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Real-world jump-diffusion term structure models

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Author Info

  • Nicola Bruti-Liberati
  • Christina Nikitopoulos-Sklibosios
  • Eckhard Platen

Abstract

This paper considers interest rate term structure models in a market attracting both continuous and discrete types of uncertainty. The event-driven noise is modelled by a Poisson random measure. Using as numeraire the growth optimal portfolio, interest rate derivatives are priced under the real-world probability measure. In particular, the real-world dynamics of the forward rates are derived and, for specific volatility structures, finite-dimensional Markovian representations are obtained. Furthermore, allowing for a stochastic short rate in a non-Markovian setting, a class of tractable affine term structures is derived where an equivalent risk-neutral probability measure may not exist.

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Bibliographic Info

Article provided by Taylor & Francis Journals in its journal Quantitative Finance.

Volume (Year): 10 (2010)
Issue (Month): 1 ()
Pages: 23-37

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Handle: RePEc:taf:quantf:v:10:y:2010:i:1:p:23-37

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Related research

Keywords: Stochastic analysis; Stochastic volatility; Quantitative finance; Numerical simulation;

References

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  1. Morten Christensen & Eckhard Platen, 2004. "A General Benchmark Model for Stochastic Jump Sizes," Research Paper Series, Quantitative Finance Research Centre, University of Technology, Sydney 139, Quantitative Finance Research Centre, University of Technology, Sydney.
  2. Ioannis Karatzas & Constantinos Kardaras, 2007. "The numéraire portfolio in semimartingale financial models," Finance and Stochastics, Springer, vol. 11(4), pages 447-493, October.
  3. Carl Chiarella & Christina Nikitopoulos-Sklibosios, 2004. "A Class of Jump-Diffusion Bond Pricing Models within the HJM Framework," Research Paper Series, Quantitative Finance Research Centre, University of Technology, Sydney 132, Quantitative Finance Research Centre, University of Technology, Sydney.
  4. Goll, Thomas & Kallsen, Jan, 2000. "Optimal portfolios for logarithmic utility," Stochastic Processes and their Applications, Elsevier, vol. 89(1), pages 31-48, September.
  5. Platen, Eckhard, 2000. "A minimal financial market model," SFB 373 Discussion Papers 2000,91, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  6. Hiroshi Shirakawa, 1991. "Interest Rate Option Pricing With Poisson-Gaussian Forward Rate Curve Processes," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 1(4), pages 77-94.
  7. Truc Le & Eckhard Platen, 2006. "Approximating the growth optimal portfolio with a diversified world stock index," Journal of Risk Finance, Emerald Group Publishing, vol. 7(5), pages 559-574, November.
  8. Eckhard Platen, 2003. "Modeling the Volatility and Expected Value of a Diversified World Index," Research Paper Series, Quantitative Finance Research Centre, University of Technology, Sydney 103, Quantitative Finance Research Centre, University of Technology, Sydney.
  9. Eckhard Platen, 2002. "Benchmark Model with Intensity Based Jumps," Research Paper Series, Quantitative Finance Research Centre, University of Technology, Sydney 81, Quantitative Finance Research Centre, University of Technology, Sydney.
  10. Das, Sanjiv R., 2002. "The surprise element: jumps in interest rates," Journal of Econometrics, Elsevier, vol. 106(1), pages 27-65, January.
  11. Hull, John & White, Alan, 1990. "Pricing Interest-Rate-Derivative Securities," Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 573-92.
  12. Shane Miller & Eckhard Platen, 2004. "Two-Factor Model for Low Interest Rate Regimes," Research Paper Series, Quantitative Finance Research Centre, University of Technology, Sydney 130, Quantitative Finance Research Centre, University of Technology, Sydney.
  13. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "A Theory of the Term Structure of Interest Rates," Econometrica, Econometric Society, Econometric Society, vol. 53(2), pages 385-407, March.
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  15. Ross, Stephen A., 1976. "The arbitrage theory of capital asset pricing," Journal of Economic Theory, Elsevier, vol. 13(3), pages 341-360, December.
  16. Filipovic, Damir, 2005. "Time-inhomogeneous affine processes," Stochastic Processes and their Applications, Elsevier, vol. 115(4), pages 639-659, April.
  17. Damir Filipovic, 2001. "A general characterization of one factor affine term structure models," Finance and Stochastics, Springer, vol. 5(3), pages 389-412.
  18. Tomas Björk & Yuri Kabanov & Wolfgang Runggaldier, 1997. "Bond Market Structure in the Presence of Marked Point Processes," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 7(2), pages 211-239.
  19. Harrison, J. Michael & Kreps, David M., 1979. "Martingales and arbitrage in multiperiod securities markets," Journal of Economic Theory, Elsevier, vol. 20(3), pages 381-408, June.
  20. Peter Ritchken & L. Sankarasubramanian, 1995. "Volatility Structures Of Forward Rates And The Dynamics Of The Term Structure," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 5(1), pages 55-72.
  21. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
  22. Chan, K C, et al, 1992. " An Empirical Comparison of Alternative Models of the Short-Term Interest Rate," Journal of Finance, American Finance Association, vol. 47(3), pages 1209-27, July.
  23. Eckhard Platen, 2004. "A Benchmark Approach to Finance," Research Paper Series, Quantitative Finance Research Centre, University of Technology, Sydney 138, Quantitative Finance Research Centre, University of Technology, Sydney.
  24. Eckhard Platen, 2001. "Arbitrage in Continuous Complete Markets," Research Paper Series, Quantitative Finance Research Centre, University of Technology, Sydney 72, Quantitative Finance Research Centre, University of Technology, Sydney.
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Citations

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Cited by:
  1. Constantinos Kardaras & Eckhard Platen, 2009. "On the Dybvig-Ingersoll-Ross Theorem," Papers 0901.2080, arXiv.org, revised Mar 2010.
  2. Claudio Fontana & Wolfgang J. Runggaldier, 2012. "Diffusion-based models for financial markets without martingale measures," Papers 1209.4449, arXiv.org, revised Feb 2013.
  3. Ke Du & Eckhard Platen, 2011. "Three-Benchmarked Risk Minimization for Jump Diffusion Markets," Research Paper Series, Quantitative Finance Research Centre, University of Technology, Sydney 296, Quantitative Finance Research Centre, University of Technology, Sydney.
  4. Eckhard Platen & Stefan Tappe, 2011. "Affine Realizations for Levy Driven Interest Rate Models with Real-World Forward Rate Dynamics," Research Paper Series, Quantitative Finance Research Centre, University of Technology, Sydney 289, Quantitative Finance Research Centre, University of Technology, Sydney.

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