A Markovian Defaultable Term Structure Model with State Dependent Volatilities
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.
|Date of creation:||01 Oct 2004|
|Publication status:||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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- Bystrom, Hans & Kwon, Oh Kang, 2007.
"A simple continuous measure of credit risk,"
International Review of Financial Analysis,
Elsevier, vol. 16(5), pages 508-523.
- Hans Byström & Oh-Kang Kwon, 2003. "A Simple Continuous Measure of Credit Risk," Research Paper Series 111, Quantitative Finance Research Centre, University of Technology, Sydney.
- Byström, Hans & Kwon, Oh Kang, 2003. "A Simple Continuous Measure of Credit Risk," Working Papers 2003:14, Lund University, Department of Economics, revised 18 Jan 2005.
- Das, Sanjiv R., 2002. "The surprise element: jumps in interest rates," Journal of Econometrics, Elsevier, vol. 106(1), pages 27-65, January.
- Tomas Björk & Yuri Kabanov & Wolfgang Runggaldier, 1997. "Bond Market Structure in the Presence of Marked Point Processes," Mathematical Finance, Wiley Blackwell, vol. 7(2), pages 211-239.
- R. Bhar & C. Chiarella, 1997. "Transformation of Heath?Jarrow?Morton models to Markovian systems," The European Journal of Finance, Taylor & Francis Journals, vol. 3(1), pages 1-26.
- Ram Bhar & Carl Chiarella, 1995. "Transformation of Heath-Jarrow-Morton Models to Markovian Systems," Working Paper Series 53, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
- Olivier Scaillet & Olivier Renault & Jean-Luc Prigent, 2000. "An Empirical Investigation in Credit Spread Indices," FMG Discussion Papers dp363, Financial Markets Group.
- Prigent, J.-L. & Renault, O. & Scaillet, O., 2000. "An Empirical Investigation in Credit Spread Indices," Discussion Papers (IRES - Institut de Recherches Economiques et Sociales) 2000028, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
- Jean -Luc Prigent & Olivier Renault & Olivier Scaillet, 2000. "An Empirical Investigation in Credit Spread Indices," Working Papers 2000-59, Centre de Recherche en Economie et Statistique.
- John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters,in: Theory Of Valuation, chapter 5, pages 129-164 World Scientific Publishing Co. Pte. Ltd..
- Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "A Theory of the Term Structure of Interest Rates," Econometrica, Econometric Society, vol. 53(2), pages 385-407, March.
- Björk, Tomas & Gombani, Andrea, 1997. "Minimal Realizations of Forward Rates," SSE/EFI Working Paper Series in Economics and Finance 182, Stockholm School of Economics.
- Inui, Koji & Kijima, Masaaki, 1998. "A Markovian Framework in Multi-Factor Heath-Jarrow-Morton Models," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 33(03), pages 423-440, September.
- David Heath & Robert Jarrow & Andrew Morton, 2008. "Bond Pricing And The Term Structure Of Interest Rates: A New Methodology For Contingent Claims Valuation," World Scientific Book Chapters,in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 13, pages 277-305 World Scientific Publishing Co. Pte. Ltd..
- Heath, David & Jarrow, Robert & Morton, Andrew, 1992. "Bond Pricing and the Term Structure of Interest Rates: A New Methodology for Contingent Claims Valuation," Econometrica, Econometric Society, vol. 60(1), pages 77-105, January.
- Carl Chiarella & Christina Sklibosios, 2003. "A Class of Jump-Diffusion Bond Pricing Models within the HJM Framework," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 10(2), pages 87-127, September.
- Carl Chiarella & Christina Nikitopoulos-Sklibosios, 2004. "A Class of Jump-Diffusion Bond Pricing Models within the HJM Framework," Research Paper Series 132, Quantitative Finance Research Centre, University of Technology, Sydney.
- Carl Chiarella & Thuy‐Duong Tô, 2003. "The jump component of the volatility structure of interest rate futures markets: An international comparison," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 23(12), pages 1125-1158, December.
- To, Thuy Duong & Carl Chiarella, 2003. "The Jump Component of the Volatility Structure of Interest Rate Futures Markets: An International Comparison," Royal Economic Society Annual Conference 2003 205, Royal Economic Society.
- Hiroshi Shirakawa, 1991. "Interest Rate Option Pricing With Poisson-Gaussian Forward Rate Curve Processes," Mathematical Finance, Wiley Blackwell, vol. 1(4), pages 77-94.
- Carl Chiarella & Oh Kwon, 2003. "Finite Dimensional Affine Realisations of HJM Models in Terms of Forward Rates and Yields," Review of Derivatives Research, Springer, vol. 6(2), pages 129-155, May.
- Sarig, Oded & Warga, Arthur, 1989. " Some Empirical Estimates of the Risk Structure of Interest Rates," Journal of Finance, American Finance Association, vol. 44(5), pages 1351-1360, December. Full references (including those not matched with items on IDEAS)