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Simplified Hedge For Path-Dependent Derivatives

Author

Listed:
  • CAROLE BERNARD

    (Department of Accounting, Law and Finance, Grenoble Ecole de Management, 12 Rue Pierre Sémard, 38003 Grenoble, France)

  • JUNSEN TANG

    (Department of Statistics and Actuarial Science, University of Waterloo, 200 University Avenue West, Waterloo, ON, Canada N2L 3G1, Canada)

Abstract

Path-dependent derivatives are typically difficult to hedge. Traditional dynamic delta hedging does not perform well because of the difficulty to evaluate the Greeks and the high cost of constantly rebalancing. We propose to price and hedge path-dependent derivatives by constructing simplified alternatives that preserve certain distributional properties of their terminal payoffs, and that can be hedged by semi-static replication. The method is illustrated by a geometric Asian option and by a lookback option in the Black–Scholes setting, for which explicit forms of the simplified alternatives exist. Extensions to a Lévy market and to a Heston stochastic volatility model are discussed as well.

Suggested Citation

  • Carole Bernard & Junsen Tang, 2016. "Simplified Hedge For Path-Dependent Derivatives," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(07), pages 1-32, November.
    • Handle: RePEc:wsi:ijtafx:v:19:y:2016:i:07:n:s021902491650045x
    DOI: 10.1142/S021902491650045X
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    3. Carole Bernard & Steven Vanduffel & Jiang Ye, 2018. "Optimal Portfolio Under State-Dependent Expected Utility," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(03), pages 1-22, May.

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