基于广义矩方法的随机波动率模型参数估计

Parametric Estimation of Stochastic Volatility Models with Generalized Moment Method

金融资产价格的风险来自于自身价格的波动,而刻画资产价格波动的指标是波动率.本文以上证综合指数作为研究对象,通过广义矩估计(GMM)方法给出随机波动模型的参数估计和统计推断.借鉴无穷小生成元,条件期望算子和微分算子Taylor展开等知识,从理论上给出GMM的必要条件,即正交矩条件,进一步应用GMM方法研究随机波动率模型的参数估计,并通过应用重度抽样粒子滤波器(SIR)给出随机波动率的过滤估计值.实证结果表明,刻画上证综合指数需要引入随机波动率,同时也发现随机波动率模型能够很好地描述一些重大的经济现象.最后,根据所得参数估计结果,分析了随机波动率模型的欧式看涨期权问题.

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.