Analytical Valuation of Contingent Claims by Stochastic Interacting Systems for Stock Market

Abstract

In the present paper, by applying the theory of stochastic processes and interacting particle systems and models, including stopping time theory and stochastic voter model, we model a financial stock price model that contains two types of investors, and we use this financial model to describe the behavior and fluctuations of a stock price process in a stock market. In the financial model, besides the professional investors, we also consider the general investors or nonprofessional investors, where the stopping time and the voter model are applied to model and study the statistical properties of investment of the nonprofessional investors. By using the stochastic methods of statistical analysis, we show that the probability distribution of the normalized random price process for this financial model converges to the corresponding distribution of the Black-Scholes model. Further, we discuss the valuation and hedging of European contingent claims for this price process model.