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RATING BASED LÉVY LIBOR MODEL
Author(s) -
Eberlein Ernst,
Grbac Zorana
Publication year - 2013
Publication title -
mathematical finance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.98
H-Index - 81
eISSN - 1467-9965
pISSN - 0960-1627
DOI - 10.1111/j.1467-9965.2011.00514.x
Subject(s) - libor , libor market model , econometrics , markov chain , credit default swap index , economics , credit risk , arbitrage , valuation (finance) , credit derivative , credit spread (options) , bond , interest rate , financial economics , credit valuation adjustment , actuarial science , mathematics , monetary economics , statistics , finance , volatility (finance) , credit reference
In this paper, we consider modeling of credit risk within the Libor market models. We extend the classical definition of the default‐free forward Libor rate and develop the rating based Libor market model to cover defaultable bonds with credit ratings. As driving processes for the dynamics of the default‐free and the predefault term structure of Libor rates, time‐inhomogeneous Lévy processes are used. Credit migration is modeled by a conditional Markov chain, whose properties are preserved under different forward Libor measures. Conditions for absence of arbitrage in the model are derived and valuation formulae for some common credit derivatives in this setup are presented.