Counterparty risk valuation on credit-linked notes under a Markov Chain framework

A credit-linked note(CLN)is a note paying an enhanced coupon to investors for bearing the credit risk of a reference entity.In this paper,we study the counterparty risk on CLNs under a Markov chain framework,and introduce a Markov copula model to describe joint defaults between the reference entity underlying the CLN and CLN issuer.Assuming that the respective default intensities are directly and inversely proportional to the interest rate,which follows a CIR process,we obtain the explicit formulae for CLN values through a PDE approach.Finally,credit valuation adjustment(CVA)formula is derived to price counterparty credit risk.