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On arbitrage and Markovian short rates in fractional bond markets

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  • Gapeev, Pavel V.

Abstract

We study a bond market model and related term structure of interest rates driven by a fractional Brownian motion with self-similarity parameter H[set membership, variant](1/2,1). We present a criterion on the deterministic forward rate volatility under which the short rate process is Markovian and construct an admissible self-financing portfolio realizing an arbitrage opportunity.

Suggested Citation

  • Gapeev, Pavel V., 2004. "On arbitrage and Markovian short rates in fractional bond markets," Statistics & Probability Letters, Elsevier, vol. 70(3), pages 211-222, December.
  • Handle: RePEc:eee:stapro:v:70:y:2004:i:3:p:211-222
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    References listed on IDEAS

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    1. Sottinen Tommi & Valkeila Esko, 2003. "On arbitrage and replication in the fractional Black–Scholes pricing model," Statistics & Risk Modeling, De Gruyter, vol. 21(2/2003), pages 93-108, February.
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    6. Gapeev, Pavel V. & Küchler, Uwe, 2003. "On Markovian Short Rates in Term Structure Models Driven by Jump-Diffusion Processes," SFB 373 Discussion Papers 2003,44, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    7. David Heath & Robert Jarrow & Andrew Morton, 2008. "Bond Pricing And The Term Structure Of Interest Rates: A New Methodology For Contingent Claims Valuation," World Scientific Book Chapters,in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 13, pages 277-305 World Scientific Publishing Co. Pte. Ltd..
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    9. Küchler, Uwe & Naumann, Eva, 2003. "Markovian short rates in a forward rate model with a general class of Lévy processes," SFB 373 Discussion Papers 2003,6, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
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    11. Andrew Carverhill, 1994. "When Is The Short Rate Markovian?," Mathematical Finance, Wiley Blackwell, vol. 4(4), pages 305-312.
    12. Le Breton, Alain, 1998. "Filtering and parameter estimation in a simple linear system driven by a fractional Brownian motion," Statistics & Probability Letters, Elsevier, vol. 38(3), pages 263-274, June.
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