Superstatistics with cut-off tails for financial time series

TL;DR

This paper introduces a superstatistics model with tail cut-offs to better describe the fat-tailed and truncated distributions observed in financial time series, and proposes an option pricing formula based on this model.

Contribution

It extends superstatistics by incorporating tail cut-offs and demonstrates its effectiveness in modeling real financial data and option pricing.

Findings

The model captures fat-tailed and cut-off tail behaviors in financial data.

The proposed option pricing formula aligns with empirical market data.

Superstatistics with cut-offs improves financial risk modeling.

Abstract

Financial time series have been investigated to follow fat-tailed distributions. Further, an empirical probability distribution sometimes shows cut-off shapes on its tails. To describe this stylized fact, we incorporate the cut-off effect in superstatistics. Then we confirm that the presented stochastic model is capable of describing the statistical properties of real financial time series. In addition, we present an option pricing formula with respect to superstatistics.