A Useful Result on First Passage OU Process

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A Useful Result on First Passage OU Process

by Chuang Yi of McMaster University

January 2008

Abstract: In this paper, we study the relationship between the Merton's probability of default (MPD) and the first passage probability of default (FPD) defined on an (Ornstein-Uhlenbeck) OU process. We find that the FPD is twice of MPD if the default barrier is the asymptotic mean of the OU process. Three different proofs are given for this result.

Keywords: First passage time, probability of default, OU process.

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