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Modelowanie struktur zależności za pomocą funkcji połączeń w analizie ryzyka ubezpieczyciela

100%
Wanat S., Uniwersytet Ekonomiczny w Krakowie; Wydział Zarządzania; Katedra Statystyki
Acta Universitatis Lodziensis. Folia Oeconomica
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2011
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vol. 254
EN
This paper aims to present copulas, as a modeling tool which will give the 'richer' dependency structures than the use of linear correlation. The paper presents definitions and basic properties of the copula function. Discusses its relationship with the basic types of dependencies used in risk management i.e. comonotonicity, countermonotonicity, independence and linear dependence and the basic measures of dependence (Pearson's correlation, Kendall's rank correlation, Spearman's rank correlation, Blomqvist's beta, upper (lower) tail dependence parameter). Then selected family of copulas have been characterized and is an example of construction of two-dimensional dis- tribution, where the marginal distributions are known and the Kendall's rank correlation between them. Calculations and graphs were performed using the package „R”.
2
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Odporność standardowej formuły wyznaczania kapitałowych wymogów wypłacalności na błędną specyfikację zależności

63%
Wanat S., Guzik K.
Prace Naukowe Uniwersytetu Ekonomicznego we Wrocławiu
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2018
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issue 541
283-294
PL
Tematyka referatu wpisuje się w dyskusję dotyczącą poprawności stosowanej w Solvency II standardowej formuły wyznaczania kapitałowych wymogów wypłacalności. Uwagę skoncentrowano na odporności tej formuły na błędną specyfikację struktury zależności. W pracy, wykorzystując jedno z najnowszych narzędzi szacowania ograniczeń dla VaR, pokazano na konkretnym przykładzie, że stosowanie formuły standardowej zgodnie z Rozporządzeniem Delegowanym Komisji (UE) 2015/35, zapisanym w art. 115, może prowadzić do wyznaczenia kapitałowych wymogów dla ryzyka składki i rezerw na niewłaściwym poziomie. Z przeprowadzonej analizy wynika, że poprawne oszacowanie SCR-ów zależy od poprawnej identyfikacji struktury zależności między zmiennymi losowymi modelującymi nieoczekiwane straty. Wykorzystanie w tym celu tylko współczynników korelacji liniowej może prowadzić do błędnych wyników, gdyż opisują one w sposób jednoznaczny tylko zależności liniowe. Ogólnie różne struktury zależności mogą charakteryzować się taką samą wartością tego współczynnika.
EN
The article subject fits into the discussion on the correctness of the standard formula for determining capital solvency requirements applied in Solvency II. Attention was focused on the robustness of this formula for an incorrect dependency specification. In the paper by using one of the latest tools of estimating VaR bounds on a concrete example it was shown that applying the standard formula according to the Commission Delegated Regulation (EU) 2015/35 provided in Article 115, may result in determining the solvency capital requirements for the non-life premium and reserve risk at an inappropriate level. The performed analysis shows that the proper estimation of SCRs depends on the correct identification of the dependence structure between the random variables modelling unexpected losses. When only Pearson correlation coefficients are used for this purpose it may lead to erroneous results, because they describe explicitly only linear dependencies. In a general case different dependence structures can be characterized by the same value of this coefficient.
3
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In Search of Hedges and Safe Havens in Global Financial Markets

51%
Wanat S., Śmiech S., Papież M.
Statistics in Transition new series
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2016
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vol. 17
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issue 3
557-574
EN
The aim of the paper is to search for hedges and safe havens within three instrument classes: assets (represented by the S&P500 index), gold and oil prices, and dollar exchange rates. Weekly series of returns of all the instruments from the period January 1995 – June 2015 are analysed. The study is based on conditional correlations between the instruments in different market regimes obtained with the use of copula-DCC GARCH models. It is assumed that different market regimes will be identified by statistical clustering techniques; however, only conditional variances (without conditional covariances) will be taken into account. The reason for this assumption is connected with the fact that variances can be understood as market risk, and, as such, are a good indicator of market conditions. A considerable advantage of such an approach is the lack of need to determine the number of market regimes, as it is established by clustering quality measures. What is more, the methodology used in the paper makes it possible to treat the relations between instruments symmetrically. The results obtained in the study reveal that only dollar exchange rates can be treated as a (strong) hedge and a (strong) safe haven for other instruments, while gold and oil are a hedge for assets.
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