Pricing credit risky swaps in an affine framework

Adam Polack & Adam Schydt

Student thesis: Master thesis

Abstract

This master’s thesis focuses on the pricing of counterparty credit risky claims. The subject hasgrown increasingly popular in recent years due to the global recognition that participants in theover-the-counter market indeed may default.We argue that the price of any risky claim can be linearly decomposed into the price of a risk freeclaim minus a certain risk premium called the Credit Value Adjustment. We choose to take acloser look at interest rate swaps, and show that under the assumption of independence betweencounterparty default risk and interest rates, the risky swap price is given as an infinite sum ofswaption prices multiplied by marginal default probabilities. So, while traditional pricing of acounterparty risk free swap requires nothing more than a zero coupon term structure, we arguethat the pricing of a risky swap requires a lot more.We choose to explore the swaption pricing model proposed in Pelsser and Schrager (2006). Byusing Fourier inversion techniques, we show that the model is able to generate prices possiblystipulating the dynamics of any affine interest rate model. In terms of modelling the defaultrisk, we choose to examine the intensity model proposed in Lando (1998). Since the driver of theintensity model, the Cox-process, can also be assumed affine, we choose to use affine models forboth purposes. This has the benefits of providing semi-analytical solutions to zero coupon rates,default probabilities, and especially the characteristic function which is the focal point in termsof the Fourier inversion which ultimately provides the swaption price.In our applicational part, we choose to specify both of the affine models in compliance withthe one-factor CIR model (Cox et al., 1985) to set a basic example. However, we emphasizethat extending the framework to a higher number of risk factors is fairly straightforward dueto the flexibility of both models. We use different estimation methods and study the interplaybetween the two models in different economical data that showcases tendencies pre- and postcrisis, respectively. This investigation is conducted for two different counterparties; the globalbank HSBC and the automobile manufacturer Fiat.

EducationsMSc in Business Administration and Management Science, (Graduate Programme) Final Thesis
LanguageEnglish
Publication date2011
Number of pages148
SupervisorsMads Stenbo Nielsen