Abstract: The risks of financial asset prices arise from their fluctuation, which can be defined by volatility. This paper develops the Generalized Moment Method (GMM) to make parametric estimations and statistical inference for stochastic volatility models by using the Shanghai Composite Index. By utilizing the infinitesimal generator, the conditional expectation operator and the Taylor expansion of the differential operator, we determine the necessary conditions for GMM, namely, the orthogonal moment condition. Meanwhile, the filtered values of the stochastic volatility will be estimated by developing a sampling-importance and resampling algorithm. The empirical results show that the established model needs to introduce stochastic volatility, and the model can describe some major economic phenomena. Finally, we carry out the numerical results for European call option by using Monte Carlo method.

Key words: stochastic volatility model, generalized moment method, European call option, Monte Carlo method