Singular mixture copulas

We present a new family of copulas??the Singular Mixture Copulas. We begin with constructing singular copulas whose supports lie on the graphs of two given quantile functions. These copulas are then mixed with respect to a continuous distribution resulting in a nonsingular parametric copula. The Singular Mixture Copulas we construct have a Lebesgue density and a closed form representation. Moreover, they have positive lower and upper tail dependence. As an application we fit the copulas to flood level data. As the results show Singular Mixture Copulas provide an alternative to elliptical copulas, e.g., Gaussian and t-copulas, in modeling strongly dependent random variables.     

Recovering copulas from limited information and an application to asset allocation

This paper proposes an entropy-based method to construct a new class of copulas - the most entropic canonical copulas (MECC). Our empirical study focuses on an investment problem for an investor with a constant relative risk aversion (CRRA) utility function allocating wealth between the Dow Jones Large-Cap and Small-Cap indices, of which the contemporaneous dependence can be modeled by the MECC or other commonly-used copulas. Both the theoretical analysis of the method and the empirical study indicate the potential for enormous statistical and economic gains as a result of using the MECC.     

Smooth nonparametric Bernstein vine copulas

We consider the problem of accurately modelling the distribution of the market risk of a multivariate financial portfolio. We employ a multivariate GARCH model in which the dependence structure between the assets is modelled via a vine copula. We address the problem of how the parametric pair-copulas in a vine copula should be chosen by proposing to use nonparametric Bernstein copulas as bivariate pair-copulas. An extensive simulation study illustrates that our smooth nonparametric vine copula model is able to match the results of a competing parametric vine model calibrated via Akaike’s Information Criterion while at the same time significantly reducing model risk. Our empirical analysis of financial market data demonstrates that our proposed model yields Value-at-Risk forecasts that are significantly more accurate than those of a benchmark parametric model.     

Measuring financial risks with copulas

This paper is concerned with the statistical modeling of the dependence structure of multivariate financial data using the concept of copulas. We select some special copulas and identify the type of dependency captured by each one. We fit copulas to daily returns and simulate from the fitted models. We compare the effect of the choice of copula on risk measures and assess the variability of one-step-ahead predictions of portfolio losses. We analyze extreme scenarios and fit extreme value copulas to the block maxima and minima from daily returns. The stress scenarios constructed are compared to those obtained using models from the extreme value theory. We illustrate the usefulness of the copula approach using two stock market indexes.     

Jackknife empirical likelihood for parametric copulas

For fitting a parametric copula to multivariate data, a popular way is to employ the so-called pseudo maximum likelihood estimation proposed by Genest, Ghoudi, and Rivest. Although interval estimation can be obtained via estimating the asymptotic covariance of the pseudo maximum likelihood estimation, we propose a jackknife empirical likelihood method to construct confidence regions for the parameters without estimating any additional quantities such as the asymptotic covariance. A simulation study shows the advantages of the new method in case of strong dependence or having more than one parameter involved.     

Extreme Value Theory and Archimedean Copulas

Using the language of copulas, we generalize the famous Fisher-Tippett Theorem of extreme value theory to the case with sequences of dependent random variables. The dependence structure is modelled using archimedean copulas. This generalization enables to study the behaviour of the maxima of dependent random sequences.     

Forecasting liquidity-adjusted intraday Value-at-Risk with vine copulas

We propose to model the joint distribution of bid-ask spreads and log returns of a stock portfolio by using Autoregressive Conditional Double Poisson and GARCH processes for the marginals and vine copulas for the dependence structure. By estimating the joint multivariate distribution of both returns and bid-ask spreads from intraday data, we incorporate the measurement of commonalities in liquidity and comovements of stocks and bid-ask spreads into the forecasting of three types of liquidity-adjusted intraday Value-at-Risk (L-IVaR). In a preliminary analysis, we document strong extreme comovements in liquidity and strong tail dependence between bid-ask spreads and log returns across the firms in our sample thus motivating our use of a vine copula model. Furthermore, the backtesting results for the L-IVaR of a portfolio consisting of five stocks listed on the NASDAQ show that the proposed models perform well in forecasting liquidity-adjusted intraday portfolio profits and losses.     

