GARCH option pricing: A semiparametric approach
AbstractOption pricing based on GARCH models is typically obtained under the assumption that the random innovations are standard normal (normal GARCH models). However, these models fail to capture the skewness and the leptokurtosis in financial data. We propose a new method to compute option prices using a nonparametric density estimator for the distribution of the driving noise. We investigate the pricing performances of this approach using two different risk neutral measures: the Esscher transform pioneered by Gerber and Shiu [Gerber, H.U., Shiu, E.S.W., 1994a. Option pricing by Esscher transforms (with discussions). Trans. Soc. Actuar. 46, 99-91], and the extended Girsanov principle introduced by Elliot and Madan [Elliot, R.J., Madan, D.G., 1998. A discrete time equivalent martingale 9 measure. Math. Finance 8, 127-152]. Both measures are justified by economic arguments and are consistent with Duan's [Duan, J.-C., 1995. The GARCH option pricing model. Math. Finance 5, 13-32] local risk neutral valuation relationship (LRNVR) for normal GARCH models. The main advantage of the two measures is that one can price derivatives using skewed or heavier tailed innovations distributions to model the returns. An empirical study regarding the European Call option valuation on S&P500 Index shows: (i) under both risk neutral measures our semiparametric algorithm performs better than the existing normal GARCH models if we allow for a leverage effect and (ii) the pricing errors when using the Esscher transform are quite small even though our estimation procedure is based only on historical return data.
Download InfoIf 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.
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 InfoArticle provided by Elsevier in its journal Insurance: Mathematics and Economics.
Volume (Year): 43 (2008)
Issue (Month): 1 (August)
Contact details of provider:
Web page: http://www.elsevier.com/locate/inca/505554
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.:
- Scott, Louis O., 1987. "Option Pricing when the Variance Changes Randomly: Theory, Estimation, and an Application," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 22(04), pages 419-438, December.
- Charles Quanwei Cao & Gurdip S. Bakshi & Zhiwu Chen, 1997. "Empirical Performance of Alternative Option Pricing Models," Yale School of Management Working Papers ysm65, Yale School of Management.
- Peter Christoffersen & Kris Jacobs, 2004. "Which GARCH Model for Option Valuation?," Management Science, INFORMS, vol. 50(9), pages 1204-1221, September.
- Darrell Duffie & Jun Pan & Kenneth Singleton, 2000.
"Transform Analysis and Asset Pricing for Affine Jump-Diffusions,"
Econometric Society, vol. 68(6), pages 1343-1376, November.
- Darrell Duffie & Jun Pan & Kenneth Singleton, 1999. "Transform Analysis and Asset Pricing for Affine Jump-Diffusions," NBER Working Papers 7105, National Bureau of Economic Research, Inc.
- Bollerslev, Tim, 1986.
"Generalized autoregressive conditional heteroskedasticity,"
Journal of Econometrics,
Elsevier, vol. 31(3), pages 307-327, April.
- Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
- Garcia, R. & Luger, R. & Renault, E., 2001.
"Empirical Assessment of an Intertemporal option Pricing Model with Latent variables,"
Cahiers de recherche
2001-10, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
- Garcia, Rene & Luger, Richard & Renault, Eric, 2003. "Empirical assessment of an intertemporal option pricing model with latent variables," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 49-83.
- GARCIA,René & LUGER, Richard & RENAULT, Éric, 2001. "Empirical Assessment of an Intertemporal Option Pricing Model with Latent variables," Cahiers de recherche 2001-10, Universite de Montreal, Departement de sciences economiques.
- René Garcia & Richard Luger & Eric Renault, 2000. "Empirical Assessment of an Intertemporal Option Pricing Model with Latent Variables," Working Papers 2000-56, Centre de Recherche en Economie et Statistique.
- Geman, Hélyette & Carr, Peter & Madan, Dilip B. & Yor, Marc, 2003. "Stochastic Volatility for Levy Processes," Economics Papers from University Paris Dauphine 123456789/1392, Paris Dauphine University.
- Robert J. Elliott & Dilip B. Madan, 1998. "A Discrete Time Equivalent Martingale Measure," Mathematical Finance, Wiley Blackwell, vol. 8(2), pages 127-152.
