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Bond markets where prices are driven by a general marked point process

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Author Info

  • Björk, T.

    ()
    (Department of Finance)

  • Kabanov, Y.

    (Laboratoire de Mathematiques)

  • Runggaldier, W.

    (Dipartimento di Matematica Pura e Applicata)

Abstract

We investigate the term structure for the case when interest rates are allowed to be driven by a general marked point process as well as by a Wiener process. Developing a theory which allows for measure-valued trading portfolios we study existence and uniqueness of a martingale measure, as well as completeness of the bond market. We also give sufficient conditions for the existence of an affine term structure. Developing the appropriate forward measures we give formulas for interest rate derivatives.

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File URL: http://swopec.hhs.se/hastef/papers/hastef0088.pdf
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Bibliographic Info

Paper provided by Stockholm School of Economics in its series Working Paper Series in Economics and Finance with number 88.

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Length: 64 pages
Date of creation: Dec 1995
Date of revision:
Publication status: Published in Mathematical Finance, 1997, pages 211-239.
Handle: RePEc:hhs:hastef:0088

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Postal: The Economic Research Institute, Stockholm School of Economics, P.O. Box 6501, 113 83 Stockholm, Sweden
Phone: +46-(0)8-736 90 00
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Web page: http://www.hhs.se/
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Related research

Keywords: Term structure of interest rates; arbitrage; bond markets; interest rates; martingales; jump processes; completeness; affine term structure;

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References

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  1. Robert A. Jarrow, 2009. "The Term Structure of Interest Rates," Annual Review of Financial Economics, Annual Reviews, Annual Reviews, vol. 1(1), pages 69-96, November.
  2. 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.
  3. Harrison, J. Michael & Kreps, David M., 1979. "Martingales and arbitrage in multiperiod securities markets," Journal of Economic Theory, Elsevier, Elsevier, vol. 20(3), pages 381-408, June.
  4. Robert Jarrow & Dilip Madan, 1995. "Option Pricing Using The Term Structure Of Interest Rates To Hedge Systematic Discontinuities In Asset Returns," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 5(4), pages 311-336.
  5. Hull, John & White, Alan, 1990. "Pricing Interest-Rate-Derivative Securities," Review of Financial Studies, Society for Financial Studies, Society for Financial Studies, vol. 3(4), pages 573-92.
  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. Robert Jarrow & Dilip B. Madan, 1999. "Hedging contingent claims on semimartingales," Finance and Stochastics, Springer, Springer, vol. 3(1), pages 111-134.
  8. Ho, Thomas S Y & Lee, Sang-bin, 1986. " Term Structure Movements and Pricing Interest Rate Contingent Claims," Journal of Finance, American Finance Association, American Finance Association, vol. 41(5), pages 1011-29, December.
  9. Harrison, J. Michael & Pliska, Stanley R., 1981. "Martingales and stochastic integrals in the theory of continuous trading," Stochastic Processes and their Applications, Elsevier, Elsevier, vol. 11(3), pages 215-260, August.
  10. Lina El-Jahel & Hans Lindberg & William Perraudin, 1996. "Yield Curves with Jump Short Rates," Archive Working Papers, Birkbeck, Department of Economics, Mathematics & Statistics 023, Birkbeck, Department of Economics, Mathematics & Statistics.
  11. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, Elsevier, vol. 5(2), pages 177-188, November.
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Citations

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Cited by:
  1. Schönbucher, Philipp J., 1996. "The Term Structure of Defaultable Bond Prices," Discussion Paper Serie B, University of Bonn, Germany 384, University of Bonn, Germany.
  2. C. Mancini, 2002. "The European options hedge perfectly in a Poisson-Gaussian stock market model," Applied Mathematical Finance, Taylor & Francis Journals, Taylor & Francis Journals, vol. 9(2), pages 87-102.
  3. Vilimir Yordanov, 2012. "The Bulgarian Foreign and Domestic Debt – A No-Arbitrage Macrofinancial View," William Davidson Institute Working Papers Series, William Davidson Institute at the University of Michigan wp1032, William Davidson Institute at the University of Michigan.

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