IDEAS home Printed from https://ideas.repec.org/a/taf/apfiec/v7y1997i4p379-394.html
   My bibliography  Save this article

Option pricing under stochastic volatility and stochastic interest rate in the Spanish case

Author

Listed:
  • Marc Saez

Abstract

Among the underlying assumptions of the Black-Scholes option pricing model, the largest empirical biases are caused by those with a fixed volatility of the underlying asset and a constant short-term riskless interest rate. Only recently has attention been paid to the simultaneous effects of the stochastic nature of both variables on the pricing of options. Using a discrete approach an attempt is made to estimate the effects of a stochastic volatility and a stochastic interest rate in the Spanish option market; symmetric and asymmetric GARCH models were tried. The presence of in-the-mean and seasonality effects was allowed. Also estimated were the stochastic processes for the MIBOR90, a Spanish short-term interest rate, from 19 March 1990 to 31 May 1994 and the stochastic processes for the volatility of the returns of the most important Spanish stock index (IBEX-35) from 1 October 1987 to 20 January 1994. These estimators were used on pricing call options on the stock index, from 30 November 1993 to 30 May 1994. Hull-White and Amin-Ng pricing formulas were used. These prices were compared with actual prices and with those derived from the Black-Scholes formula, trying to detect the biases reported previously in the literature. Whereas the conditional variance of the MIBOR90 interest rate seemed to be free of ARCH effects, an asymmetric GARCH with in-the-mean and seasonality effects and some evidence of persistence in variance, IEGARCH(1,2)-M-S, was found to be the model that best represent the behaviour of the stochastic volatility of the IBEX-35 stock returns. All the biases reported previously in the literature were found. All the formulas overpriced the options in near-the-money case and underpriced the options otherwise. Furthermore, in most option trading, Black-Scholes overpriced the options and, because of the time-to-maturity effect, implied volatility computed from the Black-Scholes formula underestimated the actual volatility.

Suggested Citation

  • Marc Saez, 1997. "Option pricing under stochastic volatility and stochastic interest rate in the Spanish case," Applied Financial Economics, Taylor & Francis Journals, vol. 7(4), pages 379-394.
    • Handle: RePEc:taf:apfiec:v:7:y:1997:i:4:p:379-394
    DOI: 10.1080/096031097333493
    as

    Download full text from publisher

    File URL: http://www.tandfonline.com/doi/abs/10.1080/096031097333493
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/096031097333493?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. Jaesun Noh & Robert F. Engle & Alex Kane, 1993. "A Test of Efficiency for the S&P Index Option Market Using Variance Forecasts," NBER Working Papers 4520, National Bureau of Economic Research, Inc.
    2. Kaehler, Jürgen & Marnet, Volker, 1993. "Markov-switching models for exchange-rate dynamics and the pricing of foreign-currency options," ZEW Discussion Papers 93-03, ZEW - Leibniz Centre for European Economic Research.
    3. Robert F. Engle & Alex Kane & Jaesun Noh, 1993. "Index-Option Pricing with Stochastic Volatility and the Value of Accurate Variance Forecasts," NBER Working Papers 4519, National Bureau of Economic Research, Inc.
    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. Degiannakis, Stavros & Floros, Christos, 2013. "Modeling CAC40 volatility using ultra-high frequency data," Research in International Business and Finance, Elsevier, vol. 28(C), pages 68-81.
    2. Stavros Degiannakis & Evdokia Xekalaki, 2007. "Assessing the performance of a prediction error criterion model selection algorithm in the context of ARCH models," Applied Financial Economics, Taylor & Francis Journals, vol. 17(2), pages 149-171.
    3. Kiyotaka Satoyoshi & Hidetoshi Mitsui, 2011. "Empirical Study of Nikkei 225 Options with the Markov Switching GARCH Model," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 18(1), pages 55-68, March.

