (CLN) is a type of credit derivative, constructed with a bond and an embedded credit default swap, which allows the issuer to transfer a specific credit risk to credit investors. In this paper, we model CLNs with and without counterparty risk in the reduced-form framework. For CLNs with counterparty risk, we consider two different scenarios, i.e. the issuer of CLNs and reference assets have either positive correlation or negative correlation. Assuming the interest rate follows the Cox–Ingersoll–Ross (CIR) model (Cox et al., 1985) and the default events mainly depend on the interest rate, we model the two different correlations. Explicit formulas for value functions are obtained through a partial differential equation approach. In addition, counterparty valuation adjustment and the dependence on related parameters are also investigated.