Advanced Search
MyIDEAS: Login to save this article or follow this journal

American Option Pricing Using GARCH Models and the Normal Inverse Gaussian Distribution

Contents:

Author Info

  • Lars Stentoft

Abstract

In this paper we propose a feasible way to price American options in a model with time-varying volatility and conditional skewness and leptokurtosis, using GARCH processes and the Normal Inverse Gaussian distribution. We show how the risk-neutral dynamics can be obtained in this model, we interpret the effect of the risk-neutralization, and we derive approximation procedures which allow for a computationally efficient implementation of the model. When the model is estimated on financial returns data the results indicate that compared to the Gaussian case the extension is important. A study of the model properties shows that there are important option pricing differences compared to the Gaussian case as well as to the symmetric special case. A large scale empirical examination shows that our model out-performs the Gaussian case for pricing options on the three large US stocks as well as a major index. In particular, improvements are found when it comes to explaining the smile in implied standard deviations. Copyright The Author 2008. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oxfordjournals.org., Oxford University Press.

Download Info

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
File URL: http://hdl.handle.net/10.1093/jjfinec/nbn013
Download Restriction: Access to full text is restricted to subscribers.

As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.

Bibliographic Info

Article provided by Society for Financial Econometrics in its journal Journal of Financial Econometrics.

Volume (Year): 6 (2008)
Issue (Month): 4 (Fall)
Pages: 540-582

as in new window
Handle: RePEc:oup:jfinec:v:6:y:2008:i:4:p:540-582

Contact details of provider:
Postal: Oxford University Press, Great Clarendon Street, Oxford OX2 6DP, UK
Fax: 01865 267 985
Email:
Web page: http://jfec.oxfordjournals.org/
More information through EDIRC

Order Information:
Web: http://www.oup.co.uk/journals

Related research

Keywords:

Other versions of this item:

Find related papers by JEL classification:

References

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
as in new window
  1. Hafner, Christian M. & Herwartz, Helmut, 1999. "Option pricing under linear autoregressive dynamics, heteroskedasticity, and conditional leptokurtosis," SFB 373 Discussion Papers, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes 1999,58, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  2. Engle, Robert F & Ng, Victor K, 1993. " Measuring and Testing the Impact of News on Volatility," Journal of Finance, American Finance Association, American Finance Association, vol. 48(5), pages 1749-78, December.
  3. Christian M. Hafner & Wolfgang HÄrdle, 2000. "Discrete time option pricing with flexible volatility estimation," Finance and Stochastics, Springer, Springer, vol. 4(2), pages 189-207.
  4. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," University of California at Los Angeles, Anderson Graduate School of Management, Anderson Graduate School of Management, UCLA qt43n1k4jb, Anderson Graduate School of Management, UCLA.
  5. Peter Christoffersen & Steve Heston & Kris Jacobs, 2003. "Option Valuation with Conditional Skewness," CIRANO Working Papers, CIRANO 2003s-50, CIRANO.
  6. K. Hsieh & P. Ritchken, 2005. "An empirical comparison of GARCH option pricing models," Review of Derivatives Research, Springer, Springer, vol. 8(3), pages 129-150, December.
  7. Bollerslev, Tim & Ole Mikkelsen, Hans, 1999. "Long-term equity anticipation securities and stock market volatility dynamics," Journal of Econometrics, Elsevier, Elsevier, vol. 92(1), pages 75-99, September.
  8. Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series, Economics and Econometrics Research Institute (EERI), Brussels EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
  9. Jing-zhi Huang & Liuren Wu, 2004. "Specification Analysis of Option Pricing Models Based on Time-Changed Lévy Processes," Journal of Finance, American Finance Association, American Finance Association, vol. 59(3), pages 1405-1440, 06.
  10. Ole E. Barndorff-Nielsen & Neil Shephard, 2001. "Non-Gaussian Ornstein-Uhlenbeck-based models and some of their uses in financial economics," Journal of the Royal Statistical Society Series B, Royal Statistical Society, Royal Statistical Society, vol. 63(2), pages 167-241.
  11. Carr, Peter & Wu, Liuren, 2004. "Time-changed Levy processes and option pricing," Journal of Financial Economics, Elsevier, Elsevier, vol. 71(1), pages 113-141, January.
  12. Morten B. Jensen & Asger Lunde, 2001. "The NIG-S&ARCH model: a fat-tailed, stochastic, and autoregressive conditional heteroskedastic volatility model," Econometrics Journal, Royal Economic Society, Royal Economic Society, vol. 4(2), pages 10.
  13. Bollerslev, Tim, 1987. "A Conditionally Heteroskedastic Time Series Model for Speculative Prices and Rates of Return," The Review of Economics and Statistics, MIT Press, MIT Press, vol. 69(3), pages 542-47, August.
  14. Bollerslev, Tim & Ole Mikkelsen, Hans, 1996. "Modeling and pricing long memory in stock market volatility," Journal of Econometrics, Elsevier, Elsevier, vol. 73(1), pages 151-184, July.
  15. Andersson, Jonas, 2001. "On the Normal Inverse Gaussian Stochastic Volatility Model," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 19(1), pages 44-54, January.
  16. Duan, Jin-Chuan & Simonato, Jean-Guy, 2001. "American option pricing under GARCH by a Markov chain approximation," Journal of Economic Dynamics and Control, Elsevier, Elsevier, vol. 25(11), pages 1689-1718, November.
  17. Peter Ritchken & Rob Trevor, 1999. "Pricing Options under Generalized GARCH and Stochastic Volatility Processes," Journal of Finance, American Finance Association, American Finance Association, vol. 54(1), pages 377-402, 02.
  18. Duan, Jin-Chuan & Zhang, Hua, 2001. "Pricing Hang Seng Index options around the Asian financial crisis - A GARCH approach," Journal of Banking & Finance, Elsevier, Elsevier, vol. 25(11), pages 1989-2014, November.
  19. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, Econometric Society, vol. 59(2), pages 347-70, March.
  20. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, Econometric Society, vol. 50(4), pages 987-1007, July.
  21. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
  22. Peter Christoffersen & Kris Jacobs, 2004. "Which GARCH Model for Option Valuation?," Management Science, INFORMS, INFORMS, vol. 50(9), pages 1204-1221, September.
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 in new window

