A Non-linear Filtering Approach to Stochastic Volatility Models with an Application to Daily Stock Returns
AbstractThis paper develops a new method for the analysis of stochastic volatility (SV) models. Since volatility is a latent variable in SV models, it is difficult to evaluate the exact likelihood. In this paper, a non-linear filter which yields the exact likelihood of SV models is employed. Solving a series of integrals in this filter by piecewise linear approximations with randomly chosen nodes produces the likelihood, which is maximized to obtain estimates of the SV parameters. A smoothing algorithm for volatility estimation is also constructed. Monte Carlo experiments show that the method performs well with respect to both parameter estimates and volatility estimates. We illustrate the method by analysing daily stock returns on the Tokyo Stock Exchange. Since the method can be applied to more general models, the SV model is extended so that several characteristics of daily stock returns are allowed, and this more general model is also estimated.
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Bibliographic InfoArticle provided by John Wiley & Sons, Ltd. in its journal Journal of Applied Econometrics.
Volume (Year): 14 (1999)
Issue (Month): 2 (March-April)
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Web page: http://www.interscience.wiley.com/jpages/0883-7252/
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- Carmen Broto & Esther Ruiz, 2002.
"Estimation Methods For Stochastic Volatility Models: A Survey,"
Statistics and Econometrics Working Papers
ws025414, Universidad Carlos III, Departamento de Estadística y Econometría.
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- Scott I. White & Adam E. Clements & Stan Hurn, 2004. "Discretised Non-Linear Filtering for Dynamic Latent Variable Models: with Application to Stochastic Volatility," Econometric Society 2004 Australasian Meetings 46, Econometric Society.
- Čížek, Pavel, 2004. "(Non) Linear Regression Modeling," Papers 2004,11, Humboldt-Universität Berlin, Center for Applied Statistics and Economics (CASE).
- Adam Clements & Scott White, 2005. "Non-linear filtering with state dependant transition probabilities: A threshold (size effect) SV model," School of Economics and Finance Discussion Papers and Working Papers Series 191, School of Economics and Finance, Queensland University of Technology.
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