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A Comparison Of Delta Hedging Under Two Price Distribution Assumptions By Likelihood Ratio

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  • Lingyan Cao
  • Zheng-Feng Guo

Abstract

This paper compares net profits from delta hedging through the Delta of a European call option, by assuming underlying stock prices follows a geometric Brownian motion (GBM) or a Variance-Gamma (VG) process. We employ the maximum likelihood estimation method to estimate corresponding parameters for each process. A Monte Carlo simulation is conducted to simulate spot prices and option prices and a likelihood ratio (LR) method is used to estimate the Delta of the call option over different sample paths. We then implement a dynamic delta hedging strategy through the simulated spot prices, option prices and Delta at different hedging frequencies. Finally, we compare net profits calculated from hedging corresponding to a GBM or a VG process.

Suggested Citation

  • Lingyan Cao & Zheng-Feng Guo, 2012. "A Comparison Of Delta Hedging Under Two Price Distribution Assumptions By Likelihood Ratio," The International Journal of Business and Finance Research, The Institute for Business and Finance Research, vol. 6(1), pages 25-34.
    • Handle: RePEc:ibf:ijbfre:v:6:y:2012:i:1:p:25-34
    as

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    References listed on IDEAS

    as
    1. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
    2. 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.
    3. Mark Broadie & Paul Glasserman, 1996. "Estimating Security Price Derivatives Using Simulation," Management Science, INFORMS, vol. 42(2), pages 269-285, February.
    4. 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.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    likelihood ratio; Variance-Gamma; geometric Brownian motion; delta hedging;
    All these keywords.

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • G15 - Financial Economics - - General Financial Markets - - - International Financial Markets
    • G17 - Financial Economics - - General Financial Markets - - - Financial Forecasting and Simulation

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