Cited by:
  1. ROMBOUTS, Jeroen V.K. & STENTOFT, Lars, 2009. "Bayesian option pricing using mixed normal heteroskedasticity models," CORE Discussion Papers, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) 2009013, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  2. ROMBOUTS, Jeroen J. K & STENTOFT, Lars, 2010. "Multivariate option pricing with time varying volatility and correlations," CORE Discussion Papers, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) 2010020, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  3. Jeroen V.K. Rombouts & Lars Stentoft & Francesco Violante, 2012. "The Value of Multivariate Model Sophistication: An Application to pricing Dow Jones Industrial Average options," CREATES Research Papers, School of Economics and Management, University of Aarhus 2012-04, School of Economics and Management, University of Aarhus.
  4. Lars Stentoft, 2011. "What we can learn from pricing 139,879 Individual Stock Options," CREATES Research Papers, School of Economics and Management, University of Aarhus 2011-52, School of Economics and Management, University of Aarhus.
  5. Alexandru Badescu & Robert J. Elliott & Juan-Pablo Ortega, 2012. "Quadratic hedging schemes for non-Gaussian GARCH models," Papers, arXiv.org 1209.5976, arXiv.org, revised Dec 2013.
  6. Badescu, Alexandru & Elliott, Robert J. & Ortega, Juan-Pablo, 2014. "Quadratic hedging schemes for non-Gaussian GARCH models," Journal of Economic Dynamics and Control, Elsevier, Elsevier, vol. 42(C), pages 13-32.
  7. Lars Stentoft, 2011. "American Option Pricing with Discrete and Continuous Time Models: An Empirical Comparison," CREATES Research Papers, School of Economics and Management, University of Aarhus 2011-34, School of Economics and Management, University of Aarhus.
  8. Kim, Young Shin & Rachev, Svetlozar T. & Bianchi, Michele Leonardo & Fabozzi, Frank J., 2011. "Tempered stable and tempered infinitely divisible GARCH models," Working Paper Series in Economics, Karlsruhe Institute of Technology (KIT), Department of Economics and Business Engineering 28, Karlsruhe Institute of Technology (KIT), Department of Economics and Business Engineering.
  9. Peter Christoffersen & Kris Jacobs & Chayawat Ornthanalai, 2012. "GARCH Option Valuation: Theory and Evidence," CREATES Research Papers, School of Economics and Management, University of Aarhus 2012-50, School of Economics and Management, University of Aarhus.
  10. Zhu, Dongming & Galbraith, John W., 2011. "Modeling and forecasting expected shortfall with the generalized asymmetric Student-t and asymmetric exponential power distributions," Journal of Empirical Finance, Elsevier, Elsevier, vol. 18(4), pages 765-778, September.
  11. Ornthanalai, Chayawat, 2014. "Lévy jump risk: Evidence from options and returns," Journal of Financial Economics, Elsevier, Elsevier, vol. 112(1), pages 69-90.
  12. Lars Stentoft, 2008. "Option Pricing using Realized Volatility," CREATES Research Papers, School of Economics and Management, University of Aarhus 2008-13, School of Economics and Management, University of Aarhus.

Lists

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

Statistics

Access and download statistics

Corrections

When requesting a correction, please mention this item's handle: RePEc:oup:jfinec:v:6:y:2008:i:4:p:540-582. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Oxford University Press) or (Christopher F. Baum).

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 references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link 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 profile, as there may be some citations waiting for confirmation.

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