A Multivariate Default Model with Spread and Event Risk

Abstract

We present a new portfolio default model based on a conditionally independent and identically distributed (CIID) structure of the default times. It combines an intensity-based ansatz in the spirit of Duffie and Gârleanu (2001). Risk and valuation of collateralized debt obligations. Financial Analysts Journal, 57(1), 41–59. with the Lévy subordinator concept introduced in Mai and Scherer (2009). A tractable multivariate default model based on a stochastic time-change. International Journal of Theoretical and Applied Finance, 12(2), 227–249. We aim at exploiting the computational advantages of the CIID framework for evaluating multiname credit derivatives, while incorporating two central drivers for credit products. More precisely, we allow for both a dynamic evolution of the portfolio credit default swap (CDS) spread (unlike static copula models) and cataclysmic events allowing for simultaneous defaults (unlike intensity-based portfolio loss processes). While the former feature is considered to be crucial for consistently hedging credit products, the second property is supposed to take into account default clusters and the market’s fear of extreme events. For applications, the model is approximated by a related top-down representation of the portfolio loss process. It is shown how to coherently calculate hedging deltas for collateralized debt obligations (CDOs) w.r.t. portfolio CDS and how to consistently calibrate the model to the two products. Both tasks solely require the computation of one-dimensional (Laplace inversion) integrals and can be carried out within fractions of a second. Illustrating the stability and functionality of the pricing approach, the new model and the models it is related to are calibrated to a daily time-series of iTraxx Europe index CDS and CDOs. We find the fitting results of the presented model to be very promising and conclude that it may be used for the dynamic pricing and hedging of credit derivatives.