Models for heavy-tailed asset returns

Borak, Szymon; Misiorek, Adam; Weron, Rafał

doi:10.1007/978-3-642-18062-0_1

Cited by 44 publications

(34 citation statements)

References 65 publications

(67 reference statements)

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“…Empirical observations confirm heavy-tailed or leptokurtic distribution of price changes see e.g. [6] and references therein. Thus, Mandelbrot [7] and Fama [8] proposed the α-stable distribution instead of Gaussian law to describe asset returns.…”

Section: Introductionmentioning

confidence: 61%

Untitled

Gajda¹

2012

Acta Phys. Pol. B

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We develop a new class of continuous-time models based on the solutions of tempered fractional Langevin equations for Ornstein-Uhlenbeck process driven by Lévy noise. We present methods of simulation of sample paths of such processes. We show how to use such models in modeling short term interest rate. We develop tempered Vasiček interest rate model by finding explicit solutions of tempered fractional Langevin equations.

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Section: Introductionmentioning

confidence: 61%

Untitled

Gajda¹

2012

Acta Phys. Pol. B

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“…Akgiray and Lamoureux (1989), Borak, Misiorek, andWeron (2011), Garcia, Renault, andVeredas (2010), Kogon and Williams (1998), Lombardi and Calzolari (2008), and Rachev and Mittnik (2000) discuss the relative merits of some methods for estimating stable 14 Here, we use three estimators of α, β, γ, and δ: the quantile estimator of McCulloch (1986), the characteristic-function regression estimator of Koutrouvelis (1980) and Kogon and Williams (1998), and the ML estimator (DuMouchel 1973;Nolan 2001). For the ML procedure, we use an algorithm and software developed by Nolan (2001), which are discussed, for example, in Borak, Misiorek, and Weron (2011, 7-8 and 13) and Rachev and Mittnik (2000, 119-136).…”

Section: Do a Var's Reduced-form Shocks Have Infinite Variances? Estimentioning

confidence: 99%

Infinite-Variance, Alpha-Stable Shocks in Monetary SVAR: Final Working Paper Version

Hannsgen

2011

SSRN Journal

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Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in August 2011* Acknowledgments: The author thanks the Levy Institute for the opportunity to issue this more definitive and encompassing version of Levy Institute Working Paper no. 596, which appeared in May 2010. This final version was substantially completed in June 2011. It adds to the earlier working paper, among other things: a new introduction; new P-P plots that allow the reader to compare the fits of estimated normal, Student's-t, and stable distributions for the innovations in one VAR; tables reporting log-likelihoods and Kolmogorov-Smirnov and Anderson-Darling statistics for four error-term models and two different VAR specifications; and tables reporting many new results from parametric-bootstrap tests. Working Paper no. 596 itself was in turn a greatly revised and expanded version of Working Paper no. 546 (Hannsgen 2008), though it, too, featured many new findings. The author wishes to thank Olivier Blanchard, an associate editor, and anonymous referees for comments on previous drafts that led to many substantial improvements in the paper. Also, he thanks John Nolan for answers and advice, and those who attended a seminar at the Levy Institute for their useful comments and suggestions. The author is also grateful to Michael Woodroofe for guidance on Woodroofe's research. Discussions with Greg Colman and Kenneth Hannsgen led to improvements in some of the explanations and arguments presented in this and the earlier papers. Though grateful to each of the scholars mentioned above, the author has, of course, not followed all of their advice throughout this paper.The Levy Economics Institute Working Paper Collection presents research in progress by Levy Institute scholars and conference participants. The purpose of the series is to disseminate ideas to and elicit comments from academics and professionals.Levy Economics Institute of Bard College, founded in 1986, is a nonprofit, nonpartisan, independently funded research organization devoted to public service. Through scholarship and economic research it generates viable, effective public policy responses to important economic problems that profoundly affect the quality of life in the United States and abroad. ABSTRACTThis paper adumbrates a theory of what might be going wrong in the monetary SVAR literature and provides supporting empirical evidence. The theory is that macroeconomists may be attempting to identify structural forms that do not exist, given the true distribu...

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“…Let us give one example of such conclusions. Arguments connected to outliers usually arise when considering such time series as the Dow Jones Industrial Average index (say, for the interesting Period from the 3 January 2000 to 31 December 2009), daily ISE-100 Index (November 2, 1987 -June 8, 2001) and many others (see, e.g., [3], [1]). The observed fact is that quite a lot of data not only fall outside the 99% confidence interval on the mean, but also outside the range of ±5 σ from the average, or even ±10 σ.…”

Section: Definition Of Distant Outliersmentioning

confidence: 99%