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

Overreaction and Multiple Tail Dependence at the High-frequency Level — The Copula Rose

This paper applies a non- and a semiparametric copula-based approach to analyze the first-order autocorrelation of returns in high frequency financial time series. Using the EUREX D3047 tick data from the German stock index, it can be shown that the temporal dependence structure of price movements is not always negatively correlated as assumed in the stylized facts in the finance literature. Depending on the sampling frequency, the estimated copulas exhibit some kind of overreaction phenomena and multiple tail dependence, revealing patterns similar to the compass rose.High Frequency Data, Non- and Semiparametric Copulas, Overreaction, Tail Dependence, Compass Rose

Decentralized learning with budgeted network load using Gaussian copulas and classifier ensembles

We examine a network of learners which address the same classification task but must learn from different data sets. The learners cannot share data but instead share their models. Models are shared only one time so as to preserve the network load. We introduce DELCO (standing for Decentralized Ensemble Learning with COpulas), a new approach allowing to aggregate the predictions of the classifiers trained by each learner. The proposed method aggregates the base classifiers using a probabilistic model relying on Gaussian copulas. Experiments on logistic regressor ensembles demonstrate competing accuracy and increased robustness in case of dependent classifiers. A companion python implementation can be downloaded at https://github.com/john-klein/DELC

Aging functions and multivariate notions of NBU and IFR

For d≥2, let X=(X1, …, Xd) be a vector of exchangeable continuous lifetimes with joint survival function $\overline{F}$. For such models, we study some properties of multivariate aging of $\overline{F}$ that are described by means of the multivariate aging function $B_{\overline{F}}$, which is a useful tool for describing the level curves of $\overline{F}$. Specifically, the attention is devoted to notions that generalize the univariate concepts of New Better than Used and Increasing Failure Rate. These multivariate notions are satisfied by random vectors whose components are conditionally independent and identically distributed having univariate conditional survival function that is New Better than Used (respectively, Increasing Failure Rate). Furthermore, they also have an interpretation in terms of comparisons among conditional survival functions of residual lifetimes, given a same history of observed survivals

Copulae: On the Crossroads of Mathematics and Economics

The central focus of the workshop was on copula theory as well as applications to multivariate stochastic modelling. The programme was intrinsically interdisciplinary and represented areas with much recent progress. The workshop included talks and dynamic discussions on construction, estimation and various applications of copulas to finance, insurance, hydrology, medicine, risk management and related fields

Systemic Weather Risk and Crop Insurance: The Case of China

The supply of affordable crop insurance is hampered by the existence of systemic weather risk which results in large risk premiums. In this article, we assess the systemic nature of weather risk for 17 agricultural production regions in China and explore the possibility of spatial diversification of this risk. We simulate the buffer load of hypothetical temperature-based insurance and investigate the relation between the size of the buffer load and the size of the trading area of the insurance. The analysis makes use of a hierarchical Archimedean copula approach (HAC) which allows flexible modeling of the joint loss distribution and reveals the dependence structure of losses in different insured regions. Our results show a significant decrease of the required risk loading when the insured area expands. Nevertheless, a considerable part of undiversifiable risk remains with the insurer. We find that the spatial diversification effect depends on the type of the weather index and the strike level of the insurance. Our findings are relevant for insurers and insurance regulators as they shed light on the viability of private crop insurance in China.crop insurance, systemic weather risk, hierarchical Archimedean copulas