Approximation of skewed and leptokurtic return distributions

References

• Anderson , TW and Darling , DA . 1952 . Asymptotic theory of certain ‘Goodness of Fit’ criteria based on stochastic processes . The Annals of Mathematical Statistics , 23 : 193 – 212 .
   Google Scholar
• Bianchi , ML , Rachev , ST , Kim , YS and Fabozzi , FJ . 2010 . Tempered infinitely divisible distributions and processes . SIAM: Theory of Probability and Its Applications , 55 : 59 – 86 .
   Web of Science ®Google Scholar
• Boyarchenko , SI and Levendorskii , SZ . 2000 . Option pricing for truncated Lévy processes . International Journal of Theoretical and Applied Finance , 3 : 549 – 52 .
   Google Scholar
• Carr , P , Geman , H , Madan , DB and Yor , M . 2002 . The fine structure of asset returns: an empirical investigation . Journal of Business , 75 : 305 – 33 .
   Web of Science ®Google Scholar
• Cramér , H . 1928 . On the composition of elementary errors . Skandinavisk Aktuarietidskrift , 11 : 13 – 74 . 141–80
   Google Scholar
• DuMouchel , WH . 1975 . Stable distributions in statistical inference: 2. Information from stably distributed samples . Journal of the American Statistical Association , 70 : 386 – 93 .
   Web of Science ®Google Scholar
• Fama , EF . 1963 . Mandelbrot and the stable Paretian hypothesis . Journal of Business , 36 : 420 – 5 .
   Web of Science ®Google Scholar
• Fritsch , FN and Carlson , RE . 1980 . Monotone piecewise cubic interpolation . SIAM Journal on Numerical Analysis , 17 : 238 – 46 .
   Web of Science ®Google Scholar
• Kim , YS , Rachev , ST , Bianchi , ML and Fabozzi , FJ . 2008a . Financial market models with Lévy processes and time-varying volatility . Journal of Banking and Finance , 32 : 1363 – 78 .
   Web of Science ®Google Scholar
• Kim , YS , Rachev , ST , Bianchi , ML and Fabozzi , FJ . 2008b . “ A new tempered stable distribution and its application to finance ” . In Risk Assessment: Decisions in Banking and Finance , Edited by: Bol , G , Rachev , ST and Wuerth , R . 77 – 110 . Heidelberg : Physika Verlag, Springer .
   Google Scholar
• Kim , YS , Rachev , ST , Bianchi , ML and Fabozzi , FJ . 2010a . Computing VaR and AVaR in infinitely divisible distributions . Probability and Mathematical Statistics , 30 : 223 – 45 .
   Web of Science ®Google Scholar
• Kim , YS , Rachev , ST , Bianchi , ML and Fabozzi , FJ . 2010b . Tempered stable and tempered infinitely divisible GARCH models . Journal of Banking and Finance , 34 : 2096 – 109 .
   Web of Science ®Google Scholar
• Kolmogorov , AN . 1933 . Sulla determinazione empirica delle leggi di probabilita . Giornale dell'Istituto Italiano Degli Attuari , 18 : 1 – 11 .
   Google Scholar
• Koponen , I . 1995 . Analytic approach to the problem of convergence of truncated Lévy flights towards the Gaussian stochastic process . Physical Review , 52 : 1197 – 9 .
   Google Scholar
• Mandelbrot , B . 1963 . The variation of certain speculative prices . Journal of Business , 36 : 394 – 419 .
   Web of Science ®Google Scholar
• Menn , C and Rachev , ST . 2006 . Calibrated FFT-based density approximations for α-stable distributions . Computational Statistics and Data Analysis , 50 : 1891 – 904 .
   Web of Science ®Google Scholar
• Mittnik , S , Doganoglu , T and Chenyao , D . 1999 . Computing the probability density function of the stable Paretian distribution . Mathematical and Computing Modelling , 29 : 235 – 40 .
   Web of Science ®Google Scholar
• Rachev , ST , Fabozzi , FJ and Menn , C . 2005 . Fat-Tailed and Skewed Asset Return Distributions: Implications for Risk Management, Portfolio Selection, and Option Pricing , New Jersey : John Wiley & Sons .
   Google Scholar
• Rachev , S and Mittnik , S . 2000 . Stable Paretian Models in Finance , Chichester : John Wiley & Sons .
   Google Scholar
• Rosiński , J . 2007 . Tempering stable processes . Stochastic Processes and Their Applications , 117 : 677 – 707 .
   Web of Science ®Google Scholar
• Sato , K . 1999 . Lévy Processes and Infinitely Divisible Distributions , Cambridge : Cambridge University Press .
   Google Scholar