Copulae in Mathematical and Quantitative Finance

Copulas are mathematical objects that fully capture the dependence structure among random variables and hence offer great flexibility in building multivariate stochastic models. Since their introduction in the early 1950s, copulas have gained considerable popularity in several fields of applied mathematics, especially finance and insurance. Today, copulas represent a well-recognized tool for market and credit models, aggregation of risks, and portfolio selection. Historically, the Gaussian copula model has been one of the most common models in credit risk. However, the recent financial crisis has underlined its limitations and drawbacks. In fact, despite their simplicity, Gaussian copula models severely underestimate the risk of the occurrence of joint extreme events. Recent theoretical investigations have put new tools for detecting and estimating dependence and risk (like tail dependence, time-varying models, etc) in the spotlight. All such investigations need to be further developed and promoted, a goal this book pursues. The book includes surveys that provide an up-to-date account of essential aspects of copula models in quantitative finance, as well as the extended versions of talks selected from papers presented at the workshop in Cracow.

• Gaussian copula model
• Random variables
• Tail dependence
• Time-varying models
• quantitative finance

• Faculty of Mathematics, Informatics, and Mechanics, University of Warsaw, Warszawa, Poland

  Piotr Jaworski

• School of Economics and Management, Free University of Bozen-Bolzano, Bozen, Italy

  Fabrizio Durante

• L.v.Bortkiewicz Chair of Statistics, C.A.S.E. Centre f. Appl. Stat. & Econ., Humboldt-Universität zu Berlin, Berlin, Germany

  Wolfgang Karl Härdle

Piotr Jaworski is a Professor at the Faculty of Mathematics, Informatics and Mechanics at the Warsaw University Institute of Mathematics. He is also active in the Section of Financial and Actuarial Mathematics. He has engaged in research stays at several universities, e.g. Moscow State University (PhD studies), University of North Carolina in Chapel Hill (USA), University of Muenster (Germany), University of Dortmund (Germany), University of Cottbus (Germany) and Johannes Kepler University of Linz (Austria). At present his researches primarily focuses on the copula approach to multivariate modeling, risk theory and portfolio analysis.

Fabrizio Durante received his PhD (2006) at the University of Lecce (Italy) and completed his postdoctoral studies (2010) at the Johannes Kepler University of Linz (Austria). From 2006-2010, he was an assistant professor at Johannes Kepler University of Linz (Austria), before he started his appointment as an assistant professor in Statistics at the Free University of Bolzano-Bozen in 2010. He has had research stays at several European universities, e.g. Humboldt University (Berlin, Germany), University "La Sapienza" (Rome, Italy), University of Bratislava (Slovakia), University of Granada (Spain), and the University of Warsaw (Poland). His research interests include stochastic models, reliability theory, and risk management.

Wolfgang Karl Härdle is a Professor of Statistics at the Humboldt-Universität zu Berlin and the Director of CASE – the Centre for Applied Statistics and Economics. He teaches quantitative finance and semi-parametric statistical methods. His research focuses on dynamic factor models, multivariate statistics in finance and computational statistics. He is an elected member of the ISI and an advisor to the Guanghua School of Management, Peking University and to National Central University, Taiwan.

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