Semi-analytic pricing formulas for basket credit-linked notes with and without counterparty risks

Abstract

This paper discusses the pricing of basket credit linked notes (BCLN) under the reduced model. Three types of BCLNs are discussed: the first, the second and the mth-to-default BCLNs with and without counterparty risks. Based on conditional independence, the joint distribution of default times can be calculated and thus the price problems are transformed into partial differential equation (PDE) forms. Then the semi-analytical pricing formulas for the above BCLNs are obtained with PDE method and the calculation of credit valuation adjustments are also obtained. Finally, numerical test results show the high precision of the derived pricing formulas.

Keywords

• basket cln
• counterparty risk
• hazard rate
• partial differential equation
• affine structure