Fat tailed Probability Distributions: Applications in Asset Pricing and Financial Econometrics

Dear Colleagues,

It is now widely established, since the seminal work of Mandelbrot (1963) that, financial time series, such as commodity prices and prices of company stocks, are better described by probability distributions that exhibit fat tails. In particular, modeling these time series with such distributions is superior to modeling with the much more commonly used Gaussian distributions.

The development of volatility models by Robert Engle (1982) sparked a debate in the literature on whether the fat tails, discovered by Mandelbrot (1963), were a consequence of volatility clustering exhibited by these models, e.g. see de Vries (1991). However, the ensuing literature has convincingly established the suitability of modeling financial time series with fat-tailed distributions, in addition to modeling their time-varying volatility through the AutoRegressive Conditionally Heteroskedastic (ARCH) class of models of Engle (1982), or its myriad variants, including stochastic volatility models.

Ignoring fat tails, when present, in models of financial time series leads to consequences for properties of estimators, such as incorrect standard errors, non-standard asymptotic distributions, and so forth. In applied work, this has consequences for myriad issues related to modeling financial series, such as testing for predictability of stock prices, measurements of value-at-risk, measurements of implied volatility, options prices, to name a few; e.g. see Fama (1992) and McCulloch (1996).

This Special Issue entitled, “Fat-tailed Probability Distributions: Applications in Asset Pricing and Financial Econometrics” aims to publish high-quality current research at the forefront of this area. It has been a while since Dufour et al (2010) edited a special volume devoted to a somewhat similar endeavor.

Sincerely yours,

Prasad V. Bidarkota
Guest Editor

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References

De Vries, C. (1991), On the Relation between GARCH and Stable Processes, Journal of Econometrics 48, p. 313‐324.
Dufour, J‐M. et al (2010), Heavy Tails and Paretian Distributions in Empirical Finance. A Volume Honoring Benoît Mandelbrot, Journal of Empirical Finance, Vol. 17, No. 2, p. 177‐282.
Engle, R.F. (1982), Autoregressive conditional heteroskedasticity with estimates of the variance of United Kingdom inflation, Econometrica, Vol. 50, No. 4, p. 987-1007.
Fama, E. F. (1992), Efficient Capital Markets: II, The Journal of Finance, Vol. XLVI, No. 5, p. 1575‐1617.
Mandelbrot, B. (1963), The Variation of Certain Speculative Prices, The Journal of Business, Vol. 36, No. 4, p. 394‐419.
McCulloch, J. H. (1996), Financial Applications of Stable Distributions, Handbook of Statistics 14, p. 393‐425.