Taking into account the rate of convergence in CLT under Risk evaluation on financial markets

Levon Kazaryan,Gregory Kantorovich

doi:10.1080/23322039.2017.1302870

Abstract

This paper examines “fat tails puzzle” in the financial markets. Ignoring the rate of convergence in Central Limit Theorem (CLT) provides the “fat tail” uncertainty. In this paper, we provide a rev...

Highlights

In economic theory and in practice, often used models have with a normal distribution
Empirical studies show that the practical use of the normal distribution does not take into account a “fat tail puzzle” of fat tails of distributions
Fat tails arise when one uses a normal distribution ignoring the rate of convergence in the Central Limit Theorem

Summary

Introduction

In economic theory and in practice, often used models have with a normal distribution. The following hypotheses have been tested: H0: G-bound evaluates risks on the financial markets more accurately than normal distribution and CLT. Building Gk, n(t), bounds follow from the well-known results on the rate of convergence to the normal distribution (Berry, 1941) and inequalities for sums of independent random variables. Based on these results, the hypothesis about the analytical construction of G-bounds corresponding to the frequency of losses in the stock markets is fully confirmed. The criterion of a random distribution of log returns of stock indexes is a fundamental issue in the study hypothesis of weak-form market efficiency (Table 3).

1.92 France

Findings

Conclusion