IDEAS home Printed from https://ideas.repec.org/a/kap/rqfnac/v40y2013i2p273-292.html
   My bibliography  Save this article

Option pricing under non-normality: a comparative analysis

Author

Listed:
  • 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

Suggested Citation

  • 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
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s11156-011-0271-y
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s11156-011-0271-y?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Jow-Ran Chang & Mao-Wei Hung & Cheng Few Lee & Hsin-Min Lu, 2020. "The Jump Behavior of a Foreign Exchange Market: Analysis of the Thai Baht," World Scientific Book Chapters, in: Cheng Few Lee & John C Lee (ed.), HANDBOOK OF FINANCIAL ECONOMETRICS, MATHEMATICS, STATISTICS, AND MACHINE LEARNING, chapter 52, pages 1943-1968, World Scientific Publishing Co. Pte. Ltd..
    2. S. G. Kou, 2002. "A Jump-Diffusion Model for Option Pricing," Management Science, INFORMS, vol. 48(8), pages 1086-1101, August.
    3. Ren Raw Chen & Cheng Few Lee & Han-Hsing Lee, 2020. "Empirical Performance of the Constant Elasticity Variance Option Pricing Model," World Scientific Book Chapters, in: Cheng Few Lee & John C Lee (ed.), HANDBOOK OF FINANCIAL ECONOMETRICS, MATHEMATICS, STATISTICS, AND MACHINE LEARNING, chapter 51, pages 1903-1942, World Scientific Publishing Co. Pte. Ltd..
    4. Travis Sapp, 2009. "Estimating continuous-time stochastic volatility models of the short-term interest rate: a comparison of the generalized method of moments and the Kalman filter," Review of Quantitative Finance and Accounting, Springer, vol. 33(4), pages 303-326, November.
    5. Christoffersen, Peter, 2011. "Elements of Financial Risk Management," Elsevier Monographs, Elsevier, edition 2, number 9780123744487.
    6. Bakshi, Gurdip & Cao, Charles & Chen, Zhiwu, 1997. "Empirical Performance of Alternative Option Pricing Models," Journal of Finance, American Finance Association, vol. 52(5), pages 2003-2049, December.
    7. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 5, pages 129-164, World Scientific Publishing Co. Pte. Ltd..
    8. Lakshman Alles & Louis Murray, 2010. "Non-Normality and Risk in Developing Asian Markets," Review of Pacific Basin Financial Markets and Policies (RPBFMP), World Scientific Publishing Co. Pte. Ltd., vol. 13(04), pages 583-605.
    9. Ravinder Kumar Arora & Himadri Das & Pramod Kumar Jain, 2009. "Stock Returns and Volatility: Evidence from Select Emerging Markets," Review of Pacific Basin Financial Markets and Policies (RPBFMP), World Scientific Publishing Co. Pte. Ltd., vol. 12(04), pages 567-592.
    10. 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.
    11. 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.
    12. Geman, Helyette, 2002. "Pure jump Levy processes for asset price modelling," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1297-1316, July.
    13. Heston, Steven L & Nandi, Saikat, 2000. "A Closed-Form GARCH Option Valuation Model," The Review of Financial Studies, Society for Financial Studies, vol. 13(3), pages 585-625.
    14. 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.
    15. Dimitris Psychoyios & George Dotsis & Raphael Markellos, 2010. "A jump diffusion model for VIX volatility options and futures," Review of Quantitative Finance and Accounting, Springer, vol. 35(3), pages 245-269, October.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    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. 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.
    4. 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.
    5. 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.
    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. 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.
    9. 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.
    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, 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Mozumder, Sharif & Dempsey, Michael & Kabir, M. Humayun & Choudhry, Taufiq, 2016. "An improved framework for approximating option prices with application to option portfolio hedging," Economic Modelling, Elsevier, vol. 59(C), pages 285-296.
