风险中性过程的非参数估计

Nonparametric Estimation of the Risk-Neutral Process

无套利定价理论说明,任何衍生证券定价都可以在基础资产价格(或收益)的风险中性过程基础上进行,而且方差函数的估计是估计风险中性过程的关键问题,由于方差不可观测,采用特定的参数模型将是危险的.本文主要讨论时间序列模型下条件方差函数的非参数估计,对核估计和局部多项式估计给出确定窗宽的M-图方法,并给出时间序列模型下衍生证券定价的风险中性调整方法,最后作了模拟计算.

According to the no-arbitrage pricing theory, any derivative security can be priced based on the risk-neutral process of the underlying assets's price (or return), and estimating of the variance function is crucial to estimate risk-neutral process. Because variance can not be observed, specification of one particular parametric model will be dangerous. In this paper, we analysis some nonparametric time series models of the conditional variance function, a M-plot method for choosing the bandwidth is presented, we also give a risk-neutral adjustment method and some practical implementation methods for valuation of derivative securities in the case of discrete models. Finally, a simulated example gives some illustrations.