Parameter Estimation for the Stochastic Volatility Model using the EM Algorithm

Article Sidebar

PDF
Published: Dec 27, 2016
DOI: https://doi.org/10.14456/nuej.2016.22
Keywords:
Parameter Estimation Stochastic Volatility EM Algorithm Kalman Method Monte Carlo Method

Main Article Content

Thanapat Iamtan
Naresuan University
Tanit Malakorn
Naresuan University

Abstract

This paper presents the application of the EM algorithm in estimating the parameters of the stochastic volatility model.  The experimental results showed that the parameters computed by the Monte Carlo method and by the Kalman method in the EM algorithm are slightly different at the 0.05 significance level compared to the true parameters.  We then applied the EM algorithm with the Monte Carlo method to estimate the parameters of the stochastic volatility model using 5 foreign exchange rates as a case study. The proper model can be used to forecast the volatility of the foreign exchange rate which is one major variable in calculating the value of the options having the exchange rate as an underlying asset.

Article Details

How to Cite
Iamtan, T., & Malakorn, T. (2016). Parameter Estimation for the Stochastic Volatility Model using the EM Algorithm. Naresuan University Engineering Journal, 11(2), 1–7. https://doi.org/10.14456/nuej.2016.22
Issue
Vol. 11 No. 2 (2016): JULY - DECEMBER
Section
Research Paper

References

Thailand Futures Exchange. [Online]. Available: http://www.tfex.co.th/th/products/set50futures-spec.html.

R. C. Merton, “The theory of rational option pricing,” Bell Journal of Economics, vol.4, pp.141-183, 1973.

F. Black, and M. Scholes, “The pricing of options and corporate liabilities,” Journal of Political Economics, 81, pp.637–654, 1973.

A. P. Dempster, N. M. Laird, and D. B. Rubin, “Maximum likelihood from incomplete data via EM algorithm,” Journal of the Royal Statistical Society, vol.39, no.1, pp.1-38, 1977.

B. D. O. Anderson, and J. B. Moore, Optimal Filtering, New York: Dover, 2005.

R. Faragher, “Understanding the basis of Kalman filter via a simple and intuitive derivation,” IEEE Signal Processing Magazine, pp 128–132, 2012.

M. Fridman, and L. Harris, “A maximum likelihood approach for non-Gaussian stochastic volatility models,” Journal of Business and Economics Statistics, vol.1, no.3, pp. 284-291, 1998.

F. J. Breidt, and A. L. Carriquiry, Improvement quasi maximum likelihood estimation for stochastic volatility models, New York: Springer, 1996, p.228-247.

S. J. Taylor, Financial returns modeled by the product of two stochastic processes–a study of daily sugar prices 1961–79. In Time Series Analysis: Theory and Practice, vol. 1. New York: Elsevier Science Publishing, p.203–226, 1982.

E. Ruiz, “Quasi-maximum likelihood estimation of stochastic volatility models,” Journal of Econometrics, vol.63, pp.289-306, 1994.

S. Chatterjee, Application of the Kalman filter for estimating continuous time term structure models-the case of UK and Germany, Department of Economics, University of Glasgow, 2005.

F. E. Racicot, and R. Theoret, “Forecasting stochastic volatility using the Kalman filter: An application to Canadian interest rates and price -earning ratio,” AESTI-MATIO, the IEB International Journal of Finance, vol.1, pp.28-47, 2010.

N. Shephard, and D. Xiu, Econometric analysis of multivariate realized QML: efficient positive semi-definite estimators of the covariation of equity prices, Department of Economics, University of Oxford, 2012.