Pricing bonds and CDS in the model with rating migration induced by a Cox process

Volume 83 / 2008

Jacek Jakubowski, Mariusz Niew/eg/lowski Banach Center Publications 83 (2008), 159-182 MSC: Primary 62P05; Secondary 60J27, 91B70. DOI: 10.4064/bc83-0-10

Abstract

We investigate the properties of a rating migration process assuming that it is given by subordination of a discrete time Markov chain and a Cox process. The problem of pricing of defaultable bonds with fractional recovery of par value with rating migration and credit default swaps is considered. As an example of applications of our results, we give an explicit solution to the pricing problem in a model with short rate and intensity processes given by the solution of a two-dimensional Ornstein-Uhlenbeck equation with a Lévy noise.

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
    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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