分式布朗运动模型下的金融市场风险度量——以上证指数为例

Financial Market Risk Measurement in Fractional Brownian Motion Model——A case study of Shanghai composite index

金融市场风险度量在金融风险度量乃至于整个金融风险管理过程中都具有十分重要的地位。本文基于2013年至2014年上证指数的收盘数据,通过对分式布朗运动驱动的随机微分方程进行离散化处理,用其解(分式几何布朗运动)模拟上证指数的未来走势。在此基础上,采用Monte Carlo模拟法模拟出上证指数的价值分布与损益分布。最后,在95%的置信水平下计算出上证指数的在险价值(VaR)。相对于传统股票价格预测模型——布朗运动模型,分式布朗运动模型更符合金融问题本身;利用Monte Carlo模拟法不再借助于股票价格历史数据。故而本模型对市场金融风险的预测精度更高。

Financial market risk measurement in financial risk measurement and even the entire process of financial risk management , has the very important position .In this paper , based on the closing data of Shanghai composite index , we discretize the stochastic differential equation driven by frational Brownian motion and use its solution to simulate the index movement in the future .On this basis,simulate value dis-tribution of the index ,and profit and loss ditribution by using Monte Carlo simulation method .Lastly, with the confidence level of 95%,we calculate “Value at Risk”（ VaR） of the index.Compared with tradition-al stock price forecasting model -Brownian motion model , fractional Brownian motion model is more conformed to the financial problem itself;Monte Carlo simulation method is no longer with the aid of the stock price history data , so in this paper , the market of financial risk prediction accuracy is higher .