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The fundamental theorem of asset pricing under proportional transaction costs

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  • Alet Roux
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    Abstract

    We extend the fundamental theorem of asset pricing to a model where the risky stock is subject to proportional transaction costs in the form of bid-ask spreads and the bank account has different interest rates for borrowing and lending. We show that such a model is free of arbitrage if and only if one can embed in it a friction-free model that is itself free of arbitrage, in the sense that there exists an artificial friction-free price for the stock between its bid and ask prices and an artificial interest rate between the borrowing and lending interest rates such that, if one discounts this stock price by this interest rate, then the resulting process is a martingale under some non-degenerate probability measure. Restricting ourselves to the simple case of a finite number of time steps and a finite number of possible outcomes for the stock price, the proof follows by combining classical arguments based on finite-dimensional separation theorems with duality results from linear optimisation.

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    File URL: http://arxiv.org/pdf/0710.2758
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 0710.2758.

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    Date of creation: Oct 2007
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    Handle: RePEc:arx:papers:0710.2758

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    1. Jouini, Elyès, 2000. "Price functionals with bid–ask spreads : an axiomatic approach," Open Access publications from Université Paris-Dauphine urn:hdl:123456789/5599, Université Paris-Dauphine.
    2. He, Hua & Pages, Henri F, 1993. "Labor Income, Borrowing Constraints, and Equilibrium Asset Prices," Economic Theory, Springer, vol. 3(4), pages 663-96, October.
    3. (**), Christophe Stricker & (*), Miklós Rásonyi & Yuri Kabanov, 2002. "No-arbitrage criteria for financial markets with efficient friction," Finance and Stochastics, Springer, vol. 6(3), pages 371-382.
    4. Shunming Zhang & Chunlei Xu & Xiaotie Deng, 2002. "Dynamic Arbitrage-Free Asset Pricing with Proportional Transaction Costs," Mathematical Finance, Wiley Blackwell, vol. 12(1), pages 89-97.
    5. repec:fth:inseep:9513 is not listed on IDEAS
    6. Nicole El Karoui & Monique Jeanblanc-Picqué, 1998. "Optimization of consumption with labor income," Finance and Stochastics, Springer, vol. 2(4), pages 409-440.
    7. A. Bensoussan & H. Julien, 2000. "On the Pricing of Contingent Claims with Frictions," Mathematical Finance, Wiley Blackwell, vol. 10(2), pages 89-108.
    8. Napp, Clotilde, 2001. "Pricing issues with investment flows Applications to market models with frictions," Journal of Mathematical Economics, Elsevier, vol. 35(3), pages 383-408, June.
    9. Perrakis, Stylianos & Lefoll, Jean, 2000. "Option pricing and replication with transaction costs and dividends," Journal of Economic Dynamics and Control, Elsevier, vol. 24(11-12), pages 1527-1561, October.
    10. Igor V. Evstigneev & Klaus Schürger & Michael I. Taksar, 2002. "On the fundamental theorem of asset pricing: random constraints and bang-bang no-arbitrage criteria," Bonn Econ Discussion Papers bgse24_2002, University of Bonn, Germany.
    11. Tepla, Lucie, 2000. "Optimal portfolio policies with borrowing and shortsale constraints," Journal of Economic Dynamics and Control, Elsevier, vol. 24(11-12), pages 1623-1639, October.
    12. Napp, C., 2003. "The Dalang-Morton-Willinger theorem under cone constraints," Journal of Mathematical Economics, Elsevier, vol. 39(1-2), pages 111-126, February.
    13. M. Dempster & I. Evstigneev & M. Taksar, 2006. "Asset Pricing and Hedging in Financial Markets with Transaction Costs: An Approach Based on the Von Neumann–Gale Model," Annals of Finance, Springer, vol. 2(4), pages 327-355, October.
