Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/56648
Authors: 
Borak, Szymon
Misiorek, Adam
Weron, Rafał
Year of Publication: 
2010
Series/Report no.: 
SFB 649 discussion paper 2010-049
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 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 heavy-tailed models. We first describe the historically oldest heavy-tailed model - the stable laws. Next, we briefly characterize their recent lighter-tailed 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.
Subjects: 
heavy-tailed distribution
stable distribution
tempered stable distribution
generalized hyperbolic distribution
asset return
random number generation
parameter estimation
JEL: 
C13
C15
C16
G32
Document Type: 
Working Paper

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