IDEAS home Printed from https://ideas.repec.org/a/ibn/ijefaa/v8y2016i3p123-136.html
   My bibliography  Save this article

Empirical Performance of Black-Scholes and GARCH Option Pricing Models during Turbulent Times: The Indian Evidence

Author

Listed:
  • Aparna Bhat
  • Kirti Arekar

Abstract

Exchange-traded currency options are a recent innovation in the Indian financial market and their pricing is as yet unexplored. The objective of this research paper is to empirically compare the pricing performance of two well-known option pricing models ¨C the Black-Scholes-Merton Option Pricing Model (BSM) and Duan¡¯s NGARCH option pricing model ¨C for pricing exchange-traded currency options on the US dollar-Indian rupee during a recent turbulent period. The BSM is known to systematically misprice options on the same underlying asset but with different strike prices and maturities resulting in the phenomenon of the ¡®volatility smile¡¯. This bias of the BSM results from its assumption of a constant volatility over the option¡¯s life. The NGARCH option pricing model developed by Duan is an attempt to incorporate time-varying volatility in pricing options. It is a deterministic volatility model which has no closed-form solution and therefore requires numerical techniques for evaluation. In this paper we have compared the pricing performance and examined the pricing bias of both models during a recent period of volatility in the Indian foreign exchange market. Contrary to our expectations the pricing performance of the more sophisticated NGARCH pricing model is inferior to that of the relatively simple BSM model. However orthogonality tests demonstrate that the NGARCH model is free of the strike price and maturity biases associated with the BSM. We conclude that the deterministic BSM does a better job of pricing options than the more advanced time-varying volatility model based on GARCH.

Suggested Citation

  • Aparna Bhat & Kirti Arekar, 2016. "Empirical Performance of Black-Scholes and GARCH Option Pricing Models during Turbulent Times: The Indian Evidence," International Journal of Economics and Finance, Canadian Center of Science and Education, vol. 8(3), pages 123-136, March.
    • Handle: RePEc:ibn:ijefaa:v:8:y:2016:i:3:p:123-136
    as

    Download full text from publisher

    File URL: http://ccsenet.org/journal/index.php/ijef/article/view/55847/30783
    Download Restriction: no
    File URL: http://ccsenet.org/journal/index.php/ijef/article/view/55847
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Hung-Hsi Huang & Ching-Ping Wang & Shiau-Hung Chen, 2011. "Pricing Taiwan option market with GARCH and stochastic volatility," Applied Financial Economics, Taylor & Francis Journals, vol. 21(10), pages 747-754.
    2. Lehar, Alfred & Scheicher, Martin & Schittenkopf, Christian, 2002. "GARCH vs. stochastic volatility: Option pricing and risk management," Journal of Banking & Finance, Elsevier, vol. 26(2-3), pages 323-345, March.
    3. T. Harikumar & Maria E. de Boyrie & Simon J. Pak, 2004. "Evaluation of Black-Scholes and GARCH Models Using Currency Call Options Data," Review of Quantitative Finance and Accounting, Springer, vol. 23(4), pages 299-312, December.
    4. Jin-Chuan Duan & Jean-Guy Simonato, 1995. "Empirical Martingale Simulation for Asset Prices," CIRANO Working Papers 95s-43, CIRANO.
    5. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    6. Duan, Jin-Chuan & Zhang, Hua, 2001. "Pricing Hang Seng Index options around the Asian financial crisis - A GARCH approach," Journal of Banking & Finance, Elsevier, vol. 25(11), pages 1989-2014, November.
    7. Johnson, Herb & Shanno, David, 1987. "Option Pricing when the Variance Is Changing," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 22(2), pages 143-151, June.
    8. Haynes H. M. Yung & Hua Zhang, 2003. "An empirical investigation of the GARCH option pricing model: Hedging performance," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 23(12), pages 1191-1207, December.
    9. Jin-Chuan Duan & Jean-Guy Simonato, 1998. "Empirical Martingale Simulation for Asset Prices," Management Science, INFORMS, vol. 44(9), pages 1218-1233, September.
    10. Bollen, Nicolas P. B & Rasiel, Emma, 2003. "The performance of alternative valuation models in the OTC currency options market," Journal of International Money and Finance, Elsevier, vol. 22(1), pages 33-64, February.
    11. Bates, David S, 1991. "The Crash of '87: Was It Expected? The Evidence from Options Markets," Journal of Finance, American Finance Association, vol. 46(3), pages 1009-1044, July.
    12. Badescu Alex & Kulperger Reg & Lazar Emese, 2008. "Option Valuation with Normal Mixture GARCH Models," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 12(2), pages 1-42, May.
    13. 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.
    14. 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.
    15. Latane, Henry A & Rendleman, Richard J, Jr, 1976. "Standard Deviations of Stock Price Ratios Implied in Option Prices," Journal of Finance, American Finance Association, vol. 31(2), pages 369-381, May.
    16. 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.
    17. Yow-Jen Jou & Chih-Wei Wang & Wan-Chien Chiu, 2013. "Is the realized volatility good for option pricing during the recent financial crisis?," Review of Quantitative Finance and Accounting, Springer, vol. 40(1), pages 171-188, January.
    18. Garman, Mark B. & Kohlhagen, Steven W., 1983. "Foreign currency option values," Journal of International Money and Finance, Elsevier, vol. 2(3), pages 231-237, December.
    19. repec:bla:jfinan:v:53:y:1998:i:6:p:2059-2106 is not listed on IDEAS
    20. Jin‐Chuan Duan, 1995. "The Garch Option Pricing Model," Mathematical Finance, Wiley Blackwell, vol. 5(1), pages 13-32, January.
    21. Hull, John C & White, Alan D, 1987. "The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June.
    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. Riko Hendrawan, 2023. "Comparison of Black-Scholes and Garch Option Models on The Kompas100 Index With a Long Straddle Strategy During 2008-2021 ," GATR Journals jfbr208, Global Academy of Training and Research (GATR) Enterprise.
    2. Riko Hendrawan, 2023. "Comparison of Black-Scholes and GARCH Option Models on The Jakarta Islamic Index with Collar Strategy," GATR Journals jfbr209, Global Academy of Training and Research (GATR) Enterprise.
    3. Daniel Erpriandy Maharsasi, 2022. "Testing Black Scholes and Garch Model Options on Gold Price Index With Long Strangle Strategy Using 1985-2020 Data ," GATR Journals jfbr207, Global Academy of Training and Research (GATR) Enterprise.

