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Link-save trading and pricing of contingent claims

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Author Info

  • Katsiaryna Kaval

    (University of Glasgow)

  • Ilya Molchanov

    (University of Bern)

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    Abstract

    Transaction costs involved while trading several assets may be described using bid-ask spread of the asset prices. We assume that the prices of several assets may be linked, so that transactions involving several assets have prices that are not necessarily equal to the sums of (bid or ask) prices of the individual assets. The family of possible price combinations forms a convex (random) set which changes in time and is called the set-valued price process. It is shown that the necessary and sufficient condition for no arbitrage is the existence of a martingale selection, i.e. a martingale that takes values in the set-valued price process. Examples and applications to option pricing are discussed.

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    File URL: http://128.118.178.162/eps/fin/papers/0511/0511017.pdf
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    Bibliographic Info

    Paper provided by EconWPA in its series Finance with number 0511017.

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    Length: 26 pages
    Date of creation: 29 Nov 2005
    Date of revision:
    Handle: RePEc:wpa:wuwpfi:0511017

    Note: Type of Document - pdf; pages: 26
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    Web page: http://128.118.178.162

    Related research

    Keywords: bid-ask spread; multiple assets; price process; set-valued process; transaction costs;

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    References

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    1. 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.
    2. 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.
    3. repec:fth:inseep:9513 is not listed on IDEAS
    4. Elyès Jouini, 1997. "Price Functionals with Bid-Ask Spreads : An Axiomatic Approach," Working Papers 97-05, Centre de Recherche en Economie et Statistique.
    5. Y.M. Kabanov, 1999. "Hedging and liquidation under transaction costs in currency markets," Finance and Stochastics, Springer, vol. 3(2), pages 237-248.
    6. Kallal, Hedi & Jouini, Elyès, 1995. "Martingales and arbitrage in securities markets with transaction costs," Economics Papers from University Paris Dauphine 123456789/5630, Paris Dauphine University.
    7. 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.
    8. M. Avellaneda & A. Levy & A. ParAS, 1995. "Pricing and hedging derivative securities in markets with uncertain volatilities," Applied Mathematical Finance, Taylor & Francis Journals, vol. 2(2), pages 73-88.
    9. Hess, Christian, 1991. "On multivalued martingales whose values may be unbounded: martingale selectors and mosco convergence," Journal of Multivariate Analysis, Elsevier, vol. 39(1), pages 175-201, October.
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