Copulas in finance and insurance

Copulas provide a potential useful modeling tool to represent the dependence structure among variables and to generate joint distributions by combining given marginal distributions. Simulations play a relevant role in finance and insurance. They are used to replicate efficient frontiers or extremal values, to price options, to estimate joint risks, and so on. Using copulas, it is easy to construct and simulate from multivariate distributions based on almost any choice of marginals and any type of dependence structure. In this paper we outline recent contributions of statistical modeling using copulas in finance and insurance. We review issues related to the notion of copulas, copula families, copula-based dynamic and static dependence structure, copulas and latent factor models and simulation of copulas. Finally, we outline hot topics in copulas with a special focus on model selection and goodness-of-fit testing

Copulas in finance and insurance

Copulas provide a potential useful modeling tool to represent the dependence structure among variables and to generate joint distributions by combining given marginal distributions. Simulations play a relevant role in finance and insurance. They are used to replicate efficient frontiers or extremal values, to price options, to estimate joint risks, and so on. Using copulas, it is easy to construct and simulate from multivariate distributions based on almost any choice of marginals and any type of dependence structure. In this paper we outline recent contributions of statistical modeling using copulas in finance and insurance. We review issues related to the notion of copulas, copula families, copula-based dynamic and static dependence structure, copulas and latent factor models and simulation of copulas. Finally, we outline hot topics in copulas with a special focus on model selection and goodness-of-fit testing.Dependence structure, Extremal values, Copula modeling, Copula review

Copulas In Finance Ten Years Later

Copula functions are mathematical tools that have been used in finance for approximately ten years. Their main selling point is to separate the dependence function (copula) from the marginal distributions. A little over a decade after the rise of copula modelling in finance, this article provides an initial assessment of their application in financial contexts. More specifically, the main purpose of this paper is to contribute to an ongoing debate in the field: the choice of copulas. Through an empirical study of two composite stock indices (S&P 500 and CAC 40) daily returns over the period 2002-2011, we show that this methodological challenge is still unsolved. With this in view, we suggest a method that enables to capture implicitly the empirical dependence structure without assuming any specific parametric form for it

A First Stochastic General Framework to Model the Project Finance Cash Flows under Monopolistic Situations

The main aim of this work is to model the cash flows and cost dynamics for a Project Finance. Large scale capital-intensive projects usually require substantial investments up front and only generate revenues to cover their costs in the long term. The abandonment flexibility affects each project independently. This is the only one that we consider in this study and it is quite different from the idea to abandon due to a common (specific) catastrophic event. This option is exercised under those situations of expected costs to completion higher than the expected cash flow, that is, during the investment period in the development phase. Including this flexibility in project finance is the same as valuing a project with an implicit American put option.Project Finance, Cash Flows, Stochastic, Real Options

Modeling the Dependency Structure of Stock Index Returns using a Copula Function Approach

In the present study we assess the dependency structure between stock indexes by econometrically estimating the empirical copula function and the parameters of various parametric copula functions. The main finding is that the t-copula and the Gumbel-Clayton mixture copula are the most appropriate copula functions to capture the dependency structure of two financial return series. With the dependency structure given by the estimated copula functions we quantify the efficient portfolio frontier using as a risk measure CVaR (Conditional VaR) computed by Monte Carlo simulation. We find that in the case of using normal distributions for modeling individual returns the market risk is underestimated no mater what copula function is employed to capture the dependency structure.copula functions, copula mixtures, the efficient portfolio frontier, Conditional VAR, Monte Carlo simulation

THE APPLICATION OF COPULAS IN PRICING DEPENDENT CREDIT DERIVATIVES INSTRUMENTS

The aim of this paper is to use copulas functions to capture the different structures of dependency when we deal with portfolios of dependent credit risks and a basket of credit derivatives. We first present the wellknown result for the pricing of default risk, when there is only one defaultable firm. After that, we expose the structure of dependency with copulas in pricing dependent credit derivatives. Many studies suggest the inadequacy of multinormal distribution and then the failure of methods based on linear correlation for measuring the structure of dependency. Finally, we use Monte Carlo simulations for pricing Collateralized debt obligation (CDO) with Gaussian an Student copulas.default risk, credit derivatives, CDO, copulas functions, Monte Carlo simulations.

Ensemble Copula Coupling as a Multivariate Discrete Copula Approach

In probability and statistics, copulas play important roles theoretically as well as to address a wide range of problems in various application areas. In this paper, we introduce the concept of multivariate discrete copulas, discuss their equivalence to stochastic arrays, and provide a multivariate discrete version of Sklar's theorem. These results provide the theoretical frame for the ensemble copula coupling approach proposed by Schefzik et al. (2013) for the multivariate statistical postprocessing of weather forecasts made by ensemble systems.Comment: references correcte