Hedging default risks of CDO tranches in non-homogeneous Markovian contagion models

Abstract

The paper is concerned with the hedging of credit derivatives, in particular synthetic collateralized debt obligations (CDOs) tranches and first to default swap (FTD) with respect to actually traded credit default swaps index (CDS index). In the model, we will relax the name homogeneity assumption, that all the names share the same risk-neutral default. We think of two homogeneous groups of names and the default intensities of each group depending both upon the number of survived names in each subgroup. This results a two dimensional Markov chain setting, since the portfolio state is characterized by the number of survived names in each group. Finally, we have achieved the numerical implementation through trinomial trees, by means of Markov chain techniques. The experimental results show that the new extended hedge model in this paper improves the hedge strategies under the name homogeneity case.