    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. Rombouts, Jeroen V.K. & Stentoft, Lars, 2015. "Option pricing with asymmetric heteroskedastic normal mixture models," International Journal of Forecasting, Elsevier, vol. 31(3), pages 635-650.
    2. Peter Christoffersen & Kris Jacobs, 2004. "Which GARCH Model for Option Valuation?," Management Science, INFORMS, vol. 50(9), pages 1204-1221, September.
    3. Lars Stentoft, 2008. "American Option Pricing Using GARCH Models and the Normal Inverse Gaussian Distribution," Journal of Financial Econometrics, Oxford University Press, vol. 6(4), pages 540-582, Fall.
    4. Christoffersen, Peter & Jacobs, Kris & Chang, Bo Young, 2013. "Forecasting with Option-Implied Information," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 2, chapter 0, pages 581-656, Elsevier.
    5. Tseng, Chih-Hsiung & Cheng, Sheng-Tzong & Wang, Yi-Hsien & Peng, Jin-Tang, 2008. "Artificial neural network model of the hybrid EGARCH volatility of the Taiwan stock index option prices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(13), pages 3192-3200.
    6. Ghysels, E. & Harvey, A. & Renault, E., 1995. "Stochastic Volatility," Papers 95.400, Toulouse - GREMAQ.
    7. Contreras, Javier & Rodríguez, Yeny E., 2014. "GARCH-based put option valuation to maximize benefit of wind investors," Applied Energy, Elsevier, vol. 136(C), pages 259-268.
    8. David S. Bates, 1995. "Testing Option Pricing Models," NBER Working Papers 5129, National Bureau of Economic Research, Inc.
    9. Rombouts, Jeroen V.K. & Stentoft, Lars, 2014. "Bayesian option pricing using mixed normal heteroskedasticity models," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 588-605.
    10. Hatem Ben-Ameur & Michèle Breton & Juan-Manuel Martinez, 2009. "Dynamic Programming Approach for Valuing Options in the GARCH Model," Management Science, INFORMS, vol. 55(2), pages 252-266, February.
    11. Peter Christoffersen & Kris Jacobs, 2002. "Which Volatility Model for Option Valuation?," CIRANO Working Papers 2002s-33, CIRANO.
    12. repec:dau:papers:123456789/2138 is not listed on IDEAS
    13. Duan, Jin-Chuan & Zhang, Hua, 2001. "Pricing Hang Seng Index options around the Asian financial crisis - A GARCH approach," Journal of Banking & Finance, Elsevier, vol. 25(11), pages 1989-2014, November.
    14. Peter Christoffersen & Kris Jacobs & Chayawat Ornthanalai, 2012. "GARCH Option Valuation: Theory and Evidence," CREATES Research Papers 2012-50, Department of Economics and Business Economics, Aarhus University.
    15. Michèle Breton & Javier de Frutos, 2010. "Option Pricing Under GARCH Processes Using PDE Methods," Operations Research, INFORMS, vol. 58(4-part-2), pages 1148-1157, August.
    16. Huang, Hung-Hsi & Lin, Shin-Hung & Wang, Chiu-Ping, 2019. "Reasonable evaluation of VIX options for the Taiwan stock index," The North American Journal of Economics and Finance, Elsevier, vol. 48(C), pages 111-130.
    17. Kim, In Joon & Kim, Sol, 2004. "Empirical comparison of alternative stochastic volatility option pricing models: Evidence from Korean KOSPI 200 index options market," Pacific-Basin Finance Journal, Elsevier, vol. 12(2), pages 117-142, April.
    18. Sol Kim & In Jung Song, 2021. "The traders' rule and long‐term options," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 41(3), pages 406-436, March.
    19. Sol Kim, 2021. "Portfolio of Volatility Smiles versus Volatility Surface: Implications for pricing and hedging options," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 41(7), pages 1154-1176, July.
    20. Torben G. Andersen & Tim Bollerslev & Peter F. Christoffersen & Francis X. Diebold, 2005. "Volatility Forecasting," PIER Working Paper Archive 05-011, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    21. Suk Joon Byun & Dong Woo Rhee & Sol Kim, 2011. "Intraday volatility forecasting from implied volatility," International Journal of Managerial Finance, Emerald Group Publishing Limited, vol. 7(1), pages 83-100, February.

    More about this item

    Keywords

    Black-Scholes-Merton; currency options; implied volatility; NGARCH; Non-Linear Least Squares;
    All these keywords.

    JEL classification:

    • R00 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General - - - General
    • Z0 - Other Special Topics - - General

    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:ibn:ijefaa:v:8:y:2016:i:3:p:123-136. 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: Canadian Center of Science and Education (email available below). General contact details of provider: https://edirc.repec.org/data/cepflch.html .

    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.