Applications of randomized low discrepancy sequences to the valuation of complex securities

This paper deals with a recent modification of the Monte Carlo method known as quasi-random Monte Carlo. Under this approach, one uses specially selected deterministic sequences rather than random sequences as in Monte Carlo. These special sequences are known as low discrepancy sequences and have the property that they tend to be evenly dispersed throughout the unit cube. For many applications in finance, the use of low discrepancy sequences seems to provide more accurate answers than random sequences. One of the main drawbacks of the use of low discrepancy sequences is that there is no obvious method of computing the standard error of the estimate. This means that in performing the calculations, there is no clear termination criterion for the number of points to use. We address this issue here and consider a partial randomization of Owen's technique for overcoming this problem. The proposed method can be applied to much higher dimensions where it would be computationally infeasible for Owen's technique. The efficiency of these procedures is compared using a particular derivative security. The exact price of this security can be calculated very simply and so we have a benchmark against which to test our calculations. We find that our procedures give promising results even for very high dimensions. Statistical tests are also conducted to support the confidence statement drawn from these procedures.     

基于二元GARCH方法对我国国债市场的分割性检验

我国的国债市场目前尚处于分割状态,本文从市场之间信息流动的角度出发,构建二元GARCH模型对我国两个国债交易市场之间的波动溢出效应进行研究,发现银行间市场与交易所市场存在稳定的一阶矩长期关系及二阶矩的双向信息流动;并构造时变的条件相关系数对市场一体化程度进行分析,发现总体上两市场一体化程度较差,在检验期末的时段,相关系数开始呈现上升趋势。这一结果更多地归因于两市场跨市交易品种较少、投资者结构的差异以及现行的转托管制度。     

Portfolio optimization based on GARCH-EVT-Copula forecasting models

This study uses GARCH-EVT-copula and ARMA-GARCH-EVT-copula models to perform out-of-sample forecasts and simulate one-day-ahead returns for ten stock indexes. We construct optimal portfolios based on the global minimum variance (GMV), minimum conditional value-at-risk (Min-CVaR) and certainty equivalence tangency (CET) criteria, and model the dependence structure between stock market returns by employing elliptical (Student-$t$ and Gaussian) and Archimedean (Clayton, Frank and Gumbel) copulas. We analyze the performances of 288 risk modeling portfolio strategies using out-of-sample back-testing. Our main finding is that the CET portfolio, based on ARMA-GARCH-EVT-copula forecasts, outperforms the benchmark portfolio based on historical returns. The regression analyses show that GARCH-EVT forecasting models, which use Gaussian or Student-$t$ copulas, are best at reducing the portfolio risk.     

Analytic moments for GJR-GARCH (1, 1) processes

For a GJR-GARCH(1, 1) specification with a generic innovation distribution we derive analytic expressions for the first four conditional moments of the forward and aggregated returns and variances. Moments for the most commonly used GARCH models are stated as special cases. We also derive the limits of these moments as the time horizon increases, establishing regularity conditions for the moments of aggregated returns to converge to normal moments. A simulation study using these analytic moments produces approximate predictive distributions which are free from the bias affecting simulations. An empirical study using almost 30 years of daily equity index, exchange rate and interest rate data applies Johnson SU and Edgeworth expansion distribution fitting to our closed-form formulae for higher moments of returns.     

The ZD-GARCH model: A new way to study heteroscedasticity

This paper proposes a first-order zero-drift GARCH (ZD-GARCH(1, 1)) model to study conditional heteroscedasticity and heteroscedasticity together. Unlike the classical GARCH model, the ZD-GARCH(1, 1) model is always non-stationary regardless of the sign of the Lyapunov exponent ${\gamma }_0$, but interestingly it is stable with its sample path oscillating randomly between zero and infinity over time when ${\gamma }_0=0$. Furthermore, this paper studies the generalized quasi-maximum likelihood estimator (GQMLE) of the ZD-GARCH(1, 1) model, and establishes its strong consistency and asymptotic normality. Based on the GQMLE, an estimator for ${\gamma }_0$, a $t$-test for stability, a unit root test for the absence of the drift term, and a portmanteau test for model checking are all constructed. Simulation studies are carried out to assess the finite sample performance of the proposed estimators and tests. Applications demonstrate that a stable ZD-GARCH(1, 1) model is more appropriate than a non-stationary GARCH(1, 1) model in fitting the KV-A stock returns in Francq and Zakoïan (2012).     

