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Optimal hedging strategies for misspecified asset price models

Author

Listed:
  • Hyungsok Ahn
  • Adviti Muni
  • Glen Swindle

Abstract

The Black-Scholes option pricing methodology requires that the model for the price of the underlying asset be completely specified. Often the underlying price is taken to be a geometric Brownian motion with a constant, known volatility. In practice one does not know precise values of parameters such as the volatility, and estimates from historical prices or implied volatilities must be used instead. In this paper optimal hedging strategies are constructed when the volatility of the asset price is misspecified. Optimality refers to maximizing the utility of the investor in a worst-case volatility scenario.

Suggested Citation

  • Hyungsok Ahn & Adviti Muni & Glen Swindle, 1999. "Optimal hedging strategies for misspecified asset price models," Applied Mathematical Finance, Taylor & Francis Journals, vol. 6(3), pages 197-208.
    • Handle: RePEc:taf:apmtfi:v:6:y:1999:i:3:p:197-208
    DOI: 10.1080/135048699334537
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    References listed on IDEAS

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    1. M. Avellaneda & A. Levy & A. ParAS, 1995. "Pricing and hedging derivative securities in markets with uncertain volatilities," Applied Mathematical Finance, Taylor & Francis Journals, vol. 2(2), pages 73-88.
    2. Harrison, J. Michael & Pliska, Stanley R., 1981. "Martingales and stochastic integrals in the theory of continuous trading," Stochastic Processes and their Applications, Elsevier, vol. 11(3), pages 215-260, August.
    3. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
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    Cited by:

    1. Revaz Tevzadze & Teimuraz Toronjadze & Tamaz Uzunashvili, 2013. "Robust utility maximization for a diffusion market model with misspecified coefficients," Finance and Stochastics, Springer, vol. 17(3), pages 535-563, July.
    2. Sebastian Herrmann & Johannes Muhle-Karbe, 2017. "Model uncertainty, recalibration, and the emergence of delta–vega hedging," Finance and Stochastics, Springer, vol. 21(4), pages 873-930, October.
    3. Sebastian Herrmann & Johannes Muhle-Karbe & Frank Thomas Seifried, 2017. "Hedging with small uncertainty aversion," Finance and Stochastics, Springer, vol. 21(1), pages 1-64, January.

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