publication . Preprint . Article . 2013

The Origin of Fat Tails

Martin Gremm;
Open Access English
  • Published: 16 Oct 2013
Abstract
We propose a random walk model of asset returns where the parameters depend on market stress. Stress is measured by, e.g., the value of an implied volatility index. We show that model parameters including standard deviations and correlations can be estimated robustly and that all distributions are approximately normal. Fat tails in observed distributions occur because time series sample different stress levels and therefore different normal distributions. This provides a quantitative description of the observed distribution including the fat tails. We discuss simple applications in risk management and portfolio construction.
doi: 10.1142/s0219024915500545 , 10.2139/ssrn.2337830
Subjects
free text keywords: Quantitative Finance - General Finance, Random walk, Financial models with long-tailed distributions and volatility clustering, Normal distribution, Volatility clustering, Heavy-tailed distribution, Financial economics, Economics, Stochastic volatility, Implied volatility, Volatility (finance), Statistical physics
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