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On free lunches in random walk markets with short-sale constraints and small transaction costs, and weak convergence to Gaussian continuous-time processes

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  • Chr. Framstad, Nils

    ()
    (Dept. of Economics, University of Oslo)

Abstract

This paper considers a sequence of discrete-time random walk markets with a single risky asset, and gives conditions for the existence of arbitrage opportunities or free lunches with vanishing risk, of the form of waiting to buy and selling the next period, with no shorting, and furthermore for weak convergence of the random walk to a Gaussian continuous-time stochastic process. The conditions are given in terms of the kernel representation with respect to ordinary Brownian motion and the discretisation chosen. Arbitrage examples are established where the continuous analogue is arbitrage-free under small transaction costs – including for the semimartingale modifications of fractional Brownian motion suggested in the seminal Rogers (1997) article proving arbitrage in fBm models.

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File URL: https://www.sv.uio.no/econ/english/research/unpublished-works/working-papers/pdf-files/2011/Memo-20-2011.pdf
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Bibliographic Info

Paper provided by Oslo University, Department of Economics in its series Memorandum with number 20/2011.

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Length: 14 pages
Date of creation: 14 Sep 2011
Date of revision:
Handle: RePEc:hhs:osloec:2011_020

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Postal: Department of Economics, University of Oslo, P.O Box 1095 Blindern, N-0317 Oslo, Norway
Phone: 22 85 51 27
Fax: 22 85 50 35
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Web page: http://www.oekonomi.uio.no/indexe.html
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Related research

Keywords: Stock price model; random walk; Gaussian processes; weak convergence; free lunch with vanishing risk; arbitrage; transaction costs;

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  1. Tommi Sottinen, 2001. "Fractional Brownian motion, random walks and binary market models," Finance and Stochastics, Springer, vol. 5(3), pages 343-355.
  2. L. C. G. Rogers, 1997. "Arbitrage with Fractional Brownian Motion," Mathematical Finance, Wiley Blackwell, vol. 7(1), pages 95-105.
  3. Paolo Guasoni & Mikl\'os R\'asonyi & Walter Schachermayer, 2008. "Consistent price systems and face-lifting pricing under transaction costs," Papers 0803.4416, arXiv.org.
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