Modelling Dependence with Copulas and Applications to Risk Management

Embrechts, Paul; Lindskog, Filip; McNeil, Alexander J.

doi:10.1016/b978-044450896-6.50010-8

Cited by 766 publications

(587 citation statements)

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“…Tam, kad būtų galima išsamiau apžvelgti į įmonės XYZ vertės tikimybių funkcijos pokyčių priklausomybes nuo rizikos faktorių tarpusavio priklausomybės įtakos, buvo atlikta aprašytų įmonės XYZ rizikos faktorių skirstinių koreliacinė analizė. Kaip teigia užsienio autoriai, kintamųjų tarpusavio įtaka -vienas iš jos matų yra koreliacija -esmingai veikia modelio rezultatus [3,4]. Koreliacinė analizė parodė, kad tarp didžiausią įmonės vertę turinčių iteracijų rizikos faktorių atsirado nauja koreliacija tarp p x8 (gaminio x kainos 8 metais) ir n x1 , n x2 , …, n x7 (gaminio x pagamintų vienetų skaičius per metus).…”

Section: Stochastinio Simuliavimo Pritaikymas Ir įDiegimasunclassified

Verslo vertės kintamųjų rizikingumas ir tarpusavio įtaka

Žaptorius

Garbanovas

2007

Business: Theory and Practice

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Santrauka. Nustatant įmonės vertę paprastai daug dėmesio skiriama vadinamajam diskontuotų pinigų srautų metodui. Čia verslo rizika įvertinama tik diskonto norma. Tai labai bendras įvertinimas, kuriame teoriškai turi atsispindėti visos įmanomos ir tikėtinosios rizikos. Modeliuojant verslo vertės dinamiką to nepakanka, nes verslo rizikos turi savo nevienodas ir kintamas tikimybes. Verslo rizikos, kurios naudojamos įmonei vertinti, neturi adekvataus tikimybių įvertinimo. Didesnės verslo vertės siekimas turi būti pagrįstas tyrimais, kuriuose modeliuojant ištiriamos vertės didinimo galimybės, remiantis vertės ir jos rizikos optimalaus santykio kriterijumi. Šio tyrimo tikslas -ištirti skirtingų verslo vertės teikėjų rizikingumo kitimo bei tarpusavio priklausomybių kitimo pasekmes verslo vertei, rezultatus išreiškiant verslo vertės rodiklio tikimybių skirstiniu. Tyrimo rezultatai parodė, kad įmonės vertės didinimas, kaip kiekvieno verslo objekto tikslas, gali ir turi būti analizuojamas neatsiejant nuo siekiamo vertės dydžio tikimybės, t. y. nuo tos verslo vertės rizikos.Reikšminiai žodžiai: vertinimas, vertės valdymas, vertės rizikingumas, simuliavimas, kintamųjų tarpusavio įtaka. Abstract. In business value calculations usualy great attention is given to the so-called discounted cash flows method. Here business risk estimation takes into account only the discount rate. This is a very general assumption, in which theoretically all possible and probable risks should be reflected. In modeling business value dynamics that is not enough, because all business risks have individual and changeable probabilities. Business risks used in business valuation are without adequate estimation of probabilities. Trying to achieve increased business value should be based on reaserches, in which by modeling we obtain possibilities for value increasening based on value and its risk optimal relationship criterion. The aim of this research is to obtain impact of changing riskiness of diferent business risk drivers on business value, and to obtain impact of interdependence of diferent business risk drivers on business value. The results are expressed with probability density function of business value variable. Research results show that increasening of business value as the goal of each business could and should be analized together with value variable probability, i.e. with value risk criterion. RISKINESS AND INTERDEPENDENCIES OF BUSINESS VALUE VARIABLES

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Section: Stochastinio Simuliavimo Pritaikymas Ir įDiegimasunclassified

Verslo vertės kintamųjų rizikingumas ir tarpusavio įtaka

Žaptorius

Garbanovas

2007

Business: Theory and Practice

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“…As shown by Embrechts et al (2001), the Pearson correlation is too restricted to describe the linear co-movements of two random processes. However, the copulas (e.g.…”

Section: Literature Reviewmentioning

confidence: 99%

Measuring and Testing Tail Dependence and Contagion Risk Between Major Stock Markets

2016

Comput Econ

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In this paper, three copula GARCH models i.e. Gaussian, Student-t, and Clayton are used to estimate and test the tail dependence measured by Kendall's tau between six stock indices.Since the contagion risk spreads from large markets to small markets, the tail dependence is studied for smaller Taiwanese and South Korean stock markets, i.e. Taiex and Kospi against four larger stock markets, i.e. S&P500, Nikkei, MSCI China, and MSCI Europe. The vector autoregression result indicates that S&P500 and MSCI China indeed impact mostly and significantly to the other four stock markets. However, the tail dependence of both Taiex and Kospi against S&P500 and MSCI Chia are lower due to unilateral impacts from US and China.Using Clayton copula GARCH, the threshold tests of Kendall's tau between most stock markets except China are significant during both subprime and Greek debt crises. The tests of Studentt copula GARCH estimated Kendall's taus are only acceptable for subprime crisis but not for Greek debt crisis. Thus, Clayton copula GARCH is found appropriate to estimate Kendall's taus as tested by threshold regression.

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“…Remark 2 Note that the inverse transformation R −1 of Rosenblatt's transformation leads to the conditional distribution method for sampling copulas, see, e.g., [10]. This link brings rise to the general idea of using sampling algorithms based on oneto-one transformations to construct goodness-of-fit tests.…”

Section: Rosenblatt's Transformation and A Corresponding Testmentioning

confidence: 99%

“…It is important to note that the inverse of this transformation leads to a popular sampling algorithm, the conditional distribution method, see, e.g., [10]. In other words, for a bijective transformation which converts d independent and identically distributed ("i.i.d.")…”

Section: Introductionmentioning

confidence: 99%

Goodness-of-fit Tests for Archimedean Copulas in High Dimensions

Hering

Hofert

2015

Innovations in Quantitative Risk Management

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A goodness-of-fit transformation for Archimedean copulas is presented from which a test can be derived. In a large-scale simulation study it is shown that the test performs well according to the error probability of the first kind and the power under several alternatives, especially in high dimensions where this test is (still) easy to apply. The test is compared to commonly applied tests for Archimedean copulas. However, these are usually numerically demanding (according to precision and runtime), especially when the dimension is large. The transformation underlying the newly proposed test was originally used for sampling random variates from Archimedean copulas. Its correctness is proven under weaker assumptions. It may be interpreted as an analogon to Rosenblatt's transformation which is linked to the conditional distribution method for sampling random variates. Furthermore, the suggested goodness-of-fit test complements a commonly used goodness-of-fit test based on the Kendall distribution function in the sense that it utilizes all other components of the transformation except the Kendall distribution function. Finally, a graphical test based on the proposed transformation is presented.

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Modelling Dependence with Copulas and Applications to Risk Management

Cited by 766 publications

References 13 publications

Verslo vertės kintamųjų rizikingumas ir tarpusavio įtaka

Verslo vertės kintamųjų rizikingumas ir tarpusavio įtaka

Measuring and Testing Tail Dependence and Contagion Risk Between Major Stock Markets

Goodness-of-fit Tests for Archimedean Copulas in High Dimensions

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