Modeling the leverage effect with copulas and realized volatility

In this paper, we propose the use of static and dynamic copulas to study the leverage effect in the S&P 500 index. Copula models can conveniently separate the leverage effect from the marginal distributions of the return and its volatility. Daily volatility is proxied by a measure of realized volatility, which is constructed from high-frequency data. We uncover a significant leverage effect in the S&P 500 index, and this leverage effect is found to be changing over time in a highly persistent manner. Moreover the dynamic copula models are shown to outperform the static counterparts.     

Multivariate autoregressive modeling of time series count data using copulas

We introduce the Multivariate Autoregressive Conditional Double Poisson model to deal with discreteness, overdispersion and both auto and cross-correlation, arising with multivariate counts. We model counts with a double Poisson and assume that conditionally on past observations the means follow a Vector Autoregression. We resort to copulas to introduce contemporaneous correlation. We apply it to the study of sector and stock-specific news related to the comovements in the number of trades per unit of time of the most important US department stores traded on the NYSE. We show that the market leaders inside a specific sector are related to their size measured by their market capitalization.     

Analysing financial contagion and asymmetric market dependence with volatility indices via copulas

This paper explores the cross-market dependence between five popular equity indices (S&P 500, NASDAQ 100, DAX 30, FTSE 100, and Nikkei 225), and their corresponding volatility indices (VIX, VXN, VDAX, VFTSE, and VXJ). In particular, we propose a dynamic mixed copula approach which is able to capture the time-varying tail dependence coefficient (TDC). The findings indicate the existence of financial contagion and significant asymmetric TDCs for major international equity markets. In some situations, although contagion cannot be clearly detected by stock index movements, it can be captured by dependence between volatility indices. The results imply that contagion is not only reflected in the first moment of index returns, but also the second moment, i.e. the volatility. Results also show that dependence between volatility indices is more easily influenced by financial shocks and reflects the instantaneous information faster than the stock market indices.     

Beneficial changes in random variables via copulas: An application to insurance

A risk-averse agent does not necessarily decrease the optimal insurance whenever a beneficial change in the distribution of final wealth occurs. This paper provides sufficient conditions to guarantee such a decrease. Beneficial changes can be induced by either a beneficial loss-distribution shift, by a modification of the dependence structure between the randomness sources, or by both of these. Conditions for each case are stated. Hadar-Seo and Meyer results turn out as special cases.     

The economic value of range-based covariance between stock and bond returns with dynamic copulas

The covariance between stock and bond returns plays important roles in the setting up of asset allocation strategies and portfolio diversification. In the present study, we propose a multivariate range-based volatility model incorporating dynamic copulas into a range-based volatility model to describe the volatility and dependence structures of stock and bond returns. We then go on to assess the economic value of the covariance forecasts based on our proposed model under a mean-variance framework. The out-of-sample forecasting performance reveals that investors would be willing to pay between 39 and 2081 basis points per year to switch from a dynamic trading strategy under the return-based volatility model to a dynamic trading strategy under the range-based volatility model, with more risk-averse investors being willing to pay even higher switching fees. Furthermore, additional economic gains of between 33 and 1471 annualized basis points are achieved when taking the leverage effect into consideration.     

Sampling from a population in which some units are duplicated and/or overlap

Abstract

In this article we discuss Sirken's multiplicity sampling along lines developed by Goodman in two earlier notes. Sampling from a list in which some units are duplicated appears as a special case.     

