American option pricing with discrete and continuous time models: An empirical comparison
AbstractThis paper considers discrete time GARCH and continuous time SV models and uses these for American option pricing. We first of all show that with a particular choice of framework the parameters of the SV models can be estimated using simple maximum likelihood techniques. We then perform a Monte Carlo study to examine their differences in terms of option pricing, and we study the convergence of the discrete time option prices to their implied continuous time values. Finally, a large scale empirical analysis using individual stock options and options on an index is performed comparing the estimated prices from discrete time models to the corresponding continuous time model prices. The results show that, while the overall differences in performance are small, for the in the money put options on individual stocks the continuous time SV models do generally perform better than the discrete time GARCH specifications.
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.
Bibliographic InfoArticle provided by Elsevier in its journal Journal of Empirical Finance.
Volume (Year): 18 (2011)
Issue (Month): 5 ()
Contact details of provider:
Web page: http://www.elsevier.com/locate/jempfin
American options; Augmented GARCH; Least squares Monte Carlo; Stochastic volatility;
Other versions of this item:
- Lars Stentoft, 2011. "American Option Pricing with Discrete and Continuous Time Models: An Empirical Comparison," CREATES Research Papers 2011-34, School of Economics and Management, University of Aarhus.
- C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models &bull Diffusion Processes
- C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
- G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
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.
- Lars Stentoft, 2004. "Convergence of the Least Squares Monte Carlo Approach to American Option Valuation," Management Science, INFORMS, vol. 50(9), pages 1193-1203, September.
- Corradi, Valentina, 2000. "Reconsidering the continuous time limit of the GARCH(1, 1) process," Journal of Econometrics, Elsevier, vol. 96(1), pages 145-153, May.
- Jeff Fleming & Chris Kirby, 2003. "A Closer Look at the Relation between GARCH and Stochastic Autoregressive Volatility," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 1(3), pages 365-419.
- 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.
- Tauchen, George E. & Gallant, A. Ronald, 1995.
"Which Moments to Match,"
95-20, Duke University, Department of Economics.
- 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 qt43n1k4jb, Anderson Graduate School of Management, UCLA.
- Duan, Jin-Chuan, 1997. "Augmented GARCH (p,q) process and its diffusion limit," Journal of Econometrics, Elsevier, vol. 79(1), pages 97-127, July.
- Nelson, Daniel B., 1990. "ARCH models as diffusion approximations," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 7-38.
- Jacquier, Eric & Polson, Nicholas G. & Rossi, P.E.Peter E., 2004. "Bayesian analysis of stochastic volatility models with fat-tails and correlated errors," Journal of Econometrics, Elsevier, vol. 122(1), pages 185-212, September.
- Bollerslev, Tim & Chou, Ray Y. & Kroner, Kenneth F., 1992. "ARCH modeling in finance : A review of the theory and empirical evidence," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 5-59.
- 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.
- Lars Stentoft, 2008.
"American Option Pricing Using GARCH Models and the Normal Inverse Gaussian Distribution,"
Journal of Financial Econometrics,
Society for Financial Econometrics, vol. 6(4), pages 540-582, Fall.
- Lars Stentoft, 2008. "American Option Pricing using GARCH models and the Normal Inverse Gaussian distribution," CREATES Research Papers 2008-41, School of Economics and Management, University of Aarhus.
- Bollerslev, Tim & Ole Mikkelsen, Hans, 1999. "Long-term equity anticipation securities and stock market volatility dynamics," Journal of Econometrics, Elsevier, vol. 92(1), pages 75-99, September.
- Bollerslev, Tim & Ole Mikkelsen, Hans, 1996.
"Modeling and pricing long memory in stock market volatility,"
Journal of Econometrics,
Elsevier, vol. 73(1), pages 151-184, July.
- Tom Doan, . "RATS program to replicate Bollerslev-Mikkelson(1996) FIEGARCH models," Statistical Software Components RTZ00173, Boston College Department of Economics.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei).
If references are entirely missing, you can add them using this form.