Valuation Of Credit Default Swaps

Credit default swap is a new kind of financial derivative in the internationalcapital market. A credit default swap is a contract agreement which allows the transferof credit risk of a risky asset or a basket of risky assets from one party to the other. Afinancial institution may use a CDS to transfer credit risk of a risky asset whilecontinues to retain the legal ownership of the asset. After 1990s, the rapid growth ofthe credit default swap market has reached to the stage where credit default swaps onreference entities are more actively traded than bonds issued by the reference entities.In the first section, we introduced the concept of credit risk, the development ofcredit derivatives market and the two primary types of models of default risk in theliterature: structural models and reduced form models. In the second section, westudied the fixed premium leg and contingent leg of a vanilla CDS contract andobtained the pricing equation according to arbitrage free principle. Under theassumption of geometric brownian motion, we obtained the PDE which defaultprobabiltiy satisfied and the analytical solution of the PDE. We analyzed the relationbetween CDS spread and maturity time, recovery rate, default barrier and the initialvalue of the reference entity.In the third section, we added the possibility of counterparty default to thevaluation model of CDS. Assume the asset values of the two reference entities satisfyjoint brownian motions, then the jonit default default probability solves a PDE with across-partial derivative term. We eliminated this term and obtained the solution of thePDE after a suitable transformation of coordinates. Finally, we compared the relationbetween CDS spread and correlation coefficient, recovery rate and maturity time etc.In the last section, we studied the valuation problem of a special type of basketcredit default swap: first to default CDS using the same method as the previoussection. In the numerical results part, we compared the relation between first todefault CDS spread and correlation coefficient, recovery rate and maturity time etc.