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Option pricing under non-normality: a comparative analysis

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  • Sharif Mozumder
  • Ghulam Sorwar
  • Kevin Dowd

Abstract

This paper carries out a comparative analysis of the calibration and performance of a variety of options pricing models. These include Black and Scholes (J Polit Econ 81:637–659, 1973 ), the Gram–Charlier (GC) approach of Backus et al. ( 1997 ), the stochastic volatility (HS) model of Heston (Rev Financ Stud 6:327–343, 1993 ), the closed-form GARCH process of Heston and Nandi (Rev Financ Stud 13:585–625, 2000 ) and a variety of Lévy processes including the Variance Gamma (VG), Normal Inverse Gaussian (NIG), and, CGMY and Kou (Manag Sci 48:1086–1101, 2002 ) jump-diffusion models. Unlike most studies of option pricing, we compare these models using a common point-in-time data which reflects the perspective of a new investor who wishes to choose between models using only the most minimal recent data set. For each of these models, we also examine the accuracy of delta and delta-gamma approximations to the valuation of both individual options and an illustrative option portfolio. Copyright Springer Science+Business Media, LLC 2013

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  • Sharif Mozumder & Ghulam Sorwar & Kevin Dowd, 2013. "Option pricing under non-normality: a comparative analysis," Review of Quantitative Finance and Accounting, Springer, vol. 40(2), pages 273-292, February.
    • Handle: RePEc:kap:rqfnac:v:40:y:2013:i:2:p:273-292
    DOI: 10.1007/s11156-011-0271-y
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    Cited by:

    1. Konstantinos Gkillas & Rangan Gupta & Mark E. Wohar, 2020. "Oil shocks and volatility jumps," Review of Quantitative Finance and Accounting, Springer, vol. 54(1), pages 247-272, January.
    2. Chen, Rongda & Zhou, Hanxian & Yu, Lean & Jin, Chenglu & Zhang, Shuonan, 2021. "An efficient method for pricing foreign currency options," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 74(C).
    3. Julien Azzaz & Stéphane Loisel & Pierre-E. Thérond, 2015. "Some characteristics of an equity security next-year impairment," Review of Quantitative Finance and Accounting, Springer, vol. 45(1), pages 111-135, July.
    4. Gong, Xiao-Li & Liu, Xi-Hua & Xiong, Xiong & Zhuang, Xin-Tian, 2018. "Modeling volatility dynamics using non-Gaussian stochastic volatility model based on band matrix routine," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 193-201.
    5. Leonidas S. Rompolis & Elias Tzavalis, 2017. "Retrieving risk neutral moments and expected quadratic variation from option prices," Review of Quantitative Finance and Accounting, Springer, vol. 48(4), pages 955-1002, May.
    6. Gong, Xiao-li & Zhuang, Xin-tian, 2016. "Option pricing and hedging for optimized Lévy driven stochastic volatility models," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 118-127.
    7. Konstantinos Skindilias & Chia Lo, 2015. "Local volatility calibration during turbulent periods," Review of Quantitative Finance and Accounting, Springer, vol. 44(3), pages 425-444, April.
    8. Fathi Abid & Bilel Kaffel, 2018. "The extent of virgin olive-oil prices’ distribution revealing the behavior of market speculators," Review of Quantitative Finance and Accounting, Springer, vol. 50(2), pages 561-590, February.
    9. Cheng-Few Lee & Oleg Sokolinskiy, 2015. "R-2GAM stochastic volatility model: flexibility and calibration," Review of Quantitative Finance and Accounting, Springer, vol. 45(3), pages 463-483, October.
    10. Hsuan-Chu Lin & Ren-Raw Chen & Oded Palmon, 2016. "Explaining the volatility smile: non-parametric versus parametric option models," Review of Quantitative Finance and Accounting, Springer, vol. 46(4), pages 907-935, May.
    11. Gong, Xiaoli & Zhuang, Xintian, 2016. "Option pricing for stochastic volatility model with infinite activity Lévy jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 455(C), pages 1-10.

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    More about this item

    Keywords

    GARCH pricing; Gram–Charlier pricing; Lévy pricing; Fast Fourier transform; C02;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics

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