Skip to main content
SpringerLink
Log in

A Class of Jump-Diffusion Bond Pricing Models within the HJM Framework

  • Published:
Asia-Pacific Financial Markets Aims and scope Submit manuscript

Abstract

This paper considers a class of term structure models that is a parameterisation of the Shirakawa (1991) extension of the Heath et al. (1992) model to the case of jump-diffusions. We consider specific forward rate volatility structures that incorporate state dependent Wiener volatility functions and time dependent Poisson volatility functions. Within this framework, we discuss the Markovianisation issue, and obtain the corresponding affine term structure of interest rates. As a result we are able to obtain a broad tractable class of jump-diffusion term structure models. We relate our approach to the existing class of jump-diffusion term structure models whose starting point is a jump-diffusion process for the spot rate. In particular we obtain natural jump-diffusion versions of the Hull and White (1990, 1994) one-factor and two-factor models and the Ritchken and Sankarasubramanian (1995) model within the HJM framework. We also give some numerical simulations to gauge the effect of the jump-component on yield curves and the implications of various volatility specifications for the spot rate distribution.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Baxter, M. and Rennie, A. (1996) Financial Calculus: An Introduction to Derivative Pricing, Cambridge University Press.

  • Bhar, R. and Chiarella, C. (1997) Transformation of Heath-Jarrow-Morton models to Markovian systems, European Journal of Finance 3, 1–26.

    Article  Google Scholar 

  • Björk, T. and Gombani, A. (1999) Minimal realisations for forward rates, Finance and Stochastics 3(4), 413–432.

    Article  Google Scholar 

  • Björk, T., Kabanov, Y., and Runggaldier, W. (1997) Bond market structure in the presence of marked point processes, Mathematical Finance 7(2), 211–239.

    Article  Google Scholar 

  • Björk, T. and Landèn, C. (2002) On the construction of finite dimensional realisations for nonlinear forward rate models, Finance and Stochastics 6(3), 303–329.

    Article  Google Scholar 

  • Björk, T. and Svensson, L. (2001) On the existence of finite dimensional realisations for nonlinear forward rate models, Mathematical Finance 11(2), 205–243.

    Article  Google Scholar 

  • Bremaud, P. (1981) Point Processes and Queues: Martingale Dynamics, Springer-Verlag.

  • Carverhill, A. (1994) When is the short rate Markovian, Mathematical Finance 4, 305–312.

    MathSciNet  Google Scholar 

  • Chacko, G. and Das, S. R. (2002) Pricing interest rate derivatives: A general approach, The Review of Financial Studies 15(1), 195–241.

    Article  Google Scholar 

  • Cheyette, O. (1992) Term structure dynamics and mortgage valuation, Journal of Fixed Income 1, 28–41.

    Google Scholar 

  • Chiarella, C. and El-Hassan, N. (1996) A preference free partial differential equation for the term structure of interest rates, Financial Engineering and the Japanese Markets 3, 217–238.

    Google Scholar 

  • Chiarella, C. and Kwon, O. (2001a) Forward rate dependent Markovian transformations of the Heath-Jarrow-Morton term structure model, Finance and Stochastics 5(2), 237–257.

    Google Scholar 

  • Chiarella, C. and Kwon, O. (2001b) Formulation of popular interest models under the HJM framework, Asia Pacific Financial Markets 8(1), 1–22.

    Article  Google Scholar 

  • Chiarella, C. and Kwon, O. (2003) Finite dimensional affine realisations of HJM models in terms of forward rates and yields, Review of Derivatives Research 6(2), 129–155.

    Article  Google Scholar 

  • Chiarella, C., Schlögl, E., and Nikitopoulos, C. S. (2003) A defaultable term structure model with state dependent volatilities, School of Finance and Economics, UTS Working Paper.

  • Chiarella, C. and Tsô, T. D. (2003) The Jump component of the volatility structure of interest rate futures markets: An international comparison, Journal of Futures Markets 23, 1125–1158.

    Article  Google Scholar 

  • Chiarella, C. and Tô, T. D. (2004) Estimation of affine term structure models within the HJM framework, School of Finance and Economics, UTS Working Paper.

  • Das, S. R. (2002) The surprise element: Jumps in the interest rates, Journal of Econometrics 106, 27–65.

    Article  Google Scholar 

  • Das, S. R. (2000) Interest rate modelling with jump-diffusion processes. In N. Jegadeesh and B. Tuckman(eds), Advanced Fixed-Income Valuation Tools, John Wiley & Sons.

  • de Jong, F. and Santa-Clara, P. (1999) The dynamics of the forward interest rate curve: A formulation with state variables, Journal of Financial and Quantitative Analysis 34(1), 131–140.

    Google Scholar 

  • Duffie, D. and Kan, R. (1996) A yield-factor model of interest rates, Mathematical Finance, 6(4), 379–406.

    Google Scholar 

  • Glasserman, P. and Kou, S. G. (2003) The term structure of simple forward rates with jump risk, Mathematical Finance 13(3), 383–410.

    Article  Google Scholar 

  • Heath, D., Jarrow, R. A., and Morton, A. (1992) Bond pricing and the term structure of interest rates: A new methodology for contingent claims valuation, Econometrica 60, 77–105.

    Google Scholar 

  • Hull, J. C. and White, A. (1990) Pricing interest rate derivative securities, The Review of Financial Studies 3(4), 573–592.

    Article  Google Scholar 

  • Hull, J. C. and White, A. (1994) Numerical procedures for implementing term structure models II: Two-facors models, Journal of Derivatives Winter, 37–49.

    Google Scholar 

  • Inui, K. and Kijima, M. (1998) A Markovian framework in multi-factor Heath-Jarrow-Morton models, Journal of Financial and Quantitative Analysis, 33(3), 423–440.

    Google Scholar 

  • Nikitopoulos, C. S. (2004) A class of Markovian models for the term structure of interest rates under jump-diffusions, School of Finance and Economics, University of Technology, Sydney, Ph.D. Thesis.

  • Ritchken, P. and Chuang, Y. (1999) Interest rate option pricing with volatility humps, Review of Derivatives Research 3, 237–262.

    Article  Google Scholar 

  • Ritchken, P. and Sankarasubramanian, L. (1995) Volatilities structures of forward rates and the dynamics of term structure, Mathematical Finance 5(1), 55–73.

    Google Scholar 

  • Runggaldier, W. J. (2003) Jump-diffusion models. In S. T. Rachev (ed.), Handbook Heavy Tailed Distributions in Finance, Elsevier, North-Holland, pp. 169–209.

    Google Scholar 

  • Shirakawa, H. (1991) Interest rate option pricing with Poisson–Gaussian forward rate curve processes, Mathematical Finance 1(4), 77–94.

    Google Scholar 

  • Vasicek, O. (1977) An equilibrium characterisation of the term structure, Journal of Financial Economics 5, 177–188.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Finance and Economics, University of Technology, Sydney, P.O. Box 123, Broadway, NSW 2007, Australia

    Carl Chiarella & Christina Nikitopoulos Sklibosios

Authors
  1. Carl Chiarella
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Christina Nikitopoulos Sklibosios
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Carl Chiarella.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Chiarella, C., Sklibosios, C.N. A Class of Jump-Diffusion Bond Pricing Models within the HJM Framework. Asia-Pacific Finan Markets 10, 87–127 (2003). https://doi.org/10.1007/s10690-005-6006-0

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10690-005-6006-0

Key words

Search

Navigation