A Markovian Defaultable Term Structure Model with State Dependent Volatilities

Carl Chiarella, Erik Schlogl and Christina Nikitopoulos-Sklibosios ()

No 135, Research Paper Series from Quantitative Finance Research Centre, University of Technology, Sydney

Abstract: The defaultable forward rate is modeled as a jump diffusion process within the Schonbucher (2000, 2003) general Heath, jarrow and Morton (1992) framework where jumps in the defaultable term structure f d (t, T) cause jumps and defaults to the defaultable bond prices P d (t, T). Within this framework, we investigate an appropriate forward rate volatility structure that results in Markovian defaultable spot rate dynamics. In particular, we consider state dependent Wiener volatility functions and time dependent Poisson volatility functions. The corresponding term structures of interest rates are expressed as finite dimensional affine realisations in terms of benchmark defaultable forward rates. In addition, we extend this model to incorporate stochastic spreads by allowing jump intensities to follow a square-root diffusion process. In that case the dynamics become non-Markovian and to restore path independence we propose either an approximate Markovian scheme or, alternatively, constant Poisson volatility functions. We also conduct some numerical simulations to gauge the effect of the stochastic intensity and the distributional implications of various volatility specifications.

Keywords: defaultable HJM model; strochastic credit spreads; defaultable bond prices (search for similar items in EconPapers)
JEL-codes: E43 G13 G33 (search for similar items in EconPapers)
Pages: 41 pages
Date: 2004-10-01
New Economics Papers: this item is included in nep-fin, nep-mac and nep-mon
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

Published as: Chiarella, C., Schlogl, E. and Nikitopoulos-Sklibosios, C., 2007, "A Markovian Defaultable Term Structure Model with State Dependent Volatilities", International Journal of Theoretical and Applied Finance, 10(1), 155-202.

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Related works:
Journal Article: A MARKOVIAN DEFAULTABLE TERM STRUCTURE MODEL WITH STATE DEPENDENT VOLATILITIES (2007)
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