Skip to main content
SpringerLink
Log in

American option pricing under GARCH diffusion model: An empirical study

  • Published:
Journal of Systems Science and Complexity Aims and scope Submit manuscript

Abstract

The GARCH diffusion model has received much attention in recent years, as it describes financial time series better when compared to many other models. In this paper, the authors study the empirical performance of American option pricing model when the underlying asset follows the GARCH diffusion. The parameters of the GARCH diffusion model are estimated by the efficient importance sampling-based maximum likelihood (EIS-ML) method. Then the least-squares Monte Carlo (LSMC) method is introduced to price American options. Empirical pricing results on American put options in Hong Kong stock market shows that the GARCH diffusion model outperforms the classical constant volatility (CV) model significantly.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Black F and Scholes M, The pricing of options and corporate liabilities, Journal of Political Economy, 1973, 81(3): 637–654.

    Article  Google Scholar 

  2. Hull J C and White A D, The pricing of options on asset with stochastic volatilities, Journal of Finance, 1987, 42(2): 281–300.

    Article  Google Scholar 

  3. Heston S L, A closed-form solution for options with stochastic volatility with applications to bond and currency options, Review of Financial Studies, 1993, 6(2): 327–343.

    Article  Google Scholar 

  4. Andersen T G, Benzoni L, and Lund J, Estimating jump-diffusions for equity returns, Journal of Finance, 2002, 57: 1239–1284.

    Article  Google Scholar 

  5. Chacko G and Viceira L, Spectral GMM estimation of continuous-time processes, Journal of Econometrics, 2003, 116: 259–292.

    Article  MATH  MathSciNet  Google Scholar 

  6. Chernov M, Gallant A R, Ghysels E, et al., Alternative models for stock price dynamics, Journal of Econometrics, 2003, 116: 225–257.

    Article  MATH  MathSciNet  Google Scholar 

  7. Jones C, The dynamics of stochastic volatility: Evidence from underlying and options markets, Journal of Econometrics, 2003, 116: 181–224.

    Article  MATH  MathSciNet  Google Scholar 

  8. Aït-Sahalia Y and Kimmel R, Maximum likelihood estimation of stochastic volatility models, Journal of Financial Economics, 2007, 83: 413–452.

    Article  Google Scholar 

  9. Nelson D B, ARCH models as diffusion approximations, Journal of Econometrics, 1990, 45: 7–38.

    Article  MATH  MathSciNet  Google Scholar 

  10. Lewis A L, Option Valuation Under Stochastic Volatility, Finance Press, California, 2000.

    MATH  Google Scholar 

  11. Barone-Adesi G, Rasmussen H, and Ravanelli C, An option pricing formula for the GARCH diffusion model, Computational Statistics and Data Analysis, 2005, 49: 287–310.

    Article  MATH  MathSciNet  Google Scholar 

  12. Christoffersen P, Jacobs K, and Mimouni K, Models for S&P 500 dynamics: Evidence from realized volatility, daily returns, and option prices, Review of Financial Studies, 2010, 23(8): 3141–3189.

    Article  Google Scholar 

  13. Chourdakis K and Dotsis G, Maximum likelihood estimation of non-affine volatility processes, Journal of Empirical Finance, 2010, 18(3): 533–545.

    Article  Google Scholar 

  14. Chernov M and Ghysels E, A study towards a unified approach to the joint estimation of objective and risk neutral measures for the purpose of options valuation, Journal of Financial Economics, 2000, 56: 407–458.

    Article  Google Scholar 

  15. Singleton K J, Estimation of affine asset pricing models using the empirical characteristic function, Journal of Econometrics, 2001, 102(1): 111–141.

    MATH  MathSciNet  Google Scholar 

  16. Jacquier E, Polson N G, and Rossi P E, Bayesian analysis of stochastic volatility models, Journal of Business and Economic Statistics, 1994, 12: 371–389.

    Google Scholar 

  17. Eraker B, MCMC analysis of diffusion models with application to finance, Journal of Business and Economic Statistics, 2001, 19: 177–191.

    Article  MathSciNet  Google Scholar 

  18. Liesenfeld R and Richard J, Univariate and multivariate stochastic volatility models: Estimation and diagnostics, Journal of Empirical Finance, 2003, 10: 505–531.

