Borak, Szymon and Misiorek, Adam and Weron, Rafal (2010): Models for Heavytailed Asset Returns.

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Abstract
Many of the concepts in theoretical and empirical finance developed over the past decades – including the classical portfolio theory, the BlackScholesMerton option pricing model or the RiskMetrics variancecovariance approach to 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. This chapter is intended as a guide to heavytailed models. We first describe the historically oldest heavytailed model – the stable laws. Next, we briefly characterize their recent lightertailed generalizations, the socalled truncated and tempered stable distributions. Then we study the class of generalized hyperbolic laws, which – like tempered stable distributions – can be classified somewhere between infinite variance stable laws and the Gaussian distribution. Finally, we provide numerical examples.
Item Type:  MPRA Paper 

Original Title:  Models for Heavytailed Asset Returns 
Language:  English 
Keywords:  Heavytailed distribution; Stable distribution; Tempered stable distribution; Generalized hyperbolic distribution; Asset return; Random number generation; Parameter estimation 
Subjects:  C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C16  Specific Distributions C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C13  Estimation: General G  Financial Economics > G3  Corporate Finance and Governance > G32  Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C15  Statistical Simulation Methods: General 
Item ID:  25494 
Depositing User:  Rafal Weron 
Date Deposited:  28. Sep 2010 20:15 
Last Modified:  15. Feb 2013 21:41 
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URI:  http://mpra.ub.unimuenchen.de/id/eprint/25494 