On tail dependence matrices

This article defines coefficient of upper-lower tail dependence and coefficient of lower-upper tail dependence based on coefficient of upper tail dependence and coefficient of lower tail dependence and does an empirical research on tail dependence in China stock market. A mixed Copula that can well describe dependence structure between Shanghai Exchange Composite Index(SHECI) and Shenzhen Exchange Component Index(SZECI) is found by empirical analysis firstly, and is used to calculate coefficients of tail dependence. The results show that there are strong upper tail dependence and lower tail dependence, but no upper-lower tail dependence and lower-upper tail dependence between daily returns of SHECI and SZECI.

Wind speed scenario generation based on dependency structure analysis

This thesis presents the concept of tail dependence in a financial context as one tool to measure dependence in the extremes of a bivariate distribution. Copulae can separate the problem of estimating a multidimensional distribution into the estimation of the marginal distributions and the dependence between the onedimensional random variables. Therefore, copulae are used in order to carry out the estimation of the tail dependence coefficient (TDC). Four estimators of the TDC are presented and compared in a simulation study for various distributions and copulae. Furthermore, an introduction into bivariate Extreme Value Theory (EVT) is given, which tries precisely to analyze the behavior at the tail of a bivariate distribution. EVT allows to construct estimators of the TDC and to derive a test for tail independence, which is recognized to be indispensable but rarely utilized in a financial context. As an application to nine different financial data sets shows, the phenomenon of tail dependence is less common than often argued in the literature: the periods where indeed tail independence can be rejected are few.

Interval estimation for a measure of tail dependence

Linear programming formulation for non-stationary, finite-horizon Markov decision process models

An important problem in WDM network design is to construct a logical topology and determine an optimal routing over that topology. Mixed integer linear program (MILP) formulations to generate optimal solutions for this problem are computationally intractable, even for moderate sized networks. A standard approach is to decouple the problem of logical topology design and the problem of routing on this logical topology. Heuristics for finding the logical topology exist and a straightforward linear program (LP), based on the node-arc formulation is normally used to solve the routing problem over a given logical topology. Such LP formulations become computationally infeasible for large networks. In this paper, we present a new formulation for optimally routing traffic over a given logical topology. Our formulation is based on the arc-chain representation and minimizes the congestion of the network. We have used an implicit column generation technique and exploited the special generalized upper bounding structure of our formulation to efficiently solve the problem.

This paper considers two-dimensional (2-D) retiming, which is the problem of retiming circuits that operate on 2-D signals. We begin by discussing two types of parallelism available in 2-D data processing, which we call inter-iteration parallelism and inter-operation parallelism. We then present two novel techniques for 2-D retiming that can be used to extract inter-operation parallelism. These two techniques are designed to minimize the amount of memory required to implement a 2-D data-flow graph while maintaining a desired clock rate for the circuit. The first technique is based on an integer linear programming (ILP) formulation of the problem, and is called ILP 2-D retiming. This technique considers the entire 2-D retiming problem as a whole, but long central processing unit times are required if the circuit is large. The second technique, called orthogonal 2-D retiming, is a linear programming formulation which is derived by partitioning ILP 2-D retiming into two parts called s- and a-retiming. This technique finds a solution in polynomial time and is much faster than the ILP 2-D retiming technique, but the two sub problems (s- and a-retiming) can give results which are not compatible with one another. To solve this incompatibility problem, a variation of orthogonal 2-D retiming called integer orthogonal 2-D retiming is developed. This technique runs in polynomial time and the s-retiming and a-retiming steps are guaranteed to give compatible results. We show that the techniques presented in this paper can result in memory hardware savings of 50% compared to previously published 2-D retiming techniques.

In this paper, we clarify dependence properties of elliptical distributions by deriving general but explicit formulae for the coefficients of upper and lower tail dependence and spectral measures with respect to different norms. We show that an elliptically distributed random vector is regularly varying if and only if the bivariate marginal distributions have tail dependence. Furthermore, the tail dependence coefficients are fully determined by the tail index of the random vector (or equivalently of its components) and the linear correlation coefficient. Whereas Kendall's tau is invariant in the class of elliptical distributions with continuous marginals and a fixed dispersion matrix, we show that this is not true for Spearman's rho. We also show that sums of elliptically distributed random vectors with the same dispersion matrix (up to a positive constant factor) remain elliptical if they are dependent only through their radial parts.

We explore extreme return-volumes dependence among different cryptocurrencies such as Bitcoin, Ethereum, Ripple, and Litecoin by using the Copula approach. We use Student-t, Frank, Clayton, Survival Clayton, Gumbel, and SJC copulas. We filter out margins by using the EGARCH model for return series and GARCH model for volume series. Evidence of significant symmetric dependence between return-volume is not found due to insignificance of student-t and Frank copula parameters. In a return-volume relationship, coefficients of lower tail dependence are significant for Bitcoin, Ripple, and Litecoin which means that low returns are followed by low volumes. Lower tail dependence for the return-volume relationship is stronger than the upper tail dependence for Bitcoin, Ripple, and Litecoin. Moreover, for negative return-volume, left tail dependence coefficients are significant for Ripple and Litecoin, which means that high returns are followed by low volumes for Ripple and Litecoin. Our investigation shows that investors (buyer or seller) are very careful in extreme market conditions for both Ripple and Litecoin. Extreme upper tail and lower tail dependence coefficients are insignificant for Ethereum.

