Nonparametric Estimation of the Risk-Neutral Process

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.