基于时变Copula模型的 基金收益率相依关系的应用研究

基于时变Copula模型,获得预测方差,确定单个基金收益率序列的边缘分布.利用常见的静态Copula和时变Copula模型对基金收益率序列间两两相依关系进行建模并进行对比分析.应用研究表明,基于MCMC方法的时变Copula模型能更有效地度量基金收益率序列的风险.     

双曲分布及其在VaR模型分析中的应用

传统的计算V aR的R iskM etrics方法不能对市场风险分布的“厚尾”现象给出较为满意的刻画和计算方法.本文引入双曲分布及其算法并将双曲分布应用到V aR模型的计算之中,事实上通过对股票市场的实证研究表明,股票市场数据呈厚尾现象,用双曲分布对数据的拟合要比R iskM etrics方法假定的正态分布更符合金融市场数据的实际情况,故本文的结论与方法对金融风险管理和其他金融建模是有价值的.     

基于Copula的金融资产相关结构建模

分析了几种相关结构函数(Copula)表示的相关结构模型,给出了用相关结构函数对金融资产间的相关结构进行建模的方法.结果表明混合Gumbel(M-Gumbel)相关结构函数能较全面地描述上海深圳两证券指数的相关结构,模拟计算VaR的结果支持了实证分析的结论.     

用VaR度量石油市场的极端风险

本文采用2001年11月到2005年6月国内原油价格的调度数据,运用基于GED分布的GARCH模型度量了国内油市的极端上涨和极端下跌时的VaR,得到如下两点结论：第一,国内油市存在ARCH in Mean 效应,表明收益与风险是正相关的,同时也意味着国内油市违背了有效市场假说,进一步的分析表明国内原油的定价机制和流通体制是造成市场非有效的主要原因;第二,上涨风险的平均水平要高于下跌风险的平均水平,这是石油市场供需双方的非对称市场地位决定的,石油生产者可以利用市场势力和上下游一体化的组织形式,将部分下跌风险转嫁给石油需求者,而石油需求者则缺少有效的措施来应对油价上涨.     

CreditRisk+模型下商业银行经济资本配置研究

对金融资产风险的度量与经济资本的分配应该体现分散化效应,传统的V aR方式不能保证分散化效应的次可加性.本文讨论了基于T a ilV aR这一新的风险度量与经济资本分配标准,并在违约率均值不变情况下,对C red itR isk+模型下的商业银行经济资本分配进行了实证分析.     

泰勒定理的妙用

论述泰勒定理在不等式证明、行列式计算、定积分计算及金融数学债券定价中的应用.     

Modelling Operational Risk Losses with Graphical Models and Copula Functions

The management of Operational Risk has been a difficult task due to the lack of data and the high number of variables. In this project, we treat operational risks as multivariate variables. In order to model them, copula functions are employed, which are a widely used tool in finance and engineering for building flexible joint distributions. The purpose of this research is to propose a new methodology for modelling Operational Risks and estimating the required capital. It combines the use of graphical models and the use of copula functions along with hyper-Markov law. Historical loss data of an Italian bank is used, in order to explore the methodology’s behaviour and its potential benefits.      

Theta series and trace operators for Г<Subscript>n</Subscript>[q]

We consider the action of suitable trace operators on non homogeneous theta series that are Siegel modular forms for the principal congruence subgroups of the symplectic group of odd levelq: Г _n [q]. This is used for investigating whether modular forms forГ _n [N], withN|q, which are linear combination of such theta series, can be expressed as combination of theta series that are modular forms with respect toГ _n [N].     

Conditional VaR estimation using Pearson’s type IV distribution

This paper presents a new value at risk (VaR) estimation model for equity returns time series and tests it extensively on Stock Indices of 14 countries. Two most important stylized facts of such series are volatility clustering, and non-normality as a result of fat tails of the return distribution. While volatility clustering has been extensively studied using the GARCH model and its various extensions, the phenomenon of non-normality has not been comprehensively explored, at least in the context of VaR estimation. A combination of extreme value theory (EVT) and GARCH has been explored to analyze financial data showing non-normal behavior. This paper proposes a combination of the Pearson’s Type IV distribution and the GARCH (1, 1) approach to furnish a new method with superior predictive abilities. The approach is back tested for the entire sample as well as for a holdout sample using rolling windows.     

Local Theory of Primitive Theta Functions

We study primitive theta functions, which were first introduced by Shintani, in a purely local setting. We investigate a metaplectic representation of U(1) acting on the space of local primitive theta functions and give its explicit irreducible decomposition. As a by-product, we give a new proof of epsilon dichotomy for (U(1),U(1)).