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Efficient Hedging Of Path–Dependent Options

Author

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  • ADAM W. KOLKIEWICZ

    (Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, Canada)

Abstract

In this paper, we propose a novel method of hedging path-dependent options in a discrete-time setup. Assuming that prices are given by the Black–Scholes model, we first describe the residual risk when hedging a path-dependent option using only an European option. Then, for a fixed hedging interval, we find the hedging option that minimizes the shortfall risk, which we define as the expectation of the shortfall weighted by some loss function. We illustrate the method using Asian options, but the methodology is applicable to other path-dependent contacts.

Suggested Citation

  • Adam W. Kolkiewicz, 2016. "Efficient Hedging Of Path–Dependent Options," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(05), pages 1-27, August.
    • Handle: RePEc:wsi:ijtafx:v:19:y:2016:i:05:n:s0219024916500321
    DOI: 10.1142/S0219024916500321
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    References listed on IDEAS

    as
    1. Hans FÃllmer & Peter Leukert, 2000. "Efficient hedging: Cost versus shortfall risk," Finance and Stochastics, Springer, vol. 4(2), pages 117-146.
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    3. Breeden, Douglas T & Litzenberger, Robert H, 1978. "Prices of State-contingent Claims Implicit in Option Prices," The Journal of Business, University of Chicago Press, vol. 51(4), pages 621-651, October.
    4. Ilhan, Aytaç & Jonsson, Mattias & Sircar, Ronnie, 2009. "Optimal static-dynamic hedges for exotic options under convex risk measures," Stochastic Processes and their Applications, Elsevier, vol. 119(10), pages 3608-3632, October.
    5. Föllmer, H. & Schweizer, M., 1988. "Hedging by Sequential Regression: An Introduction to the Mathematics of Option Trading," ASTIN Bulletin, Cambridge University Press, vol. 18(2), pages 147-160, November.
    6. Paul Glasserman & Philip Heidelberger & Perwez Shahabuddin, 1999. "Asymptotically Optimal Importance Sampling and Stratification for Pricing Path‐Dependent Options," Mathematical Finance, Wiley Blackwell, vol. 9(2), pages 117-152, April.
    7. Akihiko Takahashi & Akira Yamazaki, 2009. "Efficient static replication of European options under exponential Lévy models," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 29(1), pages 1-15, January.
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