490 research outputs found
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
Distorted Copulas: Constructions and Tail Dependence
Given a copula C, we examine under which conditions on an order isomorphism ψ of [0, 1] the distortion C ψ: [0, 1]2 → [0, 1], C ψ(x, y) = ψ{C[ψ−1(x), ψ−1(y)]} is again a copula. In particular, when the copula C is totally positive of order 2, we give a sufficient condition on ψ that ensures that any distortion of C by means of ψ is again a copula. The presented results allow us to introduce in a more flexible way families of copulas exhibiting different behavior in the tails
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Methods of Tail Dependence Estimation
Characterization and quantification of climate extremes and their dependencies are fundamental to the studying of natural hazards. This chapter reviews various parametric and nonparametric tail dependence coefficient estimators. The tail dependence coefficient describes the dependence (degree of association) between concurrent extremes at different locations. Accurate and reliable knowledge of the spatial characteristics of extremes can help improve the existing methods of modeling the occurrence probabilities of extreme events. This chapter will review these methods and use two case studies to demonstrate the application of tail dependence analysis
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
Upside and Downside Risk Exposures of Currency Carry Trades via Tail Dependence
Currency carry trade is the investment strategy that involves selling low
interest rate currencies in order to purchase higher interest rate currencies,
thus profiting from the interest rate differentials. This is a well known
financial puzzle to explain, since assuming foreign exchange risk is
uninhibited and the markets have rational risk-neutral investors, then one
would not expect profits from such strategies. That is, according to uncovered
interest rate parity (UIP), changes in the related exchange rates should offset
the potential to profit from such interest rate differentials. However, it has
been shown empirically, that investors can earn profits on average by borrowing
in a country with a lower interest rate, exchanging for foreign currency, and
investing in a foreign country with a higher interest rate, whilst allowing for
any losses from exchanging back to their domestic currency at maturity. This
paper explores the financial risk that trading strategies seeking to exploit a
violation of the UIP condition are exposed to with respect to multivariate tail
dependence present in both the funding and investment currency baskets. It will
outline in what contexts these portfolio risk exposures will benefit
accumulated portfolio returns and under what conditions such tail exposures
will reduce portfolio returns.Comment: arXiv admin note: substantial text overlap with arXiv:1303.431
Can crop yield risk be globally diversified?
In 2007 and 2008 world food markets observed a significant price boom. Crop failures simultaneously occurring in some of the world’s major production regions have been quoted as one factor among others for the price boom. Against this background, we analyse the stochasticity of crop yields in major production areas. The analysis is exemplified for wheat, which is one of the most important crops worldwide. Particular attention is given to the stochastic dependence of yields in different regions. Thereby we address the question of whether local fluctuations of yields can be smoothed by international agricultural trade, i.e. by global diversification. The analysis is based on the copula approach, which requires less restrictive assumptions compared with linear correlations. The use of copulas allows for a more reliable estimation of extreme yield shortfalls, which are of particular interest in this application. Our calculations reveal that a production shortfall, such as in 2007, is not a once in a lifetime event. Instead, from a statistical point of view, similar production conditions will occur every 15 years.crop yield risk, fully nested hierarchical Archimedean copulas (FNAC), price boom
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