Optimal investment under multi-factor stochastic volatility

We consider a model for multivariate intertemporal portfolio choice in complete and incomplete markets with a multi-factor stochastic covariance matrix of asset returns. The optimal investment strategies are derived in closed form. We estimate the model parameters and illustrate the optimal investment based on two stock indices: S&P500 and DAX. It is also shown that the model satisfies several stylized facts well known in the literature. We analyse the welfare losses due to suboptimal investment strategies and we find that investors who invest myopically, ignore derivative assets, model volatility by one factor and ignore stochastic covariance between asset returns can incur significant welfare losses.     

Elliptical families and copulas: tilting and premium; capital allocation

Elliptical copula measures with symmetrical marginals are proposed as a natural generalization of the elliptical family, which preserves the symmetrical character of marginals, but is more flexible in the choice of their shape parameters. The properties of these copulas are investigated and the elliptical copula tilting and corresponding premium are proposed as a natural tool for portfolio capital allocation. For the case of the multivariate normal family, such a tilting and premium coincide with the Esscher transform and premium.     

基于分层条件Copula的金融危机传染路径研究

本文采用分层条件Copula理论来研究次贷危机和欧债危机下的危机传染路径问题。在研究中采用t-GARCH (1,1)模型拟合各个金融市场的股指日收益率,以条件Copula分析两次危机下中国大陆股市与美国股市、英国股市、日本股市、台湾股市、香港股市2005年1月至2012年7月间的风险传染关系。实证研究表明：次贷危机期间美国股票市场将危机传染到香港股票市场,再由香港股票市场传染其他亚洲股票市场。而在欧债危机期间英国股票市场分别直接传染美国股票市场和香港股票市场,再通过香港股票市场对其他亚洲股票市场传染。两次危机下香港股票市场均是亚洲股票市场受到危机传染的媒介,因此我国在制定防范金融危机传染政策时应考虑对香港股票市场的控制,在传播层面上控制金融危机对我国的传染,减少对我国金融系统的冲击。     

Multivariate continuous-time modeling of wind indexes and hedging of wind risk

With the introduction of the exchange-traded German wind power futures, opportunities for German wind power producers to hedge their volumetric risk are present. We propose two continuous-time multivariate models for wind power utilization at different wind sites, and discuss the properties and estimation procedures for the models. Applying the models to wind index data for wind sites in Germany and the underlying wind index of exchange-traded wind power futures contracts, the estimation results of both models suggest that they capture key statistical features of the data. We show how these models can be used to find optimal hedging strategies using exchange-traded wind power futures for the owner of a portfolio of so-called tailor-made wind power futures. Both in-sample and out-of-sample hedging scenarios are considered, and, in both cases, significant variance reductions are achieved. Additionally, the risk premium of the German wind power futures is analysed, leading to an indication of the risk premium of tailor-made wind power futures.     

Modelling multivariate moments in European Stock Markets

This research extends the results of Mauleón and Perote, and derives analytically a general framework for the multivariate Edgeworth Sargan (ES) density. Its capability to account for multivariate moments beyond correlation is shown–mainly, co-skewness, co-kurtosis and co-volatility. The multivariate ES is then fitted to the residuals of a VAR model applied to three European stock market series of daily data (FTSE, DAX, CAC40), accounting for univariate as well as multivariate departures from normality. The complete model – with nearly 60 parameters – is set up and estimated jointly by maximum likelihood. Two alternative multivariate probability density functions, student's t and the normal skewed, are also estimated and compared to the ES. The empirical results show: (1) in spite of the high nonlinearity and complexity of the model, it is feasible to fit it to empirical data; (2) statistically significant multivariate effects, other than correlations, are found, and (3) the tail fit of the ES is significantly better.     

A multivariate jump-driven financial asset model

We discuss a Lévy multivariate model for financial assets which incorporates jumps, skewness, kurtosis and stochastic volatility. We use it to describe the behaviour of a series of stocks or indexes and to study a multi-firm, value-based default model. Starting from an independent Brownian world, we introduce jumps and other deviations from normality, including non-Gaussian dependence. We use a stochastic time-change technique and provide the details for a Gamma change. The main feature of the model is the fact that—opposite to other, non-jointly Gaussian settings—its risk-neutral dependence can be calibrated from univariate derivative prices, providing a surprisingly good fit.     

A supermartingale relation for multivariate risk measures

The equivalence between multiportfolio time consistency of a dynamic multivariate risk measure and a supermartingale property is proven. Furthermore, the dual variables under which this set-valued supermartingale is a martingale are characterized as the worst-case dual variables in the dual representation of the risk measure. Examples of multivariate risk measures satisfying the supermartingale property are given. Crucial for obtaining the results are dual representations of scalarizations of set-valued dynamic risk measures, which are of independent interest in the fast growing literature on multivariate risks.     

CDO pricing with nested Archimedean copulas

Companies in the same industry sector are usually more correlated than firms in different sectors, as they are similarly affected by macroeconomic effects, political decisions, and consumer trends. Despite the many stock return models taking this fact into account, there are only a few credit default models that take it into consideration. In this paper we present a default model based on nested Archimedean copulas that is able to capture hierarchical dependence structures among the obligors in a credit portfolio. Nested Archimedean copulas have a surprisingly simple and intuitive interpretation. The dependence among all companies in the same sector is described by an inner copula and the sectors are then coupled via an outer copula. Consequently, our model implies a larger default correlation for companies in the same industry sector than for companies in different sectors. A calibration to CDO tranche spreads of the European iTraxx portfolio is performed to demonstrate the fitting capability of the model. This portfolio consists of CDS on 125 companies from six different industry sectors and is therefore an excellent portfolio for a comparison of our generalized model with a traditional copula model of the same family that does not take different sectors into account.     

多元统计分析方法在钛白粉生产水解工序能力评价中的应用研究

硫酸法钛白粉生产中水解工序具有三个基本质量特性且相互有一定相关性,因而对水解工序不能直接进行一元工序能力指数有效评价。本文首次采用多元统计分析的方法解决了在钛白粉生产的水解工序实例中进行多元工序能力指数综合评价的问题,不仅为出入境检验检疫机构日常监管出口钛白粉分类管理企业的关键过程,提出了一种客观科学的评价方法,而且为企业加强水解工序的工艺指导和自我质量控制提供了依据。