    2. Sharif Mozumder & Taufiq Choudhry & Michael Dempsey, 2021. "Option Pricing Model Biases: Bayesian and Markov Chain Monte Carlo Regression Analysis," Computational Economics, Springer;Society for Computational Economics, vol. 57(4), pages 1287-1305, April.
    3. Sharif Mozumder & Bakhtear Talukdar & M. Humayun Kabir & Bingxin Li, 2024. "Non-linear volatility with normal inverse Gaussian innovations: ad-hoc analytic option pricing," Review of Quantitative Finance and Accounting, Springer, vol. 62(1), pages 97-133, January.
    4. Lim, Terence & Lo, Andrew W. & Merton, Robert C. & Scholes, Myron S., 2006. "The Derivatives Sourcebook," Foundations and Trends(R) in Finance, now publishers, vol. 1(5–6), pages 365-572, April.
    5. Kozarski, R., 2013. "Pricing and hedging in the VIX derivative market," Other publications TiSEM 221fefe0-241e-4914-b6bd-c, Tilburg University, School of Economics and Management.
    6. Cheng Few Lee & Yibing Chen & John Lee, 2020. "Alternative Methods to Derive Option Pricing Models: Review and Comparison," World Scientific Book Chapters, in: Cheng Few Lee & John C Lee (ed.), HANDBOOK OF FINANCIAL ECONOMETRICS, MATHEMATICS, STATISTICS, AND MACHINE LEARNING, chapter 102, pages 3573-3617, World Scientific Publishing Co. Pte. Ltd..
    7. Carr, Peter & Wu, Liuren, 2004. "Time-changed Levy processes and option pricing," Journal of Financial Economics, Elsevier, vol. 71(1), pages 113-141, January.
    8. Diep Duong & Norman R. Swanson, 2011. "Volatility in Discrete and Continuous Time Models: A Survey with New Evidence on Large and Small Jumps," Departmental Working Papers 201117, Rutgers University, Department of Economics.
    9. Mark Broadie & Jerome B. Detemple, 2004. "ANNIVERSARY ARTICLE: Option Pricing: Valuation Models and Applications," Management Science, INFORMS, vol. 50(9), pages 1145-1177, September.
    10. Leunga Njike, Charles Guy & Hainaut, Donatien, 2024. "Affine Heston model style with self-exciting jumps and long memory," LIDAM Discussion Papers ISBA 2024001, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    11. Geman, Hélyette, 2005. "From measure changes to time changes in asset pricing," Journal of Banking & Finance, Elsevier, vol. 29(11), pages 2701-2722, November.
    12. Ying Chang & Yiming Wang & Sumei Zhang, 2021. "Option Pricing under Double Heston Jump-Diffusion Model with Approximative Fractional Stochastic Volatility," Mathematics, MDPI, vol. 9(2), pages 1-10, January.
    13. Corsaro, Stefania & Kyriakou, Ioannis & Marazzina, Daniele & Marino, Zelda, 2019. "A general framework for pricing Asian options under stochastic volatility on parallel architectures," European Journal of Operational Research, Elsevier, vol. 272(3), pages 1082-1095.
    14. Gonçalo Faria & João Correia-da-Silva, 2014. "A closed-form solution for options with ambiguity about stochastic volatility," Review of Derivatives Research, Springer, vol. 17(2), pages 125-159, July.
    15. Carverhill, Andrew & Luo, Dan, 2023. "A Bayesian analysis of time-varying jump risk in S&P 500 returns and options," Journal of Financial Markets, Elsevier, vol. 64(C).
    16. Bin Xie & Weiping Li & Nan Liang, 2021. "Pricing S&P 500 Index Options with L\'evy Jumps," Papers 2111.10033, arXiv.org, revised Nov 2021.
    17. Khaled Salhi, 2017. "Pricing European options and risk measurement under exponential Lévy models — a practical guide," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 4(02n03), pages 1-36, June.
    18. Alberto Bueno-Guerrero & Steven P. Clark, 2023. "Option Pricing under a Generalized Black–Scholes Model with Stochastic Interest Rates, Stochastic Strings, and Lévy Jumps," Mathematics, MDPI, vol. 12(1), pages 1-39, December.
    19. Yan Qu & Angelos Dassios & Hongbiao Zhao, 2023. "Shot-noise cojumps: Exact simulation and option pricing," Journal of the Operational Research Society, Taylor & Francis Journals, vol. 74(3), pages 647-665, March.
    20. Ciprian Necula, 2008. "Asset Pricing in a Two-Country Discontinuous General Equilibrium Model," Advances in Economic and Financial Research - DOFIN Working Paper Series 24, Bucharest University of Economics, Center for Advanced Research in Finance and Banking - CARFIB.

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:kap:rqfnac:v:40:y:2013:i:2:p:273-292. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.