The Behavior of Stock Prices and Valuation by Continuum Percolation Theory

We investigate the statistical properties of fluctuations of the stock price process in a stock market by continuum percolation theory. The methods of continuum percolation are applied to construct a financial model that describes the behavior of a stock price, specifically the continuum percolation is used to describe the "herd effect" of investors in a financial market. In this paper, we show that the characteristic function of this stock price process converges to the corresponding characteristic function of Black-Scholes model. Further, we discuss the valuation and hedging of European contingent.