IDEAS home Printed from https://ideas.repec.org/a/sae/mareco/v10y2016i2p281-304.html
   My bibliography  Save this article

Pricing Efficiency in CNX Nifty Index Options Using the Black–Scholes Model: A Comparative Study of Alternate Volatility Measures

Author

Listed:
  • Tanuj Nandan

    (Tanuj Nandan is at School of Management Studies, Motilal Nehru National Institute of Technology, Allahabad 211004, India, email: tanujnandan@gmail.com)

  • Puja Agrawal

    (Puja Agrawal is at Amity University, Uttar Pradesh, India, email: pujaweb@gmail.com)

Abstract

This article attempts to determine the method of volatility estimation that prices the CNX Nifty Index options closest to the theoretical price as computed by the Black–Scholes (1973) model. Volatility has been estimated using simple variance, implied volatility, volatility index and the asymmetrical exponential generalised auto-regressive conditional heteroskedasticity (EGARCH) (1,1) model with generalised error distribution innovations. The trend in mispricing has been studied using error estimates and non-parametric tests. Our findings indicate significant mispricing in CNX Nifty Index options. The results of our study will have major implications for investors who use options as part of their portfolios and corporates who use them for risk hedging. Our study is important, as there are only a few studies that examine the pricing efficiency of options with a focus on volatility modelling. Also, our study spans a longer time period than the previous studies. JEL Classification: G14, G32, C14

Suggested Citation

  • Tanuj Nandan & Puja Agrawal, 2016. "Pricing Efficiency in CNX Nifty Index Options Using the Black–Scholes Model: A Comparative Study of Alternate Volatility Measures," Margin: The Journal of Applied Economic Research, National Council of Applied Economic Research, vol. 10(2), pages 281-304, May.
    • Handle: RePEc:sae:mareco:v:10:y:2016:i:2:p:281-304
    DOI: 10.1177/0973801015625390
    as

    Download full text from publisher

    File URL: https://journals.sagepub.com/doi/10.1177/0973801015625390
    Download Restriction: no
    File URL: https://libkey.io/10.1177/0973801015625390?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
    ---><---

