Modeling of Contagion Effects and their Influence to the Pricing of Basket Credit Derivatives
by Qian Wang of the University of Cologne
November 28, 2005
Introduction: KMV model adopts the main idea of Merton's framework. It assumes that a firm defaults when the value of its assets is lower than that of its liabilities when its debt matures. The asset value processes are driven by geometric Brownian motions. So the asset value processes are dependent to each other. This induce the dependence among default events. "Distance-to-Default" for every firm can be calculated. Using the historical data we can also estimate the default probability of a firm.
Jarrow and Yu extend the existing reduced-form model through incorporating counterparty risk. In Jarrow and Yu's model, the default intensity is influenced not only by a set of economic-wide state variables, but also a collection of counterparty-specific jump terms capturing interfirm linkages. The counterparty risk is modeled through splitting the firms into primary and secondary type. The default intensities of primary firms are only dependent on the state variables, while the default intensities of secondary firms depend not only on the state variables, but also on the default status of the primary firms.
In this paper, we try to connect the ideas of these two models. The firms are divided into two types: primary and secondary. The asset value of primary firms are driven by geometric Brownian motions, which represent the influence through common factors. The asset value of secondary firms are not only driven by the common factors. It is also dependent on the default status (default or non default) of the primary firms. Because of this feature, the default probabilities of secondary firms are dependent on the default probabilities of the primary type.
Keywords: contagion, basket credit derivative, credit risk modeling.
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