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No-Arbitrage Pricing for Dividend-Paying Securities in Discrete-Time Markets with Transaction Costs

  • Tomasz R. Bielecki
  • Igor Cialenco
  • Rodrigo Rodriguez
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    We prove a version of First Fundamental Theorem of Asset Pricing under transaction costs for discrete-time markets with dividend-paying securities. Specifically, we show that the no-arbitrage condition under the efficient friction assumption is equivalent to the existence of a risk-neutral measure. We derive dual representations for the superhedging ask and subhedging bid price processes of a derivative contract. Our results are illustrated with a vanilla credit default swap contract.

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    Paper provided by in its series Papers with number 1205.6254.

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    Date of creation: May 2012
    Date of revision: Jun 2013
    Handle: RePEc:arx:papers:1205.6254
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    1. 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.
    2. repec:crs:wpaper:9513 is not listed on IDEAS
    3. J. Jacod & A.N. Shiryaev, 1998. "Local martingales and the fundamental asset pricing theorems in the discrete-time case," Finance and Stochastics, Springer, vol. 2(3), pages 259-273.
    4. Bouchard, Bruno & Touzi, Nizar, 2000. "Explicit Solution of the Multivariate Super-Replication Problem under Transaction Costs," Economics Papers from University Paris Dauphine 123456789/1533, Paris Dauphine University.
    5. Lépinette-Denis, Emmanuel & Kabanov, Yuri, 2012. "Consistent Price Systems and Arbitrage Opportunities of the Second Kind in Models with Transaction Costs," Economics Papers from University Paris Dauphine 123456789/4652, Paris Dauphine University.
    6. HuyËn Pham & Nizar Touzi & Jaksa Cvitanic, 1999. "A closed-form solution to the problem of super-replication under transaction costs," Finance and Stochastics, Springer, vol. 3(1), pages 35-54.
    7. 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.
    8. Dimitri De Vallière & Yuri Kabanov & Christophe Stricker, 2007. "No-arbitrage criteria for financial markets with transaction costs and incomplete information," Finance and Stochastics, Springer, vol. 11(2), pages 237-251, April.
    9. 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.
    10. Bouchard, Bruno, 2006. "No-arbitrage in discrete-time markets with proportional transaction costs and general information structure," Economics Papers from University Paris Dauphine 123456789/1850, Paris Dauphine University.
    11. repec:dau:papers:123456789/9714 is not listed on IDEAS
    12. Guasoni, Paolo & Lépinette-Denis, Emmanuel & Rásonyi, Miklós, 2012. "The fundamental theorem of asset pricing under transaction costs," Economics Papers from University Paris Dauphine 123456789/9300, Paris Dauphine University.
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