A Markovian Defaultable Term Structure Model with State Dependent Volatilities

40 Pages Posted: 7 Oct 2004

See all articles by Carl Chiarella

Carl Chiarella

University of Technology, Sydney - UTS Business School, Finance Discipline Group

Erik Schlögl

University of Technology Sydney (UTS), Quantitative Finance Research Centre; University of Cape Town (UCT) - The African Institute of Financial Markets and Risk Management; Faculty of Science, Department of Statistics, University of Johannesburg; Financial Research Network (FIRN)

Christina Sklibosios Nikitopoulos

University of Technology Sydney - Business School; Financial Research Network (FIRN)

Date Written: October 2004

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 cause jumps and defaults to the defaultable bond prices. 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: Interest rates, credit risk, default, Markov property, jump diffusion

JEL Classification: E43, G33, G13

Suggested Citation

Chiarella, Carl and Schloegl, Erik and Sklibosios Nikitopoulos, Christina, A Markovian Defaultable Term Structure Model with State Dependent Volatilities (October 2004). Available at SSRN: https://ssrn.com/abstract=600402 or http://dx.doi.org/10.2139/ssrn.600402

Carl Chiarella

University of Technology, Sydney - UTS Business School, Finance Discipline Group ( email )

PO Box 123
Broadway, NSW 2007
Australia
+61 2 9514 7719 (Phone)
+61 2 9514 7711 (Fax)

HOME PAGE: http://www.business.uts.edu.au/finance/

Erik Schloegl (Contact Author)

University of Technology Sydney (UTS), Quantitative Finance Research Centre ( email )

Ultimo
PO Box 123
Sydney, NSW 2007
Australia
+61 2 9514 2535 (Phone)

HOME PAGE: http://www.schlogl.com

University of Cape Town (UCT) - The African Institute of Financial Markets and Risk Management ( email )

Leslie Commerce Building
Rondebosch
Cape Town, Western Cape 7700
South Africa

Faculty of Science, Department of Statistics, University of Johannesburg ( email )

Auckland Park, 2006
South Africa

Financial Research Network (FIRN)

C/- University of Queensland Business School
St Lucia, 4071 Brisbane
Queensland
Australia

HOME PAGE: http://www.firn.org.au

Christina Sklibosios Nikitopoulos

University of Technology Sydney - Business School ( email )

15 Broadway, Ultimo
Sydney 2007, New South Wales
Australia

Financial Research Network (FIRN)

C/- University of Queensland Business School
St Lucia, 4071 Brisbane
Queensland
Australia

HOME PAGE: http://www.firn.org.au

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