Multivariate Tail Dependence Coefficients for Archimedean Copulae

Luca, Giovanni De; Rivieccio, Giorgia

doi:10.1007/978-3-642-21037-2_26

Cited by 24 publications

(12 citation statements)

References 13 publications

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“…In the first part of this paper, we calculate multivariate tail dependence coefficients when the generator of the considered copula exhibits some regular variation properties, and we investigate the behaviour of these coefficients in cases that are close to tail independence. This first part exploits previous works of Charpentier and Segers (2009) and extends some results of Juri and Wüthrich (2003) and De Luca and Rivieccio (2012). In the second part of the paper we analyse the impact in the upper and lower multivariate tail dependence coefficients of a large class of transformations of dependence structures.…”

Section: Introductionmentioning

confidence: 57%

“…Organization of the paper The paper is organized as follow: In Section 1, we present multivariate tail dependence coefficients for copulas, starting from definition in De Luca and Rivieccio (2012). In Section 2, we present some suitable Regular Variation properties for Archimedean copulas and we provide the multivariate tail dependence coefficients introduced before, for these regular varying generators.…”

Section: Introductionmentioning

confidence: 99%

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On tail dependence coefficients of transformed multivariate Archimedean copulas

Bernardino¹,

Rullière²

2016

Fuzzy Sets and Systems

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This paper presents the impact of a class of transformations of copulas in their upper and lower multivariate tail dependence coefficients. In particular we focus on multivariate Archimedean copulas. In the first part of this paper, we calculate multivariate tail dependence coefficients when the generator of the considered copula exhibits some regular variation properties, and we investigate the behaviour of these coefficients in cases that are close to tail independence. This first part exploits previous works of Charpentier and Segers (2009) and extends some results of Juri and Wüthrich (2003) and De Luca and Rivieccio (2012). In the second part of the paper we analyse the impact in the upper and lower multivariate tail dependence coefficients of a large class of transformations of dependence structures. These results are based on the transformations exploited by Di Bernardino and Rullière (2013a) and Di Bernardino and Rullière (2013b). We extend some bivariate results of Durante et al. (2010) in a multivariate setting by calculating multivariate tail dependence coefficients for transformed copulas. We obtain new results under specific conditions involving regularly varying hazard rates of components of the transformation. In the third part, we show the utility of using transformed Archimedean copulas, as they permit to build Archimedean generators exhibiting any chosen couple of lower and upper tail dependence coefficients. Furthermore, using results in Larsson and Nešlehová (2011), we detail the extreme behaviour of the transformed radial part of Archimedean copulas. At last, we explain possible applications with Markov chains with specific dependence structure.

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Section: Introductionmentioning

confidence: 57%

Section: Introductionmentioning

confidence: 99%

On tail dependence coefficients of transformed multivariate Archimedean copulas

Bernardino¹,

Rullière²

2016

Fuzzy Sets and Systems

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“…The tail dependence expressions for many common bivariate copulae can be found in [25]. This concept was recently extended to the multivariate setting by [9].…”

Section: Definition 2 (Mixture Copula)mentioning

confidence: 99%

“…In [9], the analogous form of the generalised multivariate upper and lower tail dependence coefficients for outer power transformed Clayton copula models is provided. The derivation of Eqs.…”

Section: Definition 2 (Mixture Copula)mentioning

confidence: 99%

Upside and Downside Risk Exposures of Currency Carry Trades via Tail Dependence

Ames

Peters

Bagnarosa

et al. 2015

Innovations in Quantitative Risk Management

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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.

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“…We first study a representative simple case, with dimension d = 5 (see Definition B.4) and investigate the behaviour of the proposed algorithm for different parameters values with fixed number of particles N SM C = 250. To choose the parameters of interest we set the multivariate coefficient of (lower) tail dependence λ l (see [15] or Definition B.5 and Figure 7.1) to be approximately equals to 0.25, 0.5, 0.75 and 0.9, which led to To compare with the results presented in [1], the parameter value θ = 1 is also considered. On Figure 7.2, we present the Relative Bias (top row) and Variance Reduction (bottom row) for all the range of different copula parameters and quantile levels.…”

Section: Clayton Copula Dependence Between Risk Cellsmentioning

confidence: 99%

Sequential Monte Carlo Samplers for Capital Allocation Under Copula-Dependent Risk Models

2014

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In this paper we assume a multivariate risk model has been developed for a portfolio and its capital derived as a homogeneous risk measure. The Euler (or gradient) principle, then, states that the capital to be allocated to each component of the portfolio has to be calculated as an expectation conditional to a rare event, which can be challenging to evaluate in practice. We exploit the copuladependence within the portfolio risks to design a Sequential Monte Carlo Samplers based estimate to the marginal conditional expectations involved in the problem, showing its efficiency through a series of computational examples.

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Multivariate Tail Dependence Coefficients for Archimedean Copulae

Cited by 24 publications

References 13 publications

On tail dependence coefficients of transformed multivariate Archimedean copulas

On tail dependence coefficients of transformed multivariate Archimedean copulas

Upside and Downside Risk Exposures of Currency Carry Trades via Tail Dependence

Sequential Monte Carlo Samplers for Capital Allocation Under Copula-Dependent Risk Models

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