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Optimal hedging in an extended binomial market under transaction costs

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  • Norman Josephy
  • Lucia Kimball
  • Victoria Steblovskaya

Abstract

We develop an approach to optimal hedging of a contingent claim under proportional transaction costs in a discrete time financial market model which extends the binomial market model with transaction costs. Our model relaxes the binomial assumption on the stock price ratios to the case where the stock price ratio distribution has bounded support. Non-self-financing hedging strategies are studied to construct an optimal hedge for an investor who takes a short position in a European contingent claim settled by delivery. We develop the theoretical basis for our optimal hedging approach, extending results obtained in our previous work. Specifically, we derive a no-arbitrage option price interval and establish properties of the non-self-financing strategies and their residuals. Based on the theoretical foundation, we develop a computational algorithm for optimizing an investor relevant criterion over the set of admissible non-self-financing hedging strategies. We demonstrate the applicability of our approach using both simulated data and real market data.

Suggested Citation

  • Norman Josephy & Lucia Kimball & Victoria Steblovskaya, 2016. "Optimal hedging in an extended binomial market under transaction costs," Quantitative Finance, Taylor & Francis Journals, vol. 16(5), pages 763-776, May.
    • Handle: RePEc:taf:quantf:v:16:y:2016:i:5:p:763-776
    DOI: 10.1080/14697688.2015.1039225
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    References listed on IDEAS

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    1. 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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    1. Norman Josephy & Lucia Kimball & Victoria Steblovskaya, 2017. "On The Numerical Aspects Of Optimal Option Hedging With Transaction Costs," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(01), pages 1-22, February.

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