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

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Author Info
Alvaro Cartea (School of Economics, Mathematics & Statistics, Birkbeck)

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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.

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File URL: http://www.ems.bbk.ac.uk/research/wp/PDF/BWPEF0508.pdf
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File Function: First version, 2005
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Paper provided by Birkbeck, School of Economics, Mathematics & Statistics in its series Birkbeck Working Papers in Economics and Finance with number 0508.

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Date of creation: May 2005
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Handle: RePEc:bbk:bbkefp:0508

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This paper has been announced in the following NEP Reports: References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Peter Carr & Liuren Wu, 2002. "The Finite Moment Log Stable Process and Option Pricing," Finance 0207012, EconWPA. [Downloadable!]
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  2. Peter Carr & Liuren Wu, 2002. "Time-Changed Levy Processes and Option Pricing," Finance 0207011, EconWPA. [Downloadable!]
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  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. [Downloadable!]
  4. Peter Carr & Liuren Wu, 2002. "What Type of Process Underlies Options? A Simple Robust Test," Finance 0207019, EconWPA. [Downloadable!]
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  5. Peter Carr & Helyette Geman, 2002. "The Fine Structure of Asset Returns: An Empirical Investigation," Journal of Business, University of Chicago Press, vol. 75(2), pages 305-332, April. [Downloadable!]
  6. 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 637-54, May-June. [Downloadable!] (restricted)
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  1. Alvaro Cartea & Diego del-Castillo-Negrete, 2006. "Fractional Diffusion Models of Option Prices in Markets with Jumps," Birkbeck Working Papers in Economics and Finance 0604, Birkbeck, School of Economics, Mathematics & Statistics. [Downloadable!]
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