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International audience; In this paper we study the existence of arbitrage opportunities in a multi-asset market when risk-neutral marginal distributions of asset prices are known. We first propose an intuitive characterization of the absence of arbitrage opportunities in terms of copula functions. We then address the problem of detecting the presence of arbitrage by formalizing its resolution in two distinct ways that are both suitable for the use of optimization algorithms. The first method is valid in the general multivariate case and is based on Bernstein copulas that are dense in the set of all copula functions. The second one is easier to work with but is only valid in the bivariate case. It relies on results about improved Fréchet–Hoeffding bounds in presence of additional information. For both methods, details of implementation steps and empirical applications are provided.

In this paper we propose a clustering procedure aimed at grouping time series with an association between extremely low values, measured by the lower tail dependence coefficient. Firstly, we estimate the coefficient using an Archimedean copula function. Then, we propose a dissimilarity measure based on tail dependence coefficients and a two-step procedure to be used with clustering algorithms which require that the objects we want to cluster have a geometric interpretation. We show how the results of the clustering applied to financial returns could be used to construct defensive portfolios reducing the effect of a simultaneous financial crisis.

Contemporary financial risk management is significantly based on the analysis of time series of returns. One of the most significant errors frequently committed by analysts is the predominant use of normal distributions when it is clear that the returns are not normal. Copula models and models for non-normal multivariate distributions provide new tools to solve the problem because the obtained results are immediately applicable in portfolio management, option pricing and measuring risk without assuming normality. Therefore, both a theoretician and a practitioner are interested in multivariate models for returns and copula functions. The copula function models provide an effective and interesting technique of constructing multivariate distribution starting from marginal ones. Due to Sklar's result established in 1959, we can present any multivariate distribution with a help of corresponding marginal distributions and a selected copula function. In this work we present an application of copula function to construct multivariate conditional distributions of times series. In the last part of this paper dynamic models such as DCC-MVGARCH and conditional copula are analyzed. Moreover, we also present an application of bootstrap in the context of copula function. This work is appended by examples showing practical application of our work.

A reliable and long dataset describing urban flood locations, volumes and depths would be an ideal prerequisite for assessing flood frequency distributions. However, data are often piecemeal and long-term hydraulic modelling is often adopted to estimate floods from historical rainfall series. Long-term modelling approaches are time- and resource-consuming, and synthetically designed rainfalls are often used to estimate flood frequencies. The present paper aimsto assess the uncertainty of such an approach and for suggesting improvements in thedefinition of synthetic rainfall data for flooding frequency analysis. According to this aim, a multivariate statistical analysis based on a copulamethod was applied to rainfall features (total depth, duration and maximum intensity) to generate synthetic rainfalls that are more consistent with historical events. The procedure was applied to a real case study, and the results were compared with those obtained by simulating other typical synthetic rainfall events linked to intensity-duration-frequency (IDF) curves. The copula-based multi-variate analysis ismore robust and adapts well to experimental flood locations even if it is more complex and time-consuming. This study demonstrates that statistical correlations amongst rainfall frequency, duration, volume and peak intensity can partially explain the weak reliability of flood-frequency analyses based on synthetic rainfall events. © IWA Publishing 2011.

In this paper, we apply a spread-based real options approach to analyze the decision-making problem of an investor who has the choice between an irreversible investment in a condensing power plant without heat utilization and a plant with combined heat-and-power (CHP) generation. Our investigation focuses on large-scale fossil-fueled generation technologies and is based on a stochastic model that uses copula functions to provide the input parameters of the real options model. We define the aggregated annual spread as assessment criteria for our investigation since it contains all relevant volatile input parameters that have an impact on the evaluation of investment decisions. We show that the specific characteristics of CHP plants, such as additional revenues from heat sales, promotion schemes, specific operational features, and a beneficial allocation of CO 2 allowances, have a significant impact on the option value and therefore on the optimal timing for investment. For the two fossil-fueled CHP technologies investigated (combined-cycle gas turbine and steam turbine), we conclude from our analysis that a high share of CHP generation reduces the risk exposure for the investor. The maximal possible CHP generation depends significantly on the local heat demand in the surroundings of the power plant. Considering this, the size of the heat sink available could gain more relevance in the future selection process of sites for new large-scale fossil power plants.

In this paper we test how different choices for the dependence function can affect the prices of a set of multiasset equity options. We conduct the analysis for various 5-dimensional baskets of UK shares, and a wide range of payoffs for the multiasset options, consistent with the instruments traded on the market. We also test the relevance of the dependence specification over both volatile and quiet market scenarios. Interestingly, we find that, in most circumstances, the choice of a dependence structure richer than the standard linear correlation does not seem to affect option prices substantially. However, the dependence function becomes more relevant in particularly volatile market conditions.

The object of the paper is to compare of two approaches for the analysis of financial durations. The first is the parametric approach (Autoregressive Conditional Duration model) implemented using the exponential, the Weibull, the Burr and the Pareto density functions. The second makes use of bivariate and trivariate copula functions.

In the last decades, the international scientific literature has focused on the assessment and quantification of trends in average temperature and rainfall, underlining changes in time and space sometimes relevant. The changes concern the yearly average values, the seasonal distribution, the daily values, with marked differences both at a continental and national scale. In this paper, with reference to a database containing the records of about 8000 thermometric stations and 12000 rainfall stations for the period 1895-1997 for the USA, available on the website of the Institute for Mathematics Applied to Geosciences ( http://www.image.ucar.edu/Data/US.monthly.met/ ), an analysis on the spatial correlation between the yearly average rainfall hc and the mean of the yearly average ground temperature T was performed. In particular, with the aid of the copula distribution function, a stochastic model to define the conditional probability distribut *ion P(hc(mm)|T(°C)) was developed, analyzing the dependence of the yearly average rainfall on the thermometric changes.