A non-linear filtering approach to stochastic volatility models with an application to daily stock returns
✍ Scribed by Toshiaki Watanabe
- Publisher
- John Wiley and Sons
- Year
- 1999
- Tongue
- English
- Weight
- 199 KB
- Volume
- 14
- Category
- Article
- ISSN
- 0883-7252
No coin nor oath required. For personal study only.
✦ Synopsis
This paper develops a new method for the analysis of stochastic volatility (SV) models. Since volatility is a latent variable in SV models, it is dicult to evaluate the exact likelihood. In this paper, a non-linear ®lter which yields the exact likelihood of SV models is employed. Solving a series of integrals in this ®lter 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.