Abstract

A market with defaultable bonds where the bond dynamics is in a Heath-Jarrow-Morton setting and the forward rates are driven by an infinite number of Levy f actors is considered. The setting includes rating migrations driven by a Markov chain. All basic types of recovery are investigated. We formulate necessary and sufficient conditions (generalized HJM condi tions) under which the market is arbitrage free. Connections with consistency conditions are discussed. Keywords Levy processes, defaultable bonds, HJM postulate, credit risk, rating migration, conditional Markov chains

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