Market Volatility Based On Option Prices Is Estimated

The volatility is a very important variable in finance due to its application in investment portfolio,asset pricing and risk management.The subject of statistical inference for volatility which presented to the traditional Black-Scholes formula and new-style American option pricing formula has been and is still of considerable interest due to its application in finance.In this Paper,we first review some research on volatility estimation,then we give a new way of implied volatility estimation,in virtue of nonparametric fitting.Compare to the traditional implied volatility estimating,the new method is much more simple to carry out and have a good precision.For this reason, it is necessary to study here.In the paper below,we first review the fruit of American option pricing and volatility estimation both in theory and applications,then discussed the nonparametric estimation problem on implied volatility.The thesis is divided into two parts:In chapter 2 we discussed the way of how to get the implied volatility of American options,of which the underlying asset could be either non-dividends-paying stock or dividends-paying stock. We also discussed some classic method of nonparametric estimation.Through the disposal of the time parameter,the 2-dimentional estimation problem became a 1-dimentional one.We applied the local polynomial fitting on it and achieved the estimation of implied volatility.Further more we give the asymptotic normality and consistency of it.In chapter 3,we tested our techniques by simulating some option datas which we get from NASDAQ stock market and obtained the good results, then applied it to option pricing problem,which can show its advantage.