完备的随机波动率模型的统计推断

STATISTICAL INFERENCE IN COMPLETE MODELS WITH STOCHASTIC VOLATILITY

完备的随机波动率模型是David G.Hobson and Rogers L G 于1998年引入一类新的随机波动率模型,与现有波动率模型相比,它有很多优点.本文讨论了这类模型的估计问题。通过测度变换,将系数σ(·)的估计转化为—般回归函数的估计问题,给出了该系数的核估计量,并证明了所得估计量的均方收敛性。

The complete models with stochastic volatility is a new model with stochastic volatility given by David G. Hobson and Rogers L G in 1998. Comparing with current stochastic volatility models, David ＇model has many advantages. In this paper, we discuss the estimate problem of David＇s model. By transforming the measure, the problem is discussed in frame of estimation of regression function. We gave a kernel estimate of a（.） and the L2 consistency of the estimate is proved.