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Replication and shortfall risk in a binomial model with transaction costs

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  • Barbara Trivellato

Abstract

The shortfall risk is defined as the optimal mean value of the terminal deficit produced by a self-financing portfolio whose initial value is smaller than what is required to replicate a contingent claim. In this paper we look for an explicit expression for it, as well as for the optimal strategy, when the market model is a binomial model with proportional transaction costs. We first study replication of European claims which satisfy suitable assumptions. We then investigate the shortfall minimization problem in a framework very similar to that without transaction costs. Copyright Springer-Verlag 2009

Suggested Citation

  • Barbara Trivellato, 2009. "Replication and shortfall risk in a binomial model with transaction costs," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 69(1), pages 1-26, March.
    • Handle: RePEc:spr:mathme:v:69:y:2009:i:1:p:1-26
    DOI: 10.1007/s00186-007-0208-3
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    References listed on IDEAS

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    1. 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(1), pages 117-138, March.
    2. Bernard Bensaid & Jean‐Philippe Lesne & Henri Pagès & José Scheinkman, 1992. "Derivative Asset Pricing With Transaction Costs1," Mathematical Finance, Wiley Blackwell, vol. 2(2), pages 63-86, April.
    3. Wolfgang J. Runggaldier & Anna Zaccaria, 2000. "A Stochastic Control Approach to Risk Management Under Restricted Information," Mathematical Finance, Wiley Blackwell, vol. 10(2), pages 277-288, April.
    4. Ken Palmer, 2001. "A Note on the Boyle–Vorst Discrete‐Time Option Pricing Model with Transactions Costs," Mathematical Finance, Wiley Blackwell, vol. 11(3), pages 357-363, July.
    5. 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.
    6. Gino Favero, 2001. "Shortfall risk minimization under model uncertainty in the binomial case: adaptive and robust approaches," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 53(3), pages 493-503, July.
    7. Gino Favero & Tiziano Vargiolu, 2006. "Shortfall risk minimising strategies in the binomial model: characterisation and convergence," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 64(2), pages 237-253, October.
    8. Boyle, Phelim P & Vorst, Ton, 1992. "Option Replication in Discrete Time with Transaction Costs," Journal of Finance, American Finance Association, vol. 47(1), pages 271-293, March.
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