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Utility-Based Pricing of Defaultable Bonds and Decomposition of Credit Risk

by Tomoaki Shouda of the Mitsubishi UFJ Trust Investment Technology Institute Co., Ltd. & Hitotsubashi University

December 20, 2006

Abstract: We discussed utility-based pricing of defaultable bonds where their recovery values are unpredictable. By considering an optimal investment problem for bondholders, we have derived simultaneous partial integro-differential equations that the utility-based bond price solves. We have also illustrated their numerical solution. We aimed to extract credit risk premium from the yield spread of defaultable bonds and to classify them to default-timing risk, recovery risk, and spread risk.

JEL Classification: C65, D52, G33.

Keywords: Default-timing risk, Recovery risk, Spread risk, Doubly-stochastic model, Backward stochastic differential equation, Marginal utility-based pricing, Utility-indifference pricing.

Previously titled: Indifference Price of Defaultable Bonds with Unpredictable Recovery and Their Risk Premiums

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