Measures Of Counterparty Credit Risk And Their Applications In Equity Derivatives And Interest Rate Derivatives

This thesis focus on three important measures of Counterparty Credit Risk (CCR):Potential Future Exposure (PFE), Expected Positive Exposure (EPE) and Credit Valuation Adjustment (CVA) both analytically and numerically. The second chapter is concerned with the notions of PFE and EPE and the comparison of their advantages and disadvantages. The third chapter is concerned with CVA. We argue that the assumption of the independence between credit exposure and default intensity is irrational, which leads us to consider Wrong Way Risk (WWR). Moreover, since no institution is risk-free,it’s necessary to calculate bilateral CVA instead of unilateral CVA. More concretely, we deduce an analytical formula of CVA for European options. The fourth chapter is concerned with interest rate swap. We point out that CVA of interest rate swap can be calculated as the pricing of a basket of swaptions, which is done in the preceding chapter. Furthermore, we introduce nested Monte Carlo method and least square Monte Carlo method for CVA of exotic products, and provide a framework of their application in the calculation of CVA with WWR.Finally, we introduce the author’s experiences in France, particularly during his internship in Societe Generale. We also give several proposals concerning difficult points in the calculation of CVA, including collateralization, clearing, recovery rate etc.