Ito Process Theory And Its Application In Finance

Brownian movement refers to an unrelated random walk, the Brownian motion associated with stock price behavior, and then establish the mathe-matical model of the wiener process is a significant financial innovation of this century,which plays an important role in the modern financial mathematics.So far,the prevailing view still thinks that the stock market is random fluctua-tions,random fluctuations is the most fundamental characteristics in the stock market,is the norm of the stock market.Brownian motion assumption is the core assumption of modern capital market theory.Modern economists often use Ito process mathematical model to describe the stock price movements,so the detailed study on the Brownian motion and Ito process is very meaningful.This paper is divided into the following five parts to research the Stochas-tic Processes theory and its application in Finance. The stochastic processes this paper involves are Ito diffusion processes we often see. The first part is the introduction, it mainly includes the basic background.basic knowl-edge,significance of the topic,literature review, etc of writing this article.The second part is mainly making some monte carlo simulations and statistical inference studies on several common forms of Ito diffusion process.Here from easy to difficult,I respectively make monte carlo simulations and statistical in-ference studies from Brownian motion, Ito process with constant drift rate and volatility, Ito process with linear drift rate and volatility (that is, we often say the geometric Brownian motion),the general form of Ito process (includ-ing the O-U process).In this paper, the mainly tool I use is matlab,the main statistical inference include parameter estimation, comparative analysis, nor-mality tests, etc. The third part mainly elaborates the Ito diffusion process’s simple applications on stock price simulation and prediction with practical ex-amples.Here in the simulation and prediction of the stock price, assuming the stock price follows geometric Brownian motion fluctuation.Through simulation and prediction, we find Ito diffusion process has certain practical significance and value.The fourth part discusses the stock price fluctuation follows index O-U process stochastic model,and strictly calculates the stock price expression when stock price fluctuation follows index O-U process,and discusses the s-tock option pricing problem under the model of index O-U process.In the fifth part,I summarize the whole article,reflect the shortage and prospect the future research.