Monte Carlo-based tail exponent estimator

TL;DR

This paper introduces a Monte Carlo-based method for estimating the tail exponent in financial markets, addressing limitations of existing estimators like Hill's, especially on small samples, and demonstrating its effectiveness on stock market data.

Contribution

A novel Monte Carlo-based estimator for tail exponents that is robust to sample size and provides unbiased, reliable estimates with confidence intervals.

Findings

The Hill estimator overestimates the tail exponent in small samples.

The new estimator performs well on small data samples.

Application to stock indices demonstrates the estimator's practical utility.

Abstract

In this paper we propose a new approach to estimation of the tail exponent in financial stock markets. We begin the study with the finite sample behavior of the Hill estimator under {\alpha}-stable distributions. Using large Monte Carlo simulations, we show that the Hill estimator overestimates the true tail exponent and can hardly be used on samples with small length. Utilizing our results, we introduce a Monte Carlo-based method of estimation for the tail exponent. Our proposed method is not sensitive to the choice of tail size and works well also on small data samples. The new estimator also gives unbiased results with symmetrical confidence intervals. Finally, we demonstrate the power of our estimator on the international world stock market indices. On the two separate periods of 2002-2005 and 2006-2009, we estimate the tail exponent.