Statistical Inference And Applications For Stochastic Volatility Model

In the fields of option pricing,risk management and portfolio,stochastic volatility model has very important theoretical and practical significance in capturing the relation of asset return and volatility.This thesis mainly studies the problems of statistical inference and applications for stochastic volatility model in different market environments,including:estimation of semi-parametric stochastic volatility model,properties and estimation of generalized time-varying asymmetric semiparametric stochastic volatility model,estimation of threshold semiparametric asymmetric stochastic volatility model and the nonparametric test for the leverage effect in the stochastic volatility model.The main contents are arranged as follows:Chapter 2 focuses on the estimation of a semiparametric stochastic volatility model.Based on kernel density estimation and hidden markov models,we propose a approximated maximum likelihood estimation method for stochastic volatility model with unknown distribution of return innovation.Several numerical simulations show the robust of the method and evaluate the finite sample performance of the proposed method.Finally,an application with real data illustrates the performance of the proposed method in real data.Chapter 3 mainly investigates the properties and estimation of the generalized time-varying semiparametric asymmetric stochastic volatility model.Under the conditions of unknown dis?tribution of return innovation and time-varying leverage effect,we propose a generalized time-varying semiparametric asymmetric stochastic volatility model and discuss the statistical prop-erties of the proposed model.A Bayesian method based on MCMC is proposed to estimate the number of knots,position of knots and the model parameters when the number of knots and position of knots are unknown.Numerical simulations are carried out to demonstrate that the proposed method have a good performance in estimating the parameters when the number of knots and position of knots are known and unknown.Compared with different models,the pro-posed model and method have a good performance in empirical analysis,which provides some directed significance for practical workers.Chapter 4 mainly studies the estimation and application of semiparametric threshold asym-metric stochastic volatility model.To capture the asymmetries of return,volatility and leverage,and fit the return with sharp peak and heavy tail,based on linear spline,a semiparametric thresh-old asymmetric stochastic volatility model is proposed.Using penalized density function and efficient important sampling,a maximum likelihood estimation is developed for the proposed model.Numerical simulations and real data applications are presented to examine the finite sample performance and practical suggestive significance of the proposed procedures and model.Chapter 5 is devoted to studying the nonparametric test of leverage effect in stochastic volatility model.Based on local polynomial estimation and Kolmogorov-Smirnov nonparamet-ric test method,a new nonparametric test for leverage effect is proposed.Test statistic is constructed.Under some mild conditions,the asymptotic properties of the test statistic are established.Finally,numerical simulations and empirical analysis illustrate the superiority of the proposed statistic in testing the leverage effect.In summary,under different market environments,this thesis is concentrated on the theory and applications of stochastic volatility model,and generalizes some existing research work.The research findings are meaningful both on the theory research and practical applications and provides valuable suggestions for workers in financial and related fields.