Modeling of Contagion Effects and their Influence to the Pricing and Hedging of Basket Credit Derivatives

The financial health of a firm varies with randomly fluctuating macroeconomic factors such as changes in economic growth. This type of dependence between defaults can be and has been modelled in the standard reduced-form credit risk model with conditionally independent defaults. Credit contagion refers to the propagation of financial distress from one firm or sovereign government to another. Through credit contagion effects the classical assumption that the probabilities of default may only depend on the common factors is rejected.

Under different criteria the existing contagion models can be sorted into the following types: We pick here Jarrow & Yu‘s (2001) counterparty risk model and Schönbuchers (2003) frailty model, which can be regarded as the representatives of the respective types. We also try to construct two own models: correlated firm value model based on the Credit Metric’s model, and correlated firm value with jump model. In the correlated firm value model, the asset values of the firms depend not only on the common factors, but also on the firm specific factors of his own and of the tied firms. The tied firms here should be defined as business partners in the economic networks. In this way the asset values of all the firms depend on the same factors, so we call it factor model. Another innovation of this paper is the building of the correlated firm value with jump model. It tries to build the influence factors between asset value processes of tied firms into a jump process.

We then investigate the pricing effects caused by the conceptual differences of the four contagion models above, especially second-to-default basket credit derivative prices and CDO prices. For the CDO pricing, different contagion models will show different pricing trends.

At the end, the author tries to suggest some of the hedging strategies under contagion.

Qian Wang studied economics at the University Freiburg i. Br. from 1996 to 2000 before she started to work as a consultant at KPMG Fiduciary in Frankfurt. In October 2002 she joined the graduate school risk management at the University of Cologne. In January 2006 she finished her doctor thesis. Since October 2005 she works as assistant as the department of banking by Professor Hartmann-Wendels at the University of Cologne. Her research fields are credit portfolios, their correlation concepts and valuation of basket credit derivatives.