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Hedging Options with Transaction Costs

In: Stochastic Processes, Optimization, and Control Theory: Applications in Financial Engineering, Queueing Networks, and Manufacturing Systems

Author

Listed:
  • Wulin Suo

    (Queen’s University)

Abstract

This paper studies the optimal investment problem for an investor with a HARA type utility function. We assume the investor already has an option in her portfolio, and she will setup her invesment/hedging strategy using bonds and the underlying stock to maximize her utility. When there are transaction costs, the investor’s optimal investment/ hedging strategy can be described by three regions: the buying region, the selling region, and the no transaction region. When her portfolio falls in the buying (selling) region, she will buy (sell) enough shares of the stock to make her portfolio lie in the no transaction region (NT). When her portfolio falls in the NT region, it is optimal for the investor to make no transaction. We introduce the concept of a viscosity solution to describe the indirect utility function. A numerical scheme is proposed to compute the indirect utility function. This in turn enables the asking price for an option to be computed.

Suggested Citation

  • Wulin Suo, 2006. "Hedging Options with Transaction Costs," International Series in Operations Research & Management Science, in: Houmin Yan & George Yin & Qing Zhang (ed.), Stochastic Processes, Optimization, and Control Theory: Applications in Financial Engineering, Queueing Networks, and Manufacturing Systems, chapter 0, pages 223-247, Springer.
    • Handle: RePEc:spr:isochp:978-0-387-33815-6_12
    DOI: 10.1007/0-387-33815-2_12
    as

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