A New Method To Test Diffusion Process And Its Applications In Stock And Spot Rate Market

Before we price the derivatives, we must know the processes that underlying assets follow, such as pricing the option and interest derivatives. If we give the incorrect processes that the underlying assets follow, we will obtain the incorrect prices and may encounter big loss in financial risk management practice, and lead to the inconsistent estimates of parameters and variance-covariance matrix. Then we will have incorrect test results in empirical work. We should according to the real data's features to choose processes the underlying assets follow without the economical theories. That is to say we need a statistical view to think about this problem.In this paper I obtain a formal method which is based on the nonparametric density estimation and nonparametric regression to test whether the financial data come from the generalized diffusion process which has no parameters in the differential equation. Our method is used to test not only the stock market data, but also the spot rate market data conveniently. And I use this method to get the results that Shangzheng index log price daily data, S&P500 log price index intraday data, 7days Eurodollar rate daily data and the 1 year Chinese inter-bank interest rate daily data do not follow a diffusion process without a jump.