Analytical Valuation of Contingent Claims by Stochastic Interacting Systems for Stock Market
Analytical Valuation of Contingent Claims by Stochastic Interacting Systems for Stock Market
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DOI：
10.4304/jcp.3.12.3-10
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发表时间：
2008-01
期刊：
影响因子：
--
通讯作者：
J. Wang;Qiuyuan Wang;J. Shao
中科院分区：
文献类型：
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作者：
J. Wang;Qiuyuan Wang;J. Shao
本文应用随机过程理论和相互作用的粒子系统和模型，包括停止时间理论和随机投票者模型，建立了一个包含两类投资者的金融股票价格模型，并用这个金融模型来描述股票市场中股票价格过程的行为和波动。在金融模型中，除了考虑专业投资者外，还考虑了普通投资者和非专业投资者，其中利用停止时间和投票者模型对非专业投资者的投资统计特性进行了建模和研究。利用统计分析的随机方法，我们证明了该金融模型的归一化随机价格过程的概率分布收敛于Black-Scholes模型的相应分布。进一步，我们讨论了该价格过程模型下欧式未定权益的估值和套期保值问题。
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.