    References listed on IDEAS

    as
    1. Kelvin Wai Lung Lai & Andrew Marshall, 2002. "A Study of Mispricing and Parity in the Hang Seng Futures and Options Markets," Review of Pacific Basin Financial Markets and Policies (RPBFMP), World Scientific Publishing Co. Pte. Ltd., vol. 5(03), pages 373-394.
    2. David McMillan & Alan Speight & Owain Apgwilym, 2000. "Forecasting UK stock market volatility," Applied Financial Economics, Taylor & Francis Journals, vol. 10(4), pages 435-448.
    3. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-370, March.
    4. Galai, Dan, 1977. "Tests of Market Efficiency of the Chicago Board Options Exchange," The Journal of Business, University of Chicago Press, vol. 50(2), pages 167-197, April.
    5. Diebold, Francis X & Mariano, Roberto S, 2002. "Comparing Predictive Accuracy," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 134-144, January.
    6. Varma, Jayanth R., 1999. "Rupee-Dollar Option Pricing and Risk Measurement: Jump Processes, Changing Volatility and Kurtosis Shifts," IIMA Working Papers WP1999-04-02, Indian Institute of Management Ahmedabad, Research and Publication Department.
    7. Twm Evans & David McMillan, 2007. "Volatility forecasts: the role of asymmetric and long-memory dynamics and regional evidence," Applied Financial Economics, Taylor & Francis Journals, vol. 17(17), pages 1421-1430.
    8. Franck Moraux & Patrick Navatte & Christophe Villa, 1999. "The Predictive Power of the French Market Volatility Index: A Multi Horizons Study," Review of Finance, European Finance Association, vol. 2(3), pages 303-320.
    9. Holger Claessen & Stefan Mittnik, 2002. "Forecasting stock market volatility and the informational efficiency of the DAX-index options market," The European Journal of Finance, Taylor & Francis Journals, vol. 8(3), pages 302-321.
    10. John S. Cotner & James F. Horrell, 1989. "An analysis of index option pricing," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 9(5), pages 449-459, October.
    11. Charlotte Strunk Hansen, 2001. "The relation between implied and realised volatility in the Danish option and equity markets," Accounting and Finance, Accounting and Finance Association of Australia and New Zealand, vol. 41(3), pages 197-228, November.
    12. Steven Li & Qianqian Yang, 2009. "The relationship between implied and realized volatility: evidence from the Australian stock index option market," Review of Quantitative Finance and Accounting, Springer, vol. 32(4), pages 405-419, May.
    13. Chiras, Donald P. & Manaster, Steven, 1978. "The information content of option prices and a test of market efficiency," Journal of Financial Economics, Elsevier, vol. 6(2-3), pages 213-234.
    14. Vipul, 2005. "Futures and options expiration‐day effects: The Indian evidence," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 25(11), pages 1045-1065, November.
    15. Kanniainen, Juho & Lin, Binghuan & Yang, Hanxue, 2014. "Estimating and using GARCH models with VIX data for option valuation," Journal of Banking & Finance, Elsevier, vol. 43(C), pages 200-211.
    16. Ser-Huang Poon & Clive W.J. Granger, 2003. "Forecasting Volatility in Financial Markets: A Review," Journal of Economic Literature, American Economic Association, vol. 41(2), pages 478-539, June.
    17. Black, Fischer & Scholes, Myron S, 1972. "The Valuation of Option Contracts and a Test of Market Efficiency," Journal of Finance, American Finance Association, vol. 27(2), pages 399-417, May.
    18. Canina, Linda & Figlewski, Stephen, 1993. "The Informational Content of Implied Volatility," Review of Financial Studies, Society for Financial Studies, vol. 6(3), pages 659-681.
    19. Lamoureux, Christopher G & Lastrapes, William D, 1993. "Forecasting Stock-Return Variance: Toward an Understanding of Stochastic Implied Volatilities," Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 293-326.
    20. 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.
    21. Robert Engle, 2001. "GARCH 101: The Use of ARCH/GARCH Models in Applied Econometrics," Journal of Economic Perspectives, American Economic Association, vol. 15(4), pages 157-168, Fall.
    22. Guan Wang & Pierre Yourougou & Yue Wang, 2012. "Which implied volatility provides the best measure of future volatility?," Journal of Economics and Finance, Springer;Academy of Economics and Finance, vol. 36(1), pages 93-105, January.
    23. Christensen, B. J. & Prabhala, N. R., 1998. "The relation between implied and realized volatility," Journal of Financial Economics, Elsevier, vol. 50(2), pages 125-150, November.
    24. Saurabha, Rritu & Tiwari, Manvendra, 2007. "Empirical Study of the effect of including Skewness and Kurtosis in Black Scholes option pricing formula on S&P CNX Nifty index Options," MPRA Paper 6329, University Library of Munich, Germany.
    25. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
    Full references (including those not matched with items on IDEAS)

