Modeling the Distance-to-Default Process of a Firm

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Modeling the Distance-to-Default Process of a Firm

by Marco Avellaneda of New York University, and
Jingyi Zhu of the University of Utah

October 26, 2001

Introduction: Credit derivatives provide synthetic protection against bond and loan default. A simple example of a credit derivative is the credit default swap, in which one counterparty makes periodic payments to another in exchange for the right to be paid a notional amount if a credit event happens. Recently, we have seen the emergence of "wholesale" credit protection in the form of first-to-default swaps written on a basket of underlying credits. Pricing of credit derivatives requires quantifying the likelihood of default of the reference entity. Default probabilities can be estimated from the spreads of the bond issued by the reference entity.

Two kinds of mathematical frameworks for pricing credit derivatives have been proposed to this date: the structural models, introduced by Merton [11] and others [3, 4, 13, 9, 12, 6], and the reduced form models of Duffie and Singleton [5]. Here, we will be concerned with the structural approach, and in particular with the "default barrier" methodology recently introduced by Hull and White [8]. This paper draws from Hull and White [8] and extends it in several directions.