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The Origin of Fat Tails

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  • Martin Gremm

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.

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  • Martin Gremm, 2013. "The Origin of Fat Tails," Papers 1310.4538, arXiv.org, revised May 2014.
  • Handle: RePEc:arx:papers:1310.4538
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    File URL: http://arxiv.org/pdf/1310.4538
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    1. Lux, Thomas, 1998. "The socio-economic dynamics of speculative markets: interacting agents, chaos, and the fat tails of return distributions," Journal of Economic Behavior & Organization, Elsevier, vol. 33(2), pages 143-165, January.
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