On arbitrage and Markovian short rates in fractional bond markets
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.
Volume (Year): 70 (2004)
Issue (Month): 3 (December)
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- 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.
- Ernst Eberlein & Sebastian Raible, 1999. "Term Structure Models Driven by General Lévy Processes," Mathematical Finance, Wiley Blackwell, vol. 9(1), pages 31-53.
- Tomas Björk & Yuri Kabanov & Wolfgang Runggaldier, 1997. "Bond Market Structure in the Presence of Marked Point Processes," Mathematical Finance, Wiley Blackwell, vol. 7(2), pages 211-239.
- Rimas Norvaisa, 2000. "Modelling of stock price changes: A real analysis approach," Finance and Stochastics, Springer, vol. 4(3), pages 343-369.
- Tommi Sottinen, 2001. "Fractional Brownian motion, random walks and binary market models," Finance and Stochastics, Springer, vol. 5(3), pages 343-355.
- 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.
- 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..
- Heath, David & Jarrow, Robert & Morton, Andrew, 1992. "Bond Pricing and the Term Structure of Interest Rates: A New Methodology for Contingent Claims Valuation," Econometrica, Econometric Society, vol. 60(1), pages 77-105, January.
- Andrew Carverhill, 1994. "When Is The Short Rate Markovian?," Mathematical Finance, Wiley Blackwell, vol. 4(4), pages 305-312.
- 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.
- L. C. G. Rogers, 1997. "Arbitrage with Fractional Brownian Motion," Mathematical Finance, Wiley Blackwell, vol. 7(1), pages 95-105.
- Salopek, D. M., 1998. "Tolerance to arbitrage," Stochastic Processes and their Applications, Elsevier, vol. 76(2), pages 217-230, August.
- 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.
- Giovanni Di Masi & Tomas Björk & Wolfgang Runggaldier & Yuri Kabanov, 1997. "Towards a general theory of bond markets (*)," Finance and Stochastics, Springer, vol. 1(2), pages 141-174.
- Björk, Tomas & di Masi, Giovanni & Kabanov, Yuri & Runggaldier, Wolfgang, 1996. "Towards a General Theory of Bond Markets," SSE/EFI Working Paper Series in Economics and Finance 143, Stockholm School of Economics.
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