Nonparametric Estimation Of Drift And Volatility Functions In Stochastic Diffusion Models

With the development of society and economy, in order to meet customers'demands and facilitate financial markets, a large number of financial derivatives have been introduced to gradually our financial markets. For the purpose of describing, pricing, managing and controlling these financial derivatives, economic and financial researchers proposed some stochastic diffusion models under different conditions. Once a model for the dynamics of underlying state variables is given, the determination of parameters of a model is directly related to asset pricing, portfolio management, securities regulation, proprietary trading, financial consulting and risk management and it is an important factor, and it is considered as the object of study. Drift parameters and volatility parameters are the basic parameters of the stochastic diffusion models. Accurate asset pricing and true reflection depends on the determination of parameters and its structure. Their research on the financial markets has important significance.This dissertation studied drift function (parameter) and volatility function (parameter) of the stochastic diffusion models in financial derivatives. Firstly, we introduce some models, which are frequently used to model asset prices; sampling methods and the nonparametric techniques in financial econometrics in the applications. Then, one proposed respectively the adaptive nonparametric estimation methods to the drift function (parameter) and volatility function (parameter)-dynamically integrated method base on time and state domains, which different from the old ones. And we discuss deeply the existed estimation methods of the functions and the forms of structure. Furthermore asymptotic properties of estimators under reasonable assumptions are established. By simulations and compared with previous estimation methods, we found that our proposed methods possessed a certain superior performance. Finally, we give the results of related study and the existing problems. In this paper, the results have a certain practical value and research value for asset description, pricing, management.