Abstract
A model of a market driven by a fractional Brownian motion is considered. We apply stochastic dominance arguments to derive a lower bound and an upper bound on the price of European options in the presence of proportional transaction costs. A numerical example with the data drawn from the Russian options market is presented.
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References
Babajtsev, V.A., & Gisin, V.B. (2005). The arbitrage concept in the mathematical theory of the effective market. Finance Academy Bulletin, 2, 64–68.
Bender, C., Sottinen, T., & Valkeila, E. (2007). Arbitrage with fractional Brownian motion? Theory of Stochastic Processes 13(29), 1–2, 23–34.
Biagini, F., Hu, Y., Oksendal, B., & Zhang, T. (2008). Stochastic Calculus for Fractional Brownian Motion and Applications. London, England: Springer-Verlag London Limited.
Constantinides, G.M. (1979). Multiperiod consumption and investment behavior with convex transactions costs. Management Science, 25(11), 1127– 1137.
Constantinides, G.M., & Perrakis, S. (2002). Stochastic dominance bounds on derivatives prices in a multiperiod economy with proportional transaction costs. Journal of Economic Dynamics & Control, 26, 1323–1352.
Guasoni, P. (2006). No arbitrage under transaction costs, with fractional Brownian motion and beyond. Mathematical Finance, 16(3), 569–582.
Guasoni, P., & Rasonyi, M. (2008). The Fundamental Theorem of Asset Pricing under Transaction Costs, preprint.
Haritonov, V.V., & Ezhov, A.A. (2007). Econophysics. Moscow, Russia: MIPhI.
Kolmogorov, A.N. (1940). Wienershe Spiralen und einige andere interessante Kurven im Hilbertishen Raum. DAS of the USSR (Nat. Sciences), 26, 115–118.
Mandelbrot, B.B., & van Ness, J.W. (1968). Fractional Brownian motions, fractional noises and applications. SIAM Rev., 10, 422–437.
Mantegna, R.M., & Stanley H.E. (2000). An Introduction to Econophysics. – Correlations and Complexity in Finance. Cambridge, England: Cambridge University Press.
Markov, A.A. (2009). Some fractional properties of stock indices. Today and Tomorrow of Russian Economy, 30, 101–110.
Mishura, Y. (2008). Stochastic Calculus for Fractional Brownian Motion and Related Processes. Springer Lecture Notes in Mathematics, 1929, 393.
Norros, I., Valkeila, E., & Virtamo J. (1999). An elementary approach to a Girsanov formula and other analytical results on fractional Brownian motion. Bernoulli, 5, 571–587.
Rostek, S. (2009). Option Pricing in Fractional Brownian Markets. Berlin, Germany: Springer-Verlag Berlin Heidelberg.
Shiryaev, A.N. (1998). On arbitrage and replication for fractional models. MaPhySto, Department of Mathematical Sciences, Univ. of Aarhus. Research Reports, 20.
Sornette, D. (2003). How to predict crashes of the financial markets. oscow, Russia: Internet trading.
Sottinen, T. (2001). Fractional Brownian motion, random walks, and binary market models. Finance Stoch., 5, 343–355.
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Gisin, V., Markov, A. (2012). Asset Pricing in a Fractional Market Under Transaction Costs. In: Sornette, D., Ivliev, S., Woodard, H. (eds) Market Risk and Financial Markets Modeling. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27931-7_7
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DOI: https://doi.org/10.1007/978-3-642-27931-7_7
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