基于BSP－HAR－RV模型的最优抽样频率研究

金融高频时间序列数量大、周期短、信息丰富,可以很好地反映金融市场特征。通过绘出平均双幂变差已实现波动率散点图(Bi Powe realized volatility Signature Plot,BSP),建立BSP-HAR-RV模型,改进以往国内通过列举法选择最优频率的方法。最后对TCL集团股票价格的高频数据进行实证分析,验证模型结果 ,并将其在最优频率下得到的HAR-RV模型预测结果与以往广泛使用的5min、10min频率得到的结果进行比较,发现最优抽样频率下模型预测能力较好,具有可行性。     

The dynamic dependence between stock markets in the greater China economic area: a study based on extreme values and copulas

This study employs the dynamic copula method and extreme value theory to investigate the dependence structure between pairs of greater China economic area (GCEA) stock markets consisting of Shanghai (SHSE), Shenzhen (SZSE), Hong Kong (HKSE), and Taiwan (TWSE) stock exchanges from July 2000 to June 2017. We also examine the impact of financial crisis on the dependence structure by considering the global financial crisis and the Chinese stock market crash (2015–2016). Many studies have shown that the benefits of portfolio diversification across the stock markets in the same region could be diminishing. However, it is interesting to see that the diversification benefits appear to be viable for investing in some GCEA pairs of stock markets (SHSE–TWSE and SZSE–HKSE).     

信用评分模型开发中的抽样技术

信用评分是运用数据挖掘技术对已知客户的信息进行分析，建立能预测未来客户信用表现的模型。数据准备是评分模型开发过程中非常重要的步骤，数据质量的好坏直接决定了模型的成败。由于银行内部的数据量非常庞大，为了使分析更加有效率，需要对数据进行抽样。因此，如何进行抽样，如何保证样本能够充分代表总体就非常重要。根据信用评分模型的开发经验以及数据挖掘中的抽样理论，现提出如下建立评分模型时应用的抽样技术以及注意事项。     

Properties of Bias-Corrected Realized Variance Under Alternative Sampling Schemes

In this article I study the statistical properties of a bias-correctedrealized variance measure when high-frequency asset prices arecontaminated with market microstructure noise. The analysisis based on a pure jump process for asset prices and explicitlydistinguishes among different sampling schemes, including calendartime, business time, and transaction time sampling. Two mainfindings emerge from the theoretical and empirical analysis.First, based on the mean-squared error (MSE) criterion, a biascorrection to realized variance (RV) allows for the more efficientuse of higher frequency data than the conventional RV estimator.Second, sampling in business time or transaction time is generallysuperior to the common practice of calendar time sampling inthat it leads to a further reduction in MSE. Using IBM transactiondata, I estimate a 2.5-minute optimal sampling frequency forRV in calendar time, which drops to about 12 seconds when afirst-order bias correction is applied. This results in a morethan 65% reduction in MSE. If, in addition, prices are sampledin transaction time, a further reduction of about 20% can beachieved.     

Modelling Accounting Populations for Ratio Estimation in Audit Sampling

The classical ratio estimator is one of the auxiliary information estimators frequently discussed in the audit sampling literature. The major weakness of this estimator is its unreliability when accounting populations have only one-sided errors or when the error rate is low. Efforts have been made to improve the classical estimator by using techniques such as the Jackknifed ratio discussed by Frost and Tamura (1982). This paper proposes a new method to estimate the population total error based on the ratio of error over book value, i.e., taintings.

The special features of the proposed procedure are that (1) it specifically models the special characteristics of the typical accounting populations, and (2) it is the first study we know of in the audit sampling literature that uses simulation to capture the characteristics of the specific distribution of the estimator each time a confidence interval is constructed. This new approach became possible because of the recent publication of several studies on the empirical characteristics of accounting errors. Results of empirical tests indicate that the proposed method can significantly improve the reliability of the classical ratio under circumstances where the classical ratio needs improvements. Empirical comparisons are also made with a third ratio estimator under dollar-unit sampling. Again, the proposed method provides better reliability.