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在传统的期权定价理论中,我们需要假设股票价格行为在短期服从于几何布朗运动,以此为基础我们发展出了Black-Scholes等期权定价公式。但现实中股票价格是否真能如假设一样服从几何布朗运动?本文利用2012年11月29日至2013年11月29日的上证综指每日数据,采用蒙特卡罗模拟法进行分析,通过比较在几何布朗运动情况下股票价格的模拟值和现实中股票价格行为的拟合优度,判断现实生活中股票价格行为是否服从几何布朗运动。利用线性回归方程对模型进行修正,进一步判断模拟结果的拟合情况。
In the traditional option pricing theory, we need to assume that the stock price behavior obeys the geometric Brownian motion in the short run. Based on this, we develop the Black-Scholes option pricing formula. However, in reality, can the stock price really follow the geometric Brownian motion as hypothesized? Using the daily data of Shanghai Stock Exchange from November 29, 2012 to November 29, 2013, the paper uses the Monte Carlo simulation method to analyze, Geometric Brownian motion stock price simulation value and the reality of the stock price behavior goodness of fit to determine the real life behavior of the stock price obeys the geometric Brownian motion. The linear regression equation was used to modify the model to further determine the fitting results of the simulation results.