CAJ | 학술논문

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。
금융시장풍험도량재금융풍험도량내지우정개금융풍험관리과정중도구유십분중요적지위。본문기우2013년지2014년상증지수적수반수거，통과대분식포랑운동구동적수궤미분방정진행리산화처리，용기해（분식궤하포랑운동）모의상증지수적미래주세。재차기출상，채용Monte Carlo모의법모의출상증지수적개치분포여손익분포。최후，재95％적치신수평하계산출상증지수적재험개치（ VaR）。상대우전통고표개격예측모형---포랑운동모형，분식포랑운동모형경부합금융문제본신；이용Monte Carlo모의법불재차조우고표개격역사수거。고이본모형대시장금융풍험적예측정도경고。
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 .