Abstract

In the paper, we begin with introducing a novel scale mixture of normal distribution such that its leptokurticity and fat-tailedness are only local, with this “locality” being separately controlled by two censoring parameters. This new, locally leptokurtic and fat-tailed (LLFT) distribution makes a viable alternative for other, globally leptokurtic, fat-tailed and symmetric distributions, typically entertained in financial volatility modelling. Then, we incorporate the LLFT distribution into a basic stochastic volatility (SV) model to yield a flexible alternative for common heavy-tailed SV models. For the resulting LLFT-SV model, we develop a Bayesian statistical framework and effective MCMC methods to enable posterior sampling of the parameters and latent variables. Empirical results indicate the validity of the LLFT-SV specification for modelling both “non-standard” financial time series with repeating zero returns, as well as more “typical” data on the S&P 500 and DAX indices. For the former, the LLFT-SV model is also shown to markedly outperform a common, globally heavy-tailed, t-SV alternative in terms of density forecasting. Applications of the proposed distribution in more advanced SV models seem to be easily attainable.

Highlights

  • Received: 30 April 2021Accepted: 26 May 2021Published: 30 May 2021Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims inMost of leptokurtic and heavy-tailed distributions, commonly entertained in financial volatility modelling, may be derived as scale mixtures of normal (SMN) distributions, with the concept dating back to [1]

  • We present the results obtained for the original MSAG.DE data set and assumea priori that the values of c very close to 0 are unlikely

  • We illustrate the validity of the locally both leptokurtic and fat-tailed (LLFT)-stochastic volatility (SV) model in the case where repeated observations do no occur per se, but the series still contains values that concentrate tightly around the mode

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Summary

Introduction

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in. Most of leptokurtic and heavy-tailed distributions, commonly entertained in financial volatility modelling, may be derived as scale mixtures of normal (SMN) distributions, with the concept dating back to [1]. SMN is a very wide and useful class of distributions, which belongs to an even wider class of elliptical distributions (see [2]). We say that a random variable e follows a scale mixture of normals if it has the following stochastic representation: published maps and institutional affile = V −1/2 Z, iations. Where Z has a standard normal distribution independent from a positive random variable

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