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Dynamic Hedging of Financial Instruments When the Underlying Follows a Non-Gaussian Process

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  • Alvaro Cartea

    (Department of Economics, Mathematics & Statistics, Birkbeck)

Abstract

Traditional dynamic hedging strategies are based on local information (ie Delta and Gamma) of the financial instruments to be hedged. We propose a new dynamic hedging strategy that employs non-local information and compare the profit and loss (P&L) resulting from hedging vanilla options when the classical approach of Delta- and Gammaneutrality is employed, to the results delivered by what we label Delta- and Fractional-Gamma-hedging. For specific cases, such as the FMLS of Carr and Wu (2003a) and Merton’s Jump-Diffusion model, the volatility of the P&L is considerably lower (in some cases only 25%) than that resulting from Delta- and Gamma-neutrality.

Suggested Citation

  • Alvaro Cartea, 2005. "Dynamic Hedging of Financial Instruments When the Underlying Follows a Non-Gaussian Process," Birkbeck Working Papers in Economics and Finance 0508, Birkbeck, Department of Economics, Mathematics & Statistics.
    • Handle: RePEc:bbk:bbkefp:0508
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    File URL: https://eprints.bbk.ac.uk/id/eprint/27035
    File Function: First version, 2005
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    References listed on IDEAS

    as
    1. S. G. Kou, 2002. "A Jump-Diffusion Model for Option Pricing," Management Science, INFORMS, vol. 48(8), pages 1086-1101, August.
    2. repec:bla:jfinan:v:58:y:2003:i:2:p:753-778 is not listed on IDEAS
    3. Peter Carr & Liuren Wu, 2003. "The Finite Moment Log Stable Process and Option Pricing," Journal of Finance, American Finance Association, vol. 58(2), pages 753-777, April.
    4. Carr, Peter & Wu, Liuren, 2004. "Time-changed Levy processes and option pricing," Journal of Financial Economics, Elsevier, vol. 71(1), pages 113-141, January.
    5. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    6. Andrew Matacz, 1997. "Financial modeling and option theory with the truncated Lévy process," Science & Finance (CFM) working paper archive 500035, Science & Finance, Capital Fund Management.
    7. Madan, Dilip B & Seneta, Eugene, 1990. "The Variance Gamma (V.G.) Model for Share Market Returns," The Journal of Business, University of Chicago Press, vol. 63(4), pages 511-524, October.
    8. Peter Carr & Liuren Wu, 2003. "What Type of Process Underlies Options? A Simple Robust Test," Journal of Finance, American Finance Association, vol. 58(6), pages 2581-2610, December.
    9. 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.
    10. Andrew Matacz, 2000. "Financial Modeling And Option Theory With The Truncated Levy Process," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 3(01), pages 143-160.
    11. Peter Carr & Helyette Geman, 2002. "The Fine Structure of Asset Returns: An Empirical Investigation," The Journal of Business, University of Chicago Press, vol. 75(2), pages 305-332, April.
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    Cited by:

    1. Cartea, Álvaro & del-Castillo-Negrete, Diego, 2007. "Fractional diffusion models of option prices in markets with jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 374(2), pages 749-763.

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