Defaultable bonds with an infinite number of Lévy factors

Volume 37 / 2010

Jacek Jakubowski, Mariusz Niew/eg/lowski Applicationes Mathematicae 37 (2010), 275-307 MSC: Primary 60H30, 91B28; Secondary 60G51. DOI: 10.4064/am37-3-2

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 Lévy factors 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 conditions) under which the market is arbitrage-free. Connections with consistency conditions are discussed.

Authors

  • Jacek JakubowskiInstitute of Mathematics
    University of Warsaw
    Banacha 2
    02-097 Warszawa, Poland
    and
    Faculty of Mathematics
    and Information Science
    Warsaw University of Technology
    Plac Politechniki 1
    00-661 Warszawa, Poland
    e-mail
  • Mariusz Niew/eg/lowskiFaculty of Mathematics
    and Information Science
    Warsaw University of Technology
    Plac Politechniki 1
    00-661 Warszawa, Poland
    e-mail

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