A Markovian Defaultable Term Structure Model with State Dependent Volatilities
AbstractThe 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.
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Bibliographic InfoPaper provided by Quantitative Finance Research Centre, University of Technology, Sydney in its series Research Paper Series with number 135.
Date of creation: 01 Oct 2004
Date of revision:
defaultable HJM model; strochastic credit spreads; defaultable bond prices;
Other versions of this item:
- Carl Chiarella & Christina Nikitopoulos Sklibosios & Erik Schlögl, 2007. "A Markovian Defaultable Term Structure Model With State Dependent Volatilities," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 10(01), pages 155-202.
- E43 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Interest Rates: Determination, Term Structure, and Effects
- G33 - Financial Economics - - Corporate Finance and Governance - - - Bankruptcy; Liquidation
- G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
This paper has been announced in the following NEP Reports:
- NEP-ALL-2004-11-22 (All new papers)
- NEP-FIN-2004-11-22 (Finance)
- NEP-MAC-2004-11-22 (Macroeconomics)
- NEP-MON-2005-01-10 (Monetary Economics)
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