The stabilizing effect of volatility in financial markets

TL;DR

This paper reveals that both high and low volatility levels can lead to market instability, challenging the traditional view that only high volatility indicates risk, by analyzing mean first hitting times in stock returns.

Contribution

It introduces the use of mean first hitting time as a stability indicator and demonstrates its nonmonotonic relationship with volatility using empirical data and a nonlinear Heston model.

Findings

Mean first hitting time peaks at intermediate volatility levels.

Empirical data shows nonmonotonic stability behavior.

Nonlinear Heston model reproduces observed phenomena.

Abstract

In financial markets, greater volatility is usually considered synonym of greater risk and instability. However, large market downturns and upturns are often preceded by long periods where price returns exhibit only small fluctuations. To investigate this surprising feature, here we propose using the mean first hitting time, i.e. the average time a stock return takes to undergo for the first time a large negative or positive variation, as an indicator of price stability, and relate this to a standard measure of volatility. In an empirical analysis of daily returns for $1071$ stocks traded in the New York Stock Exchange, we find that this measure of stability displays nonmonotonic behavior, with a maximum, as a function of volatility. Also, we show that the statistical properties of the empirical data can be reproduced by a nonlinear Heston model. This analysis implies that, contrary to conventional wisdom, not only high, but also low volatility values can be associated with higher instability in financial markets.