Nonparametric Kernel Estimation Of The Implied Volatility For Options

To pricing the value of the underlying asset,the key is to select the volatility. There are two important kinds:one is the historical volatility, it is concluded from the statistical analysis of the underlying asset prices changes in the past history on the market, it is also the standard deviation; the another one is the implied volatility of options market, It is predicted the underlying asset volatility in the duration of the options. The implied volatility is more valued by traders.To pricing the option more accurately, in this paper, we study some problem about the implied volatility. Through nonparametric estimation theory and methods, by numerical simulation, we get the implied volatility nonparametric kernel estimation and the optimal window width. It proved that when the optimal window width approaches zero, the non-parametric estimate option price bias also tends to zero, which proves the implied volatility non-parametric kernel estimation error tends to zero. This paper discusses three estimates of implied volatility, through numerical simulations show that the standard of mean square error, the nonparametric kernel estimation error for implied volatility to a minimum. In addition, we study the problem of option pricing error. Select the 2011 January-September actual transactions of S & P 500 Index Options in the empirical analysis, then given the option pricing error.Using the method of least squares estimation theory and the actual market price options price options were fitting, given the mathematical expressions and characteristics of both the pricing error probability, which characterizes the market price of the option, we have the nonparametric kernel estimation of the option price by nonparametric kernel estimation method. The empirical analysis showed that the mean square error standard, the option pricing nonparametric kernel estimation error is minimized in the sample, nonparametric kernel estimate of the option price formula than to get closer to the market price options.