Pricing credit-linked notes issued by the protection buyer and an SPV

We first derive the closed-form solutions of the CLNs issued by an SPV or the protection buyer both the with reference and counterparty risk under the consideration of default events correlated with the short-term interest rate. We derive the fair fees that are paid by a protection buyer to an SPV for the purpose of issuing the CLNs. From numerical analyses, we find that the values of CLNs are negatively correlated with the interest rate volatility and the default intensity of reference obligation. Further, if the short-term interest rate changes dramatically or the credit qualities of the reference entity and the protection buyer get worse, it is a better timing for the CLNs issued through an SPV.