    14. Roy Kouwenberg & Jacek Gondzio & Ton Vorst, 1999. "Hedging Options under Transaction Costs and Stochastic Volatility," Computing in Economics and Finance 1999 911, Society for Computational Economics.
    15. Alexander Melnikov & Yury Petrachenko, 2005. "On option pricing in binomial market with transaction costs," Finance and Stochastics, Springer, vol. 9(1), pages 141-149, January.
    16. Lukasz Stettner, 2000. "Option Pricing in Discrete-Time Incomplete Market Models," Mathematical Finance, Wiley Blackwell, vol. 10(2), pages 305-321.
    17. Harrison, J. Michael & Pliska, Stanley R., 1981. "Martingales and stochastic integrals in the theory of continuous trading," Stochastic Processes and their Applications, Elsevier, vol. 11(3), pages 215-260, August.
    18. (*), Thaleia Zariphopoulou & George M. Constantinides, 1999. "Bounds on prices of contingent claims in an intertemporal economy with proportional transaction costs and general preferences," Finance and Stochastics, Springer, vol. 3(3), pages 345-369.
    19. Leland, Hayne E, 1985. " Option Pricing and Replication with Transactions Costs," Journal of Finance, American Finance Association, vol. 40(5), pages 1283-1301, December.
    20. Freddy Delbaen & Yuri M. Kabanov & Esko Valkeila, 2002. "Hedging under Transaction Costs in Currency Markets: a Discrete-Time Model," Mathematical Finance, Wiley Blackwell, vol. 12(1), pages 45-61.
    21. Kabanov, Yu. M. & Stricker, Ch., 2001. "The Harrison-Pliska arbitrage pricing theorem under transaction costs," Journal of Mathematical Economics, Elsevier, vol. 35(2), pages 185-196, April.
    22. Edirisinghe, Chanaka & Naik, Vasanttilak & Uppal, Raman, 1993. "Optimal Replication of Options with Transactions Costs and Trading Restrictions," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 28(01), pages 117-138, March.
    23. repec:fth:inseep:9514 is not listed on IDEAS
    24. Ioannis Karatzas & (*), S. G. Kou, 1998. "Hedging American contingent claims with constrained portfolios," Finance and Stochastics, Springer, vol. 2(3), pages 215-258.
    25. Albanese, Claudio & Tompaidis, Stathis, 2008. "Small transaction cost asymptotics and dynamic hedging," European Journal of Operational Research, Elsevier, vol. 185(3), pages 1404-1414, March.
    26. Bernard Bensaid & Jean-Philippe Lesne & Henri Pagès & José Scheinkman, 1992. "Derivative Asset Pricing With Transaction Costs," Mathematical Finance, Wiley Blackwell, vol. 2(2), pages 63-86.
    27. Pham, Huyen & Touzi, Nizar, 1999. "The fundamental theorem of asset pricing with cone constraints," Journal of Mathematical Economics, Elsevier, vol. 31(2), pages 265-279, March.
    28. Perrakis, Stylianos & Lefoll, Jean, 1997. "Derivative Asset Pricing with Transaction Costs: An Extension," Computational Economics, Society for Computational Economics, vol. 10(4), pages 359-76, November.
    29. Cuoco, Domenico, 1997. "Optimal Consumption and Equilibrium Prices with Portfolio Constraints and Stochastic Income," Journal of Economic Theory, Elsevier, vol. 72(1), pages 33-73, January.
    30. Jérˆme Detemple & Marcel Rindisbacher, 2005. "Closed-Form Solutions For Optimal Portfolio Selection With Stochastic Interest Rate And Investment Constraints," Mathematical Finance, Wiley Blackwell, vol. 15(4), pages 539-568.
    31. Boyle, Phelim P & Vorst, Ton, 1992. " Option Replication in Discrete Time with Transaction Costs," Journal of Finance, American Finance Association, vol. 47(1), pages 271-93, March.
    32. Perrakis, Stylianos & Lefoll, Jean, 2004. "The American put under transactions costs," Journal of Economic Dynamics and Control, Elsevier, vol. 28(5), pages 915-935, February.
    33. Laurence Carassus & Elyès Jouini, 1998. "Investment and Arbitrage Opportunities with Short Sales Constraints," Mathematical Finance, Wiley Blackwell, vol. 8(3), pages 169-178.
    34. Jouini Elyes & Kallal Hedi, 1995. "Martingales and Arbitrage in Securities Markets with Transaction Costs," Journal of Economic Theory, Elsevier, vol. 66(1), pages 178-197, June.
    35. Elyégs Jouini & Hédi Kallal, 1995. "Arbitrage In Securities Markets With Short-Sales Constraints," Mathematical Finance, Wiley Blackwell, vol. 5(3), pages 197-232.
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