Pricing Credit Default Index Swaptions A numerical evaluation of pricing models

Abstract

This study examines the background and nature of the credit default index swaption (CDIS) and presents relevant methods for modelling credit risk. A CDIS is a credit derivative contract that gives the buyer right to enter into a credit default index swap (CDS index) contract at a given point in time. A CDS index, in turn, is a multi-name credit default swap (CDS). Within the eld of research, this thesis identi es the CDIS pricing models presented by Jackson (2005), Rutkowski & Armstrong (2009) and Morini & Brigo (2011) as the most recognized and developed. These models are evaluated by reconstruction in a numerical software environment. Although the considered models are well-behaving under economic interpretation, they di er in constructional features regarding whether to model the so-called Armageddon event inside or outside the Black (1976) model. An Armadageddon event refers to a total default of the CDS index up to the expiry of the CDIS. Based on the criteria of required assumption boldness and calculation transparency, the model presented by Morini & Brigo (2011) have been evaluated in depth. The expected value of the front-end protection, i.e. the insurance against default events during the lifetime of the CDIS, is found to increase with pairwise correlation among reference names and the e ect of the Armageddon scenario is only observable as the pairwise correlation approaches one. This implies that the choice of pricing model is found to be crucial during stressed economic climates and of less importance during calm economic climates.