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Stochastic Percolation Stock Price Modeling and Option Price Research

Author: DingRong
Tutor: WangJun
School: Beijing Jiaotong University
Course: Probability Theory and Mathematical Statistics
Keywords: Long-range seepage Compound Poisson process Stock price Option Pricing Black-Scholes formula
CLC: F830.91
Type: Master's thesis
Year: 2010
Downloads: 62
Quote: 0
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Abstract


The traditional theory is that the process is similar to a Gaussian distribution in a stock market , stock prices and stock index gains . However, recent empirical studies have shown that the distribution of the proceeds of the price of financial time series generally obey center the Levi distribution and demonstrate the nature of the \In this article , we will Statistical physics percolation theory is applied to the stock market , stock price , research , simulation and analysis , and study the corresponding European option pricing problem . We consider a stock price model includes two groups of investors in group A and group B . A group of investors is seen as institutional investors , they are very sensible , manifested in the use of historical data and the analysis of investment strategies to determine the direction of their investment , their investment behavior will make the stock price movements obey Black.Scholes formula Kt = ( ? ) uA ( t ) dt ( ? ) σ (t) dB ( t) ; B group of investors as retail investors , and they get the information from a long-range percolation model and completely follow investment trends in the market investment , which will cause a stock price fluctuations . Stock price will appear in their investment behavior under the influence of a line with a compound Poisson process jumps (? =) (?) Hiμ. In the process of the research option pricing problem , we will combine the part we get a compound Poisson process jump stock price model gives a reasonable no-arbitrage price formula .

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CLC: > Economic > Fiscal, monetary > Finance, banking > Finance, banking theory > Financial market > Securities market
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