A matrix exponential multivariate asymmetric stochastic volatility model with realized covariance matrix measurement is proposed. A Bayesian inference method using Markov chain Monte Carlo is developed. A new high-frequency quasi risk factors: market, size, and value factors are calculated using the Tokyo stock market index (TOPIX) size-based sub-indices and style indices.Daily factor series and their realized covariance are calculated and used in our analysis.Proposed three risk factors account for the variation of individual stock returns, and have time-varying volatilities and correlations, and volatility asymmetry.Proposed several models are fit to the proposed risk factors, and the model comparison based on the volatility prediction is conducted. For the latent volatility prediction, the results are consistent with preceding studies about univariate realized stochastic volatility models. The asymmetric covariance structure of the three factors can be shown by the news impact curves.

This article introduces copula-based Markov chain models to be fitted for a serially correlated time series. As their major applications, we also review statistical process control methods under the normal distribution model. We first give a general introduction to copulas and Markov chain models to explain the mathematical properties of copulas for modeling correlated data. Next, we introduce copula-based Markov chain models and various statistical inference procedures, such as the maximum likelihood estimation under the normal distribution model. We provide several real data examples to demonstrate the usefulness of the proposed methods. Appendix contains our R codes for reproducing the data analysis results.

A minimum information copula is a copula that is closest to the independent one under given moment restrictions. The obtained class is interpreted as a copula version of exponential families and is mathematically of interest. In this paper, we review the definition and fundamental properties together with concrete examples. In particular, we overview its relationship with information geometry, matrix scaling and optimal transport theoryvia discrete approximation of copulas. Estimation methods of parameters are also discussed.

In this article, we first review the essence of copula modeling, which became very popular around the beginningof twenty-first century, and take a retrospective glance at its historical development. Then, through examining severalexamples of applications in finance, actuarial science, survival analysis and life testing, we shed light onthe characteristics, and pros and cons of copula modeling. Special emphasis is on its role and criticism against itin the Global Financial Crisis of 2007–2009.

Multivariate extreme value theories are reviewed in the point of view of the intensity of Poisson process of generating the extreme values. Componentwise maxima (CM) have been principally studied in the conventional researches while the multivariate Pareto distribution was derived a quarter century ago to deal with threshold excess multivariate extremes (TEXMEX). It will be found that the essential concepts and perspectives are not yet complete to comprehend the properties of the multivariate extreme value in the practical sense. Thus the mutual connections between CM and TEXMEX are discussed, and it is especially shown not only CM but also TEXMEX employ their own simple distributions to manifest a method of generating their random values simultaneously.

In the risk management of the credit portfolio of a bank, Normal copula is standard for modelling dependencies between each credit in the portfolio. The Normal copula modelling is criticized by the tendency of underestimation of the risk due to its asymptotic independence. This paper analyses the effect of dependence between each extreme value movement in the credit portfolio. First, the relation between the extreme tail dependence or tail asymmetry and the joint default probability is summarized by referring to preceding works on bivariate extreme value. Second, the risk valuation of the credit portfolio and the pricing of CLO tranche are done by simulation where the credit portfolio and the CLO pool consists of 1,000 firms' credit. The simulation results imply the effect of extreme or tail dependence and tail asymmetry in the credit portfolio risk or CLO tranche value through the strength of the joint default probabilities of each pair in the portfolio.

It is often the case, in design of experiments for estimating the models, that we are concerned with optimal allocation of observation points under a given sample size. In particular when experimental domain is the surface or interior of a ball, there have been numerous works concerning designs with a certain rotation equivariance property called rotatability. Rotatable designs and related notions have been extensively and independently studied from the viewpoint of not only design theory but also quadrature theory in numerical analysis and Euclidean design theory in combinatorics. In this article, while exploring the theories of rotatable designs and Euclidean designs, we give an overview of the construction theory of high-dimensional quadrature formulas. We also elucidate the advantages of reconstructing various design-theoretic concepts in the framework of quadrature theory, as exemplified by the determination of maximum number t for which classical response surface designs such as Box-Behnken designs, central composite designs and Doehlert designs are of t-th-order rotatable.