- Stein, Elias M & Stein, Jeremy C, 1991. "Stock Price Distributions with Stochastic Volatility: An Analytic Approach," Review of Financial Studies, Society for Financial Studies, vol. 4(4), pages 727-52.
- Martin Schweizer & Christophe Stricker & Freddy Delbaen & Pascale Monat & Walter Schachermayer, 1997. "Weighted norm inequalities and hedging in incomplete markets," Finance and Stochastics, Springer, vol. 1(3), pages 181-227.
- HARDLE, Wolfgang & HAFNER, Christian M., .
"Discrete time option pricing with flexible volatility estimation,"
CORE Discussion Papers RP
-1439, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Christian M. Hafner & Wolfgang HÄrdle, 2000. "Discrete time option pricing with flexible volatility estimation," Finance and Stochastics, Springer, vol. 4(2), pages 189-207.
- HÄRDLE, Wolfgang & HAFNER, Christian, 1997. "Discrete time option pricing with flexible volatility estimation," CORE Discussion Papers 1997047, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Härdle, Wolfgang & Hafner, Christian M., 1997. "Discrete time option pricing with flexible volatility estimation," SFB 373 Discussion Papers 1997,56, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
- Peter Christoffersen & Steve Heston & Kris Jacobs, 2003.
"Option Valuation with Conditional Skewness,"
CIRANO Working Papers
- Yacine Ait-Sahalia & Andrew W. Lo, 2000.
"Nonparametric Risk Management and Implied Risk Aversion,"
NBER Working Papers
6130, National Bureau of Economic Research, Inc.
- Ait-Sahalia, Yacine & Lo, Andrew W., 2000. "Nonparametric risk management and implied risk aversion," Journal of Econometrics, Elsevier, vol. 94(1-2), pages 9-51.
- Pagan, A.R. & Schwert, G.W., 1989.
"Alternative Models For Conditional Stock Volatility,"
89-02, Rochester, Business - General.
- Pagan, Adrian R. & Schwert, G. William, 1990. "Alternative models for conditional stock volatility," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 267-290.
- Adrian R. Pagan & G. William Schwert, 1990. "Alternative Models For Conditional Stock Volatility," NBER Working Papers 2955, National Bureau of Economic Research, Inc.
- 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 637-54, May-June.
- Stentoft, Lars, 2005. "Pricing American options when the underlying asset follows GARCH processes," Journal of Empirical Finance, Elsevier, vol. 12(4), pages 576-611, September.
- Bai, Xuezheng & Russell, Jeffrey R. & Tiao, George C., 2003. "Kurtosis of GARCH and stochastic volatility models with non-normal innovations," Journal of Econometrics, Elsevier, vol. 114(2), pages 349-360, June.
- Bakshi, Gurdip & Cao, Charles & Chen, Zhiwu, 1997. " Empirical Performance of Alternative Option Pricing Models," Journal of Finance, American Finance Association, vol. 52(5), pages 2003-49, December.
- Marco Frittelli, 2000. "The Minimal Entropy Martingale Measure and the Valuation Problem in Incomplete Markets," Mathematical Finance, Wiley Blackwell, vol. 10(1), pages 39-52.
- Charles Quanwei Cao & Gurdip S. Bakshi & Zhiwu Chen, 1997. "Empirical Performance of Alternative Option Pricing Models," Yale School of Management Working Papers ysm54, Yale School of Management.
- Jin-Chuan Duan, 1995. "The Garch Option Pricing Model," Mathematical Finance, Wiley Blackwell, vol. 5(1), pages 13-32.
- Badescu, Alex & Elliott, Robert J. & Siu, Tak Kuen, 2009. "Esscher transforms and consumption-based models," Insurance: Mathematics and Economics, Elsevier, vol. 45(3), pages 337-347, December.
- Alexandru Badescu & Robert J. Elliott & Juan-Pablo Ortega, 2012. "Quadratic hedging schemes for non-Gaussian GARCH models," Papers 1209.5976, arXiv.org, revised Dec 2013.
- repec:eme:jrfpps:v:10:y:2010:i:5:p:496-507 is not listed on IDEAS
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei).
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.