Properties of Hierarchical Archimedean Copulas

In this paper we analyse the properties of hierarchical Archimedean copulas. This class is a generalisation of the Archimedean copulas and allows for general non-exchangeable dependency structures. We show that the structure of the copula can be uniquely recovered from all bivariate margins. We derive the distribution of the copula value, which is particularly useful for tests and constructing con¯dence intervals. Furthermore, we analyse dependence orderings, multivariate dependence measures and extreme value copulas. Special attention we pay to the tail dependencies and derive several tail dependence indices for general hierarchical Archimedean copulas.copula; multivariate distribution; Archimedean copula; stochastic ordering; hierarchical copula

Modeling Dependencies in Finance using Copulae

In this paper we provide a review of copula theory with applications to finance. We illustrate the idea on the bivariate framework and discuss the simple, elliptical and Archimedean classes of copulae. Since the cop- ulae model the dependency structure between random variables, next we explain the link between the copulae and common dependency measures, such as Kendall's tau and Spearman's rho. In the next section the copulae are generalized to the multivariate case. In this general setup we discuss and provide an intensive literature review of estimation and simulation techniques. Separate section is devoted to the goodness-of-fit tests. The importance of copulae in finance we illustrate on the example of asset allocation problems, Value-at-Risk and time series models. The paper is complemented with an extensive simulation study and an application to financial data.Distribution functions, Dimension Reduction, Risk management, Statistical models

A partial correlation vine based approach for modeling and forecasting multivariate volatility time-series

A novel approach for dynamic modeling and forecasting of realized covariance matrices is proposed. Realized variances and realized correlation matrices are jointly estimated. The one-to-one relationship between a positive definite correlation matrix and its associated set of partial correlations corresponding to any vine specification is used for data transformation. The model components therefore are realized variances as well as realized standard and partial correlations corresponding to a daily log-return series. As such, they have a clear practical interpretation. A method to select a regular vine structure, which allows for parsimonious time-series and dependence modeling of the model components, is introduced. Being algebraically independent the latter do not underlie any algebraic constraint. The proposed model approach is outlined in detail and motivated along with a real data example on six highly liquid stocks. The forecasting performance is evaluated both with respect to statistical precision and in the context of portfolio optimization. Comparisons with Cholesky decomposition based benchmark models support the excellent prediction ability of the proposed model approach

Properties of Hierarchical Archimedean Copulas

In this paper we analyse the properties of hierarchical Archimedean copulas. This class is a generalisation of the Archimedean opulas and allows for general non-exchangeable dependency structures. We show that the structure of the copula can be uniquely recovered from all bivariate margins. We derive the distribution of the copula value, which is particularly useful for tests and constructing confidence intervals. Furthermore, we analyse dependence orderings, multivariate dependence measures and extreme value copulas. Special attention we pay to the tail dependencies and derive several tail dependence indices for general hierarchical Archimedean copulas

General uncertainty in portfolio selection: a case-based decision approach

Often a portfolio investor can hardly imagine all states of nature relevant to his investment problem, causing general uncertainty concerning an asset allocation model. We quantify general uncertainty as the weakness of an investor’s belief in a conventional portfolio procedure, then we develop the case-based decision-making approach for determining the optimal belief degree. The economic effect of the proposed case-based methodology is investigated in the empirical study. The empirical results suggest two successful patterns of case-based decisions that could be linked to the issue of market efficiency. Moreover, our case-based modeling reflects some behavioral phenomena observed on financial markets

Uniform confidence bands for pricing kernels

Pricing kernels implicit in option prices play a key role in assessing the risk aversion over equity returns. We deal with nonparametric estimation of the pricing kernel (Empirical Pricing Kernel) given by the ratio of the risk-neutral density estimator and the subjective density estimator. The former density can be represented as the second derivative w.r.t. the European call option price function, which we estimate by nonparametric regression. The subjective density is estimated nonparametrically too. In this framework, we develop the asymptotic distribution theory of the EPK in the L1 sense. Particularly, to evaluate the overall variation of the pricing kernel, we develop a uniform confidence band of the EPK. Furthermore, as an alternative to the asymptotic approach, we propose a bootstrap confidence band. The developed theory is helpful for testing parametric specifications of pricing kernels and has a direct extension to estimating risk aversion patterns. The established results are assessed and compared in a Monte-Carlo study. As a real application, we test risk aversion over time induced by the EPK.Empirical Pricing Kernel, Confidence band, Bootstrap; Kernel Smoothing; Nonparametric

Bayesian Estimation of the Global Minimum Variance Portfolio

In this paper we consider the estimation of the weights of optimal portfolios from the Bayesian point of view under the assumption that the conditional distribution of the logarithmic returns is normal. Using the standard priors for the mean vector and the covariance matrix, we derive the posterior distributions for the weights of the global minimum variance portfolio. Moreover, we reparameterize the model to allow informative andnon-informative priors directly for the weights of the global minimum variance portfolio. The posterior distributions of the portfolio weights are derived in explicit form for almost all models. The models are compared by using the coverage probabilities of credible intervals. In an empirical study we analyze the posterior densities of the weights of an international portfolio

Statistical inference for the EU portfolio in high dimensions

In this paper, using the shrinkage-based approach for portfolio weights and modern results from random matrix theory we construct an effective procedure for testing the efficiency of the expected utility (EU) portfolio and discuss the asymptotic behavior of the proposed test statistic under the high-dimensional asymptotic regime, namely when the number of assets $p$ increases at the same rate as the sample size $n$ such that their ratio $p/n$ approaches a positive constant $c\in(0,1)$ as $n\to\infty$. We provide an extensive simulation study where the power function and receiver operating characteristic curves of the test are analyzed. In the empirical study, the methodology is applied to the returns of S\&P 500 constituents.Comment: 27 pages, 5 figures, 2 table

Reddit financial image post sentiment dataset

The dataset presented in this paper consists of sentiment information extracted from image and text data of financial subreddit posts. Members of these subreddits post about their trading behavior, express their opinions, and discuss capital market trends. Their posts contain sentiment information on financial topics as well as signaling information on trading decisions. Frequently, members post screenshots of their portfolios from their mobile broker apps. We collected the posts, processed them to extract sentiment scores using various methods, and anonymized them. The dataset consists therefore not of any content from the posts or information about the author, but the processed sentiment information within the post. Further financial tickers mentioned in the posts are tracked, such that the effect of sentiment in the posts can be attributed to financial products and used in the context of financial forecasting. The posts were collected using the Reddit [2] and Pushshift APIs [3] and processed using an Amazon Web Services architecture. A fine-tuned MobileNets artificial neural network [4] was used to classify images into four distinct categories, which had been determined in a preliminary analysis. The categories included classical memes, number posts (e.g. screenshots of mobile broker portfolios), text posts (e.g. screenshots from twitter) and chart posts (e.g. other financial screenshots, such as charts). The reason for the classification of images into the four categories is that the images are so inherently different, that different extraction methods had to be applied for each category. OCR – methods [5] were used to extract text from images. Custom methods were applied to extract sentiment and other information from the resulting text. The data [1] is available on a 20-minute basis and can be used in many areas, such as financial forecasting and analyzing sentiment dynamics in social media posts