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On the Generalized Brownian Motion and its Applications in Finance

Author

Listed:
  • Høg, Esben

    (Department of Business Studies, Aarhus School of Business)

  • Frederiksen, Per

    (Equity and Fund Linked Derivatives)

  • Schiemert, Daniel

    (Universität Stuttgart;)

Abstract
This paper deals with dynamic term structure models (DTSMs) and proposes a new way to handle the limitation of the classical affine models. In particular, the paper expands the exibility of the DTSMs by applying generalized Brownian motions with dependent increments as the governing force of the state variables instead of standard Brownian motions. This is a new direction in pricing non defaultable bonds. By extending the theory developed by Dippon & Schiemert (2006a), the paper developes a bond market with memory, and proves the absence of arbitrage. The framework is readily extendable to other markets or multi factors. As a complement the paper shows an example of how to derive the implied bond pricing parameters using the ordinary Kalman filter.

Suggested Citation

  • Høg, Esben & Frederiksen, Per & Schiemert, Daniel, 2008. "On the Generalized Brownian Motion and its Applications in Finance," Finance Research Group Working Papers F-2008-07, University of Aarhus, Aarhus School of Business, Department of Business Studies.
    • Handle: RePEc:hhb:aarbfi:2008-07
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    File URL: http://research.asb.dk/fbspretrieve/3516/F_2008_07.PDF
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    References listed on IDEAS

    as
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    9. Ang, Andrew & Bekaert, Geert, 2002. "Regime Switches in Interest Rates," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(2), pages 163-182, April.
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    13. repec:bla:jfinan:v:59:y:2004:i:1:p:227-260 is not listed on IDEAS
    14. Jefferson Duarte, 2004. "Evaluating an Alternative Risk Preference in Affine Term Structure Models," The Review of Financial Studies, Society for Financial Studies, vol. 17(2), pages 379-404.
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