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Tempered Stable Laws for Modeling Financial Returns

Article arXiv papers · Author: A. H. Nzokem
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Summary

The document describes two probability distributions linked to the Generalized Tempered Stable (GTS) distribution: its background driving Lévy process and a self-decomposable law constructed using that process. It also places these distributions in an Ornstein–Uhlenbeck framework, where they can serve as stationary distributions for modeling evolving returns.

For simulation, the paper samples from a random integral representation and applies the method to daily cumulative returns for the S&P 500 Index and Bitcoin. This gives a way to generate return paths using distributions designed to represent non-Gaussian behavior. The provided description does not report quantitative comparisons, parameter choices, or evidence that the simulated paths forecast returns or improve trading performance. Its examples therefore illustrate a modeling and simulation approach rather than a validated trading strategy.

Key ideas

  • The paper derives a background driving Lévy process associated with the Generalized Tempered Stable distribution.
  • It constructs a self-decomposable distribution using the GTS distribution as its background driving process.
  • The resulting distributions can be used as stationary laws in Ornstein–Uhlenbeck type processes.
  • A random integral representation provides a simulation method for daily cumulative return processes.
  • The method is illustrated with S&P 500 Index and Bitcoin returns, without reported evidence of predictive trading value.

Tags

StatisticsVolatilityEquitiesCrypto
Full text
# Self-Decomposable Laws Associated with General Tempered Stable (GTS) Distribution and their Simulation Applications


# Self-Decomposable Laws Associated with General Tempered Stable (GTS) Distribution and their Simulation Applications









The paper describes the self-decomposable distribution and the background driving Lévy process (BDLP) associated with the Generalized Tempered Stable (GTS) distribution. Two distributions are provided: the background driving Lévy process (BDLP) of the GTS distribution and the self-decomposable distribution generated by the GTS distribution as BDLP. The derived self-decomposable distribution and the GTS distribution are used as stationary distribution in the Ornstein-Uhlenbeck type process. A simulation method, based on sampling the random integral representation, is applied to mimic S&P 500 Index and Bitcoin daily cumulative return process.

Shown in full with attribution under the source's licence. Licence: abstract CC0

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.