    Article  Google Scholar 

  19. Durham G B, Monte Carlo methods for estimating, smoothing, and filtering one and two-factor stochastic volatility models, Journal of Econometrics, 2006, 133: 273–305.

    Article  MathSciNet  Google Scholar 

  20. Liesenfeld R and Richard J, Classical and bayesian analysis of univariate and multivariate stochastic volatility models, Econometric Reviews, 2006, 25: 335–360.

    Article  MATH  MathSciNet  Google Scholar 

  21. Richard J F and Zhang W, Efficient high-dimensional importance sampling, Journal of Econometrics, 2007, 127(2): 1385–1411.

    Article  MathSciNet  Google Scholar 

  22. Carriere J F, Valuation of early-exercise price of options using simulations and nonparametric regression, Insurance: Mathematics and Economics, 1996, 19(1): 19–30.

    MATH  MathSciNet  Google Scholar 

  23. Longstaff F A and Schwartz E S, Valuing American options by simulation: A simple least-squares approach, Review of Financial Studies, 2001, 14(1): 113–147.

    Article  Google Scholar 

  24. Boyle P P, Kolkiewicz A W, and Tan K S, Pricing American derivatives using simulation: A biased low approach, Proceedings in Monte Carlo and Quasi-Monte Carlo Methods (eds. by Fang K T, Hickernell F J, and Niederreiter H), Berlin, 2002.

    Google Scholar 

  25. Boyle P P, Kolkiewicz A W, and Tan K S, An improved simulation method for pricing highdimensional American derivatives, Mathematics and Computers in Simulation, 2003, 62: 315–322.

    Article  MATH  MathSciNet  Google Scholar 

  26. Clément E, Lamberton D, and Protter P, An analysis of a least squares regression algorithm for American option pricing, Finance and Stochastic, 2002, 6(4): 449–471.

    Article  MATH  Google Scholar 

  27. Glasserman P, Monte Carlo Methods in Financial Engineering, Springer-Verlag, New York, 2004.

    MATH  Google Scholar 

  28. Cortazar G, Gravet M, and Urzua J, The valuation of multidimensional American real options using the LSMC simulation method, Computers and Operations Research, 2008, 35: 113–129.

    Article  MATH  Google Scholar 

  29. Yu J, On leverage in a stochastic volatility model, Journal of Econometrics, 2005, 127: 165–178.

    Article  MathSciNet  Google Scholar 

  30. Eraker B, Do stock prices and volatility jump? Reconciling evidence from spot and option prices, Journal of Finance, 2004, 59(3): 1367–1404.

    Article  Google Scholar 

  31. Koopman S J, Shephard N, and Creal D, Testing the assumptions behind importance sampling, Journal of Econometrics, 2009, 149: 2–11.

    Article  MathSciNet  Google Scholar 

  32. Duffie D, Dynamic Asset Pricing Theory, Princeton University Press, New Jersey, 2001.

    MATH  Google Scholar 

  33. Gordon N J, Salmond D J, and Smith A F, Novel approach to nonlinear/non-Gaussian Bayesian state estimation, IEE Proceedings-F, 1993, 140: 107–113.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Finance, Anhui University of Finance and Economics, Bengbu, 233030, China

    Xinyu Wu

  2. School of Business Administration, Hunan University, Changsha, 410082, China

    Wenyu Yang & Chaoqun Ma

  3. School of Economics and Management, Beijing University of Posts and Telecommunications, Beijing, 100876, China

    Xiujuan Zhao

Authors
  1. Xinyu Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Wenyu Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Chaoqun Ma
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Xiujuan Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xinyu Wu.

Additional information

This research was supported by the National Natural Science Foundations of China under Grant No. 71201013, the National Science Fund for Distinguished Young Scholars of China under Grant No. 70825006, the Program for Changjiang Scholars and Innovative Research Team in University under Grant No. IRT0916, and the National Natural Science Innovation Research Group of China under Grant No. 71221001.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Wu, X., Yang, W., Ma, C. et al. American option pricing under GARCH diffusion model: An empirical study. J Syst Sci Complex 27, 193–207 (2014). https://doi.org/10.1007/s11424-014-3279-2

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11424-014-3279-2

Keywords

Search

Navigation