Evaluating GARCH models

In this paper, a unified framework for testing the adequacy of an estimated GARCH model is presented. Parametric Lagrange multiplier (LM) or LM type tests of no ARCH in standardized errors, linearity, and parameter constancy are proposed. The asymptotic null distributions of the tests are standard, which makes application easy. Versions of the tests that are robust against nonnormal errors are provided. The finite sample properties of the test statistics are investigated by simulation. The robust tests prove superior to the nonrobust ones when the errors are nonnormal. They also compare favourably in terms of power with misspecification tests previously proposed in the literature.     

The time-varying correlation between output and prices in the United States over the period 1800–2014

In this study, we examine the time-varying correlations between output and prices, while controlling for the impact of the monetary policy stance and output and inflation uncertainties over the period 1800–2014. The results of the empirical analysis reveal that the dynamic correlations of output and prices were typically negative, suggesting a countercyclical behaviour of prices, apart from the early 1840s and from the beginning until the middle of the 20th century, when the correlation was positive, indicating a procyclicality of prices. A historical decomposition analysis based on a sign-restricted structural vector autoregressive model is able to relate the procyclical and countercyclical behaviour to the predominance of aggregate supply and aggregate demand and/or monetary policy shocks, respectively. Moreover, inflation uncertainty (monetary policy stance) was found to have a positive (negative) effect on inflation over the last 215 years.     

实物期权方法在科技评价中的应用

本文通过对科技评价现状以及科技项目特殊性的分析，提出出于提高科技评价水平的目的，现实要求必须选取一个更加客观的标准和评价方法来对科技进行评价，并实现对科技项目更加优化的监督和管理。考察各种投资评价工具可以发现，实物期权概念的引入可以很好地实现这几个功能。本文将通过对北京市科委提供的一个真实科技项目，使用实物期权的方法进行评价来具体说明应该如何使用此方法进行科技评价，以便使读者对应用实物期权方法进行科技评价的过程有一个更为清晰和直观的认识。     

关于企业价值的内涵极其评估方法

对价值与企业价值的内涵进行分析,认为企业价值是企业现有基础上的获利能力与潜在的获利能力之和,对目前比较流行的评估方法进行分析,得出收益现值法是最能体现公允价值的一种评估方法。     

MEASURING RISK IN ENVIRONMENTAL FINANCE

Abstract.  Environmental sustainability indices, such as the Dow Jones Sustainability Indexes and the Ethibel Sustainability Index, quantify the development and promotion of sustainable social, ethical and environmental values in the community. Moreover, such indices provide a benchmark for managing sustainability portfolios, and developing financial products and services that are linked to sustainable economic, environmental, social and ethical criteria. This paper reviews the existing data and risk indices in environmental finance. The main purpose of the paper is to analyse existing sustainability and ethical indices in environmental finance, and evaluate empirical environmental risk by estimating conditional volatility clustering that is inherent in these indices. Financial volatility models are estimated to analyse the underlying conditional volatility or time-varying risk that is inherent in alternative environmental sustainability indices. Volatility clustering is observed for most series, but some extreme observations are also evident. The log- and second-moment conditions suggest that valid inferences can be drawn for purposes of sensible empirical analysis.     

条件自回归极差模型与波动率估计

无论是在理论研究领域还是在应用领域,波动率的预测已经成为现代金融经济学和金融工程的重要课题。Chou（2005）针对极差提出了条件自回归极差模型（CARR）。本文在Parkinson（1980）的基础上,对极差作出了一个简单的修正,使得相应的CARR模型成为标准差的动态模型;然后以上证指数2001年4月27日至2005年12月5日的周收益率数据为样本,采用滚动样本的方法,利用CARR模型和GARCH模型分析了样本数据,作出了上证指数波动率样本外1至8周的预测,在多种事后波动率的测度下比较了修正后的CARR模型与GARCH模型对上证指数波动率的预测能力,证实了CARR模型在理论上的有效性。     

对中国股市有效性及波动性的实证检验

利用最近几年的数据和EVIEWS软件分析了中国证券市场的有效性及波动性,使用经典线性回归方程做了时间序列回归和横截面回归。并且依次放松假设,采用WHITE检验和Glejser检验分析了股票收益率的异方差问题;采用DW检验及Breusch-Godfrey检验分析了股票收益率的自相关问题等;还采用DF检验了时间序列的平稳性。接着对股市的弱式有效假说予以检验,最后使用ARCH、GARCH模型对我国股市做波动性检验。