Tail dependence is understood as the dependence between the variables assuming that these variables take the values from the tails of univariate distributions. In the paper two approaches of tail dependence determination are discussed: conditional correlation coefficient and tail dependence coefficients. It can be argued that both approaches are the generalizations of the well-known univariate approach, based on conditional excess distribution. In the paper the proposal is also given to extend tail dependence coefficients to the general multivariate case and to represent these coefficients through copula function.

Multivariate dependence measures and data analysis

Bitcoin and major precious metals are frequently discussed as hedges against equity drawdowns, inflation surprises, and policy uncertainty, which implicitly assumes a degree of functional equivalence in their risk behavior. Existing work remains limited in assessing high-dimensional dependence structures in the Bitcoin and precious metals system, without relying on bivariate conditional risk measures or restrictive copula frameworks. This study therefore aims to quantify bilateral and multivariate tail dependence and systemic spillovers between Bitcoin and selected precious metals and to identify the best-performing multivariate tail-risk specification, with model comparison conducted using AIC and BIC. The analysis uses 3,665 daily observations of adjusted closing prices spanning January 2013 to September 2024, sourced from Yahoo Finance. Marginal returns are fitted with an ARFIMA–FIGARCH skewed-t model, while cross-asset tail dependence is estimated via vine-copula quantile regression (C- and D-vines) using a 252-day rolling window (one-day step) with 10,000 copula simulations. Results indicate that Bitcoin exhibits substantially larger downside systemic contributions than precious metals, whereas gold displays the smallest systemic risk profile. Across information criteria, the D-vine–based SCoVaR specification provides the best overall fit, indicating that vine-based multivariate tail-risk measures better characterize systemic spillovers between the cryptocurrency and traditionally defensive assets under extreme market conditions. These results motivate future research on broader cryptocommodity networks and macro-financial conditioning, while practitioners and regulators can use the D-vine SCoVaR to monitor and mitigate downside spillovers in mixed-asset portfolios.

This paper is concerned with a procedure for financial time series clustering, aimed at creating groups of time series characterized by similar behavior with regard to extreme events. The core of our proposal is a double clustering procedure: the former is based on the lower tail dependence of all the possible pairs of time series, the latter on the upper tail dependence. Tail dependence coefficients are estimated with copula functions. The final goal is to exploit the two clustering solutions in an algorithm designed to create a portfolio that maximizes the probability of joint positive extreme returns while minimizing the risk of joint negative extreme returns. In financial crisis scenarios, such a portfolio is expected to outperform portfolios generated by the traditional methods. We describe the results of a simulation study and, finally, we apply the procedure to a dataset composed of the 50 assets included in the EUROSTOXX index.

We show that the problem of computing sharp upper and lower static-arbitrage bounds on the price of a European basket option, given the prices of other similar options, can be cast as a linear program (LP). The LP formulations readily yield super-replicating (subreplicating) strategies for the upper (lower) bound problem. The dual counterparts of the LP formulations in turn yield underlying asset price distributions that replicate the given option prices, and the bound on the new basket option’s price. In the special case when the given option prices are those of vanilla options on the underlying assets, we show that the LP formulations admit further simplifications. In particular, for the upper bound problem we derive closed-form formulas for the basket’s price bound, and for the corresponding superreplicating strategy. In addition, our LP approach admits efficient modeling of additional features such as basket options with negative weights, bid/ask spreads, transaction costs, and diversification constraints. We provide numerical experiments to illustrate some of our results.

Motivated by [12], we provide a framework for studying the size of linear programming formulations as well as semidefinite programming formulations of combinatorial optimization problems without encoding them first as linear programs. This is done via a factorization theorem for the optimization problem itself (and not a specific encoding of such). As a result we define a consistent reduction mechanism that degrades approximation factors in a controlled fashion and which, at the same time, is compatible with approximate linear and semidefinite programming formulations. Moreover, our reduction mechanism is a minor restriction of classical reductions establishing inapproximability in the context of PCP theorems. As a consequence we establish strong linear programming inapproximability (for LPs with a polynomial number of constraints) for several problems that are not 0/1-CSPs: we obtain a 3/2-epsilon inapproximability for Vertex Cover (which is not of the CSP type) answering an open question in [12], we answer a weak version of our sparse graph conjecture posed in [6] showing an inapproximability factor of 1/2+e for bounded degree IndependentSet, and we establish inapproximability of MaxMULTICUT (a non-binary CSP). In the case of SDPs, we obtain relative inapproximability results for these problems.