A MARKOVIAN DEFAULTABLE TERM STRUCTURE MODEL WITH STATE DEPENDENT VOLATILITIES

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

International Journal of Theoretical and Applied Finance (IJTAF), 2007, vol. 10, issue 01, 155-202

Abstract: The defaultable forward rate is modelled as a jump diffusion process within the Schönbucher [26,27] general Heath, Jarrow and Morton [20] framework where jumps in the defaultable term structure fd(t,T) cause jumps and defaults to the defaultable bond prices Pd(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 realizations 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; stochastic credit spreads; defaultable bond prices (search for similar items in EconPapers)
Date: 2007
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Citations: View citations in EconPapers (3)

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Working Paper: A Markovian Defaultable Term Structure Model with State Dependent Volatilities (2004)
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DOI: 10.1142/S0219024907004147

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