Volatility Effects on the Escape Time in Financial Market Models

TL;DR

This paper examines how volatility influences the time it takes for stock prices to reach certain levels, comparing model predictions with real market data to understand underlying statistical properties.

Contribution

It introduces a detailed analysis of escape times in a stochastic volatility model with nonlinear dynamics, highlighting effects of noise and initial conditions.

Findings

Model's escape time distribution matches real data

Noise significantly affects escape times

Initial conditions influence market model behavior

Abstract

We shortly review the statistical properties of the escape times, or hitting times, for stock price returns by using different models which describe the stock market evolution. We compare the probability function (PF) of these escape times with that obtained from real market data. Afterwards we analyze in detail the effect both of noise and different initial conditions on the escape time in a market model with stochastic volatility and a cubic nonlinearity. For this model we compare the PF of the stock price returns, the PF of the volatility and the return correlation with the same statistical characteristics obtained from real market data.