Credit Risk Under the Benchmark Approach

Abstract

Credit risk has recently been a very prominent topic in the finance literature. This chapter demonstrates how this important topic can be discussed under the benchmark approach. In the first section of the chapter, we use the techniques from Chaps. 7, 8, and 9 to formulate a tractable affine model under the real world probability measure and demonstrate how to price credit default swaps under the benchmark approach in the second section. The third section builds on the second and introduces the important topic of credit valuation adjustment. In particular, our model is able to capture right-way and wrong-way exposure. This means that we can capture the dependence structure of the default event and the value of the transaction under consideration. For standard contracts, we provide closed-form solutions, however, due to the fact that we allow for a dependence between the default event and the value of the transaction, closed-form solutions are difficult to obtain in general. For this reason, we conclude the chapter with a reduced form model, which is more tractable than the model from the first section of the chapter.