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Models for Heavy-tailed Asset Returns

  • Szymon Borak
  • Adam Misiorek
  • Rafal Weron

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.

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File URL: http://www.im.pwr.wroc.pl/~hugo/RePEc/wuu/wpaper/HSC_10_01.pdf
File Function: Original version, 2010
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Paper provided by Hugo Steinhaus Center, Wroclaw University of Technology in its series HSC Research Reports with number HSC/10/01.

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Length: 38 pages
Date of creation: 2010
Date of revision:
Handle: RePEc:wuu:wpaper:hsc1001
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  1. Hautsch, Nikolaus & Hess, Dieter E. & Veredas, David, 2011. "The impact of macroeconomic news on quote adjustments, noise, and informational volatility," CFR Working Papers 11-06, University of Cologne, Centre for Financial Research (CFR).
  2. Ulrich Horst & Traian A. Pirvu & Gonçalo Dos Reis, 2010. "On Securitization, Market Completion and Equilibrium Risk Transfer," SFB 649 Discussion Papers SFB649DP2010-010, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  3. Agnieszka Janek & Tino Kluge & Rafal Weron & Uwe Wystup, 2010. "FX Smile in the Heston Model," HSC Research Reports HSC/10/02, Hugo Steinhaus Center, Wroclaw University of Technology.
  4. Nikolaus Hautsch & Fuyu Yang, 2010. "Bayesian Inference in a Stochastic Volatility Nelson-Siegel Model," SFB 649 Discussion Papers SFB649DP2010-004, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  5. Keith Kuester & Stefan Mittnik & Marc S. Paolella, 2006. "Value-at-Risk Prediction: A Comparison of Alternative Strategies," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 4(1), pages 53-89.
  6. Nikolaus Hautsch & Mark Podolskij, 2010. "Pre-Averaging Based Estimation of Quadratic Variation in the Presence of Noise and Jumps: Theory, Implementation, and Empirical Evidence," CREATES Research Papers 2010-29, School of Economics and Management, University of Aarhus.
  7. Philipp Hartmann & Jon Danielsson, 1998. "The Cost of Conservatism: Extreme Returns, Value-at Risk, and the Basle Multiplicaiton Factor," FMG Special Papers sp100, Financial Markets Group.
  8. Rafal Weron, 2006. "Modeling and Forecasting Electricity Loads and Prices: A Statistical Approach," HSC Books, Hugo Steinhaus Center, Wroclaw University of Technology, number hsbook0601.
  9. Ulrich Horst & Santiago Moreno-Bromberg, 2011. "Efficiency and Equilibria in Games of Optimal Derivative Design," Papers 1107.0839, arXiv.org.
  10. Johanna Kappus & Markus Reiß, 2011. "Estimation of the characteristics of a Lévy process observed at arbitrary frequency," SFB 649 Discussion Papers SFB649DP2011-027, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  11. Wolfgang Karl Härdle & Yarema Okhrin & Weining Wang, 2010. "Uniform confidence bands for pricing kernels," SFB 649 Discussion Papers SFB649DP2010-003, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  12. Wolfgang Karl Härdle & Rainer Schulz & Weining Wang, 2010. "Prognose mit nichtparametrischen Verfahren," SFB 649 Discussion Papers SFB649DP2010-041, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  13. repec:ulb:ulbeco:2013/136280 is not listed on IDEAS
  14. Burnecki, Krzysztof & Janczura, Joanna & Weron, Rafal, 2010. "Building Loss Models," MPRA Paper 25492, University Library of Munich, Germany.
  15. Richard B. Olsen & Ulrich A. Müller & Michel M. Dacorogna & Olivier V. Pictet & Rakhal R. Davé & Dominique M. Guillaume, 1997. "From the bird's eye to the microscope: A survey of new stylized facts of the intra-daily foreign exchange markets (*)," Finance and Stochastics, Springer, vol. 1(2), pages 95-129.
  16. GARCIA, René & RENAULT, Eric & VEREDAS, David, 2006. "Estimation of stable distributions by indirect inference," CORE Discussion Papers 2006112, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  17. Fiocco Raffaele, 2013. "The Optimal Institutional Design of Vertically Related Markets with Unknown Upstream Costs," Review of Network Economics, De Gruyter, vol. 12(2), pages 183-210, June.
  18. Rafal Weron, 2001. "Levy-stable distributions revisited: tail index > 2 does not exclude the Levy-stable regime," HSC Research Reports HSC/01/01, Hugo Steinhaus Center, Wroclaw University of Technology.
  19. Rosinski, Jan, 2007. "Tempering stable processes," Stochastic Processes and their Applications, Elsevier, vol. 117(6), pages 677-707, June.
  20. Abbassi, Puriya & Nautz, Dieter, 2010. "Monetary transmission right from the start: The (dis)connection netween the money market and the ECB's main refinancing rates," Discussion Papers 2010/7, Free University Berlin, School of Business & Economics.
  21. Burda, Michael C. & Weder, Mark, 2010. "Payroll Taxes, Social Insurance and Business Cycles," IZA Discussion Papers 5150, Institute for the Study of Labor (IZA).