    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. Chun, Dohyun & Cho, Hoon & Ryu, Doojin, 2019. "Forecasting the KOSPI200 spot volatility using various volatility measures," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 514(C), pages 156-166.
    2. Imlak Shaikh & Puja Padhi, 2014. "The forecasting performance of implied volatility index: evidence from India VIX," Economic Change and Restructuring, Springer, vol. 47(4), pages 251-274, November.
    3. Neely, Christopher J., 2009. "Forecasting foreign exchange volatility: Why is implied volatility biased and inefficient? And does it matter?," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 19(1), pages 188-205, February.
    4. Tsiaras, Leonidas, 2009. "The Forecast Performance of Competing Implied Volatility Measures: The Case of Individual Stocks," Finance Research Group Working Papers F-2009-02, University of Aarhus, Aarhus School of Business, Department of Business Studies.
    5. Chuang, Wen-I & Huang, Teng-Ching & Lin, Bing-Huei, 2013. "Predicting volatility using the Markov-switching multifractal model: Evidence from S&P 100 index and equity options," The North American Journal of Economics and Finance, Elsevier, vol. 25(C), pages 168-187.
    6. Imlak Shaikh & Puja Padhi, 2013. "On the Linkages among Ex-ante and Ex-post Volatility: Evidence from NSE Options Market (India)," Global Business Review, International Management Institute, vol. 14(3), pages 487-505, September.
    7. Athanasia Gavala & Nikolay Gospodinov & Deming Jiang, 2006. "Forecasting volatility," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 25(6), pages 381-400.
    8. Mittnik, Stefan & Robinzonov, Nikolay & Spindler, Martin, 2015. "Stock market volatility: Identifying major drivers and the nature of their impact," Journal of Banking & Finance, Elsevier, vol. 58(C), pages 1-14.
    9. 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.
    10. Ghysels, E. & Harvey, A. & Renault, E., 1995. "Stochastic Volatility," Papers 95.400, Toulouse - GREMAQ.
    11. Szakmary, Andrew & Ors, Evren & Kyoung Kim, Jin & Davidson, Wallace III, 2003. "The predictive power of implied volatility: Evidence from 35 futures markets," Journal of Banking & Finance, Elsevier, vol. 27(11), pages 2151-2175, November.
    12. Bali, Turan G. & Weinbaum, David, 2007. "A conditional extreme value volatility estimator based on high-frequency returns," Journal of Economic Dynamics and Control, Elsevier, vol. 31(2), pages 361-397, February.
    13. David S. Bates, 1995. "Testing Option Pricing Models," NBER Working Papers 5129, National Bureau of Economic Research, Inc.
    14. Benavides, Guillermo & Capistrán, Carlos, 2012. "Forecasting exchange rate volatility: The superior performance of conditional combinations of time series and option implied forecasts," Journal of Empirical Finance, Elsevier, vol. 19(5), pages 627-639.
    15. Yu, Wayne W. & Lui, Evans C.K. & Wang, Jacqueline W., 2010. "The predictive power of the implied volatility of options traded OTC and on exchanges," Journal of Banking & Finance, Elsevier, vol. 34(1), pages 1-11, January.
    16. Viteva, Svetlana & Veld-Merkoulova, Yulia V. & Campbell, Kevin, 2014. "The forecasting accuracy of implied volatility from ECX carbon options," Energy Economics, Elsevier, vol. 45(C), pages 475-484.
    17. Peter Carr & Liuren Wu, 2004. "Variance Risk Premia," Finance 0409015, University Library of Munich, Germany.
    18. Bronka Rzepkowski, 2001. "Pouvoir prédictif de la volatilité implicite dans le prix des options de change," Économie et Prévision, Programme National Persée, vol. 148(2), pages 71-97.
    19. Murad Samsudin, Najmi Ismail & Mohamad, Azhar & Sifat, Imtiaz Mohammad, 2021. "Implied volatility of structured warrants: Emerging market evidence," The Quarterly Review of Economics and Finance, Elsevier, vol. 80(C), pages 464-479.
    20. Imlak Shaikh & Puja Padhi, 2015. "On the Relationship of Ex-ante and Ex-post Volatility: A Sub-period Analysis of S&P CNX Nifty Index Options," Journal of Emerging Market Finance, Institute for Financial Management and Research, vol. 14(2), pages 140-175, August.

    More about this item

    Keywords

    Pricing efficiency; Black–Scholes model; Volatility Modelling; EGARCH Model; Non-parametric Tests; Options Market;
    All these keywords.

    JEL classification:

    • G14 - Financial Economics - - General Financial Markets - - - Information and Market Efficiency; Event Studies; Insider Trading
    • G32 - Financial Economics - - Corporate Finance and Governance - - - Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: 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:sae:mareco:v:10:y:2016:i:2:p:281-304. 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: SAGE Publications (email available below). General contact details of provider: http://www.ncaer.org/ .

    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.