基于统计模拟法的上证综指定价及VaR估算

发布时间：2018-04-04 19:23

本文选题：分式布朗运动　切入点：VaR　出处：《兰州商学院》2014年硕士论文

【摘要】：随着金融市场的不断发展，金融产品的逐渐增多，金融产品的交易量也增多，同时金融数据也呈爆炸式增长。要研究金融问题，最好分析天量的金融数据。因此，在金融领域中，统计模拟技术被更多的应用。它用机理上模拟实际的金融系统，从而使复杂的金融系统建模得到实现。经典的投资组合理论假定股价服从布朗运动模型。这种假定无法解释股票的价格波动具有的自相似性、长相依性等特征。实证表明，分式布朗运动的许多性质能很好的解释金融市场的变化。本文对统计模拟算法中使用最为广泛的Monte Carlo模拟法进行了研究和改进，建立了基于Monte Carlo模拟法的金融资产定价模型、金融风险管理模型。 Monte Carlo模拟法在金融资产定价方面的应用，本文引入了能较好解释金融市场变化的分式布朗运动。分别用布朗运动模型、随机表示法估计的分式布朗运动模型、谱密度法估计的分式布朗运动模型和改进的Monte Carlo模拟法估计了上证综指的收盘价，，并对六种模型模拟结果进行了比较。在分式布朗运动模型的计算过程中，采用随机表示法和谱密度法对模型进行离散化处理。 Monte Carlo模拟法在金融风险管理中的应用，本文将Monte Carlo模拟法应用在股票市场的风险价值估算上，分别用对上证综指定价效果较好的模型对上证综指的VaR进行了估算。
[Abstract]:With the development of financial market and the increasing of financial products, the trading volume of financial products is also increasing, and the financial data is also increasing explosively.To study financial problems, it is best to analyze the amount of financial data.Therefore, in the field of finance, statistical simulation technology has been more and more applied.It uses the mechanism to simulate the actual financial system, so that the complex financial system modeling can be realized.Classical portfolio theory assumes that stock prices are convinced by Brownian motion models.This assumption cannot explain the characteristics of stock price volatility such as self-similarity and long-dependence.Empirical results show that many properties of fractional Brownian motion can explain the change of financial market.In this paper, the Monte Carlo simulation method, which is widely used in statistical simulation algorithm, is studied and improved, and the financial asset pricing model and financial risk management model based on Monte Carlo simulation method are established.In this paper, the fractional Brownian motion which can explain the change of financial market is introduced.The closing price of Shanghai Composite Index is estimated by the Brownian motion model, the fractional Brownian motion model estimated by stochastic representation, the fractional Brownian motion model estimated by spectral density method and the improved Monte Carlo simulation method.The simulation results of six models are compared.In the calculation of fractional Brownian motion model, the stochastic representation method and spectral density method are used to discretize the model.The application of Monte Carlo simulation method in financial risk management. In this paper, Monte Carlo simulation method is applied to estimate the value of risk in the stock market, and the VaR of Shanghai Composite Index is estimated by using the model with good pricing effect.
【学位授予单位】：兰州商学院
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：F832.51;F224

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