JOURNAL OF COMPUTERS (JCP)
ISSN : 1796-203X
Volume : 3    Issue : 12    Date : December 2008

Analytical Valuation of Contingent Claims by Stochastic Interacting Systems for Stock Market
Jun Wang, Qiuyuan Wang, and Jiguang Shao
Page(s): 3-10
Full Text:
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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.

Index Terms
interacting particle systems, stochastic processes, stock price model, fluctuation, European
contingent claims, valuation, hedging