    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. Ahmad M. Talafha & Emmanuel Thompson, 2017. "On Valuing European Option: VAR-COVAR Approach," Journal of Finance and Investment Analysis, SCIENPRESS Ltd, vol. 6(3), pages 1-1.
    2. Miguel A. Ferreira, 2005. "Evaluating Interest Rate Covariance Models Within a Value-at-Risk Framework," Journal of Financial Econometrics, Oxford University Press, vol. 3(1), pages 126-168.
    3. 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.
    4. Maheu, John M. & McCurdy, Thomas H., 2000. "Volatility dynamics under duration-dependent mixing," Journal of Empirical Finance, Elsevier, vol. 7(3-4), pages 345-372, November.
    5. Stavros Degiannakis & Alexandra Livada & Epaminondas Panas, 2008. "Rolling-sampled parameters of ARCH and Levy-stable models," Applied Economics, Taylor & Francis Journals, vol. 40(23), pages 3051-3067.
    6. Angelidis, Timotheos & Degiannakis, Stavros, 2008. "Volatility forecasting: intra-day vs. inter-day models," MPRA Paper 80434, University Library of Munich, Germany.
    7. Ayla Ogus, 2002. "Pricing of S&P 100 Index Options Based On Garch Volatility Estimates," Working Papers 0201, Izmir University of Economics.
    8. Çepni, Oğuzhan & Gupta, Rangan & Pienaar, Daniel & Pierdzioch, Christian, 2022. "Forecasting the realized variance of oil-price returns using machine learning: Is there a role for U.S. state-level uncertainty?," Energy Economics, Elsevier, vol. 114(C).
    9. Hans Dewachter, 1997. "Sign predictions of exchange rate changes: Charts as proxies for Bayesian inferences," Review of World Economics (Weltwirtschaftliches Archiv), Springer;Institut für Weltwirtschaft (Kiel Institute for the World Economy), vol. 133(1), pages 39-55, March.
    10. Eric Jacquier & Robert Jarrow, "undated". "Model Error in Contingent Claim Models (Dynamic Evaluation)," Rodney L. White Center for Financial Research Working Papers 07-96, Wharton School Rodney L. White Center for Financial Research.
    11. Kaehler, Jürgen, 1993. "Forecasting volatility and option pricing for exchange-rate dynamics: a comparison of models," ZEW Discussion Papers 93-19, ZEW - Leibniz Centre for European Economic Research.
    12. Dajiang Guo, 2000. "Dynamic Volatility Trading Strategies in the Currency Option Market," Review of Derivatives Research, Springer, vol. 4(2), pages 133-154, May.
    13. Bonato, Matteo & Cepni, Oguzhan & Gupta, Rangan & Pierdzioch, Christian, 2023. "Climate risks and realized volatility of major commodity currency exchange rates," Journal of Financial Markets, Elsevier, vol. 62(C).
    14. Eduardo Rossi, 2010. "Univariate GARCH models: a survey (in Russian)," Quantile, Quantile, issue 8, pages 1-67, July.
    15. Brian H. Boyer & Michael S. Gibson, 1997. "Evaluating forecasts of correlation using option pricing," International Finance Discussion Papers 600, Board of Governors of the Federal Reserve System (U.S.).
    16. Stanislav Anatolyev & Nikolay Gospodinov, 2012. "Asymptotics of near unit roots (in Russian)," Quantile, Quantile, issue 10, pages 57-71, December.
    17. Gregory Connor & Lisa R. Goldberg & Robert A. Korajczyk, 2010. "Portfolio Risk Analysis," Economics Books, Princeton University Press, edition 1, number 9224.
    18. Jaesun Noh & Robert F. Engle & Alex Kane, 1993. "A Test of Efficiency for the S&P Index Option Market Using Variance Forecasts," NBER Working Papers 4520, National Bureau of Economic Research, Inc.
    19. David S. Bates, 1995. "Testing Option Pricing Models," NBER Working Papers 5129, National Bureau of Economic Research, Inc.
    20. LUBRANO, Michel, 1998. "Smooth transition GARCH models: a Bayesian perspective," LIDAM Discussion Papers CORE 1998066, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).

    More about this item

    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:taf:apfiec:v:7:y:1997:i:4:p:379-394. 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: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/RAFE20 .

    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.