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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: http://www.bbk.ac.uk/ems/research/wp/PDF/BWPEF0508.pdf
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    References listed on IDEAS

    as
    1. 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.
    2. Carr, Peter & Wu, Liuren, 2004. "Time-changed Levy processes and option pricing," Journal of Financial Economics, Elsevier, vol. 71(1), pages 113-141, January.
    3. 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.
    4. S. G. Kou, 2002. "A Jump-Diffusion Model for Option Pricing," Management Science, INFORMS, vol. 48(8), pages 1086-1101, August.
    5. Peter Carr & Liuren Wu, 2003. "The Finite Moment Log Stable Process and Option Pricing," Journal of Finance, American Finance Association, vol. 58(2), pages 753-778, April.
    6. repec:wsi:ijtafx:v:03:y:2000:i:01:n:s0219024900000073 is not listed on IDEAS
    7. 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.
    8. 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. 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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