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Models for heavy-tailed asset returns

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Statistical Tools for Finance and Insurance

Abstract

Many of the concepts in theoretical and empirical finance developed over the past decades – including the classical portfolio theory, the Black-Scholes-Merton option pricing model or the RiskMetrics variance-covariance approach to Value at Risk (VaR) – rest upon the assumption that asset returns follow a normal distribution. But this assumption is not justified by empirical data! Rather, the empirical observations exhibit excess kurtosis, more colloquially known as fat tails or heavy tails (Guillaume et al., 1997; Rachev and Mittnik, 2000). The contrast with the Gaussian law can be striking, as in Figure 1.1 where we illustrate this phenomenon using a ten-year history of the Dow Jones Industrial Average (DJIA) index.

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Author information

Authors and Affiliations

  1. Center for Applied Statistics and Economics, Humboldt-Universität zu Berlin, Berlin, Germany

    Szymon Borak

  2. Santander Consumer Bank S.A., Wrocław, Poland

    Adam Misiorek

  3. Institute of Organization and Management, Wrocław University of Technology, Wrocław, Poland

    Rafał Weron

Authors
  1. Szymon Borak
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  2. Adam Misiorek
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  3. Rafał Weron
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Editor information

Editors and Affiliations

  1. Fac. Economics & Business Administration, Dept. Econometrics &, Tilburg University, Tilburg, 5000, Netherlands

    Pavel Cizek

  2. L.v.Bortkiewicz Chair of Statistics, C.A.S.E. Centre f. Appl. Stat. & Econ., Humboldt-Universität zu Berlin, Unter den Linden 6, Berlin, 10099, Germany

    Wolfgang Karl Härdle

  3. , Institute of Organization and, Wrocław University of Technology, Wyb. Wyspiańskiego 27, Wrocław, 50-370, Poland

    Rafał Weron

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Borak, S., Misiorek, A., Weron, R. (2011). Models for heavy-tailed asset returns. In: Cizek, P., Härdle, W., Weron, R. (eds) Statistical Tools for Finance and Insurance. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-18062-0_1

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