  22. Benoit Mandelbrot, 1963. "The Variation of Certain Speculative Prices," The Journal of Business, University of Chicago Press, vol. 36, pages 394.
  23. Aleksander Janicki & Aleksander Weron, 1994. "Simulation and Chaotic Behavior of Alpha-stable Stochastic Processes," HSC Books, Hugo Steinhaus Center, Wroclaw University of Technology, number hsbook9401.
  24. Schmidt, Sandra & Nautz, Dieter, 2010. "Why do financial market experts misperceive future monetary policy decisions?," ZEW Discussion Papers 10-045, ZEW - Zentrum für Europäische Wirtschaftsforschung / Center for European Economic Research.
  25. Vladimir Panov, 2010. "Non-Gaussian Component Analysis: New Ideas, New Proofs, New Applications," SFB 649 Discussion Papers SFB649DP2010-026, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  26. Lombardi, Marco J., 2007. "Bayesian inference for [alpha]-stable distributions: A random walk MCMC approach," Computational Statistics & Data Analysis, Elsevier, vol. 51(5), pages 2688-2700, February.
  27. Szymon Borak & Adam Misiorek & Rafał Weron, 2010. "Models for Heavy-tailed Asset Returns," SFB 649 Discussion Papers SFB649DP2010-049, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  28. Rafal Weron & Adam Misiorek, 2005. "Modeling and forecasting electricity loads: A comparison," Econometrics 0502004, EconWPA.
  29. Dominicy, Yves & Veredas, David, 2013. "The method of simulated quantiles," Journal of Econometrics, Elsevier, vol. 172(2), pages 235-247.
  30. Jérémy Poirot & Peter Tankov, 2006. "Monte Carlo Option Pricing for Tempered Stable (CGMY) Processes," Asia-Pacific Financial Markets, Springer, vol. 13(4), pages 327-344, December.
  31. Thomas Post & Katja Hanewald, 2010. "Stochastic Mortality, Subjective Survival Expectations, and Individual Saving Behavior," SFB 649 Discussion Papers SFB649DP2010-040, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  32. Chen, Ying & Härdle, Wolfgang & Jeong, Seok-Oh, 2008. "Nonparametric Risk Management With Generalized Hyperbolic Distributions," Journal of the American Statistical Association, American Statistical Association, vol. 103(483), pages 910-923.
  33. Rama Cont & Marc Potters & Jean-Philippe Bouchaud, 1997. "Scaling in stock market data: stable laws and beyond," Papers cond-mat/9705087, arXiv.org.
  34. Andrew Matacz, 1997. "Financial modeling and option theory with the truncated Lévy process," Science & Finance (CFM) working paper archive 500035, Science & Finance, Capital Fund Management.
  35. Mengmeng Guo & Wolfgang Karl Härdle, 2010. "Adaptive Interest Rate Modelling," SFB 649 Discussion Papers SFB649DP2010-029, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  36. Peter Carr & Helyette Geman, 2002. "The Fine Structure of Asset Returns: An Empirical Investigation," The Journal of Business, University of Chicago Press, vol. 75(2), pages 305-332, April.
  37. Lillestøl, Jostein, 2000. "Bayesian estimation of NIG-parameters by Markov Chain Monte Carlo Methods," SFB 373 Discussion Papers 2000,112, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  38. Christian Basteck & Tijmen R. Daniëls & Frank Heinemann, 2010. "Characterising Equilibrium Selection in Global Games with Strategic Complementarities," SFB 649 Discussion Papers SFB649DP2010-008, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  39. Ulrich Horst & Felix Naujokat, 2008. "Illiquidity and Derivative Valuation," Papers 0901.0091, arXiv.org.
  40. Maria Grith & Wolfgang Karl Härdle & Melanie Schienle, 2010. "Nonparametric Estimation of Risk-Neutral Densities," SFB 649 Discussion Papers SFB649DP2010-021, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  41. Winfried Stute & Wenceslao Manteiga & Manuel Quindimil, 1993. "Bootstrap based goodness-of-fit-tests," Metrika, Springer, vol. 40(1), pages 243-256, December.
  42. Juliane Scheffel, 2010. "Honey, I’ll Be Working Late Tonight. The Effect of Individual Work Routines on Leisure Time Synchronization of Couples," SFB 649 Discussion Papers SFB649DP2010-016, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  43. Wolfgang Karl Härdle & Yuichi Mori & Jürgen Symanzik, 2012. "Computational Statistics (Journal)," SFB 649 Discussion Papers SFB649DP2012-004, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  44. Fang Yao, 2010. "Aggregate Hazard Function in Price-Setting: A Bayesian Analysis Using Macro Data," SFB 649 Discussion Papers SFB649DP2010-020, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  45. Weron, Rafal, 1996. "On the Chambers-Mallows-Stuck method for simulating skewed stable random variables," Statistics & Probability Letters, Elsevier, vol. 28(2), pages 165-171, June.
  46. Weron, Rafał, 2004. "Computationally intensive Value at Risk calculations," Papers 2004,32, Humboldt-Universität Berlin, Center for Applied Statistics and Economics (CASE).
  47. Aleksander Janicki & Aleksander Weron, 1994. "Can One See Alpha-stable Variables and Processes?," HSC Research Reports HSC/94/01, Hugo Steinhaus Center, Wroclaw University of Technology.
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