Role of Noise in a Market Model with Stochastic Volatility

TL;DR

This paper explores how noise influences a generalized stochastic volatility market model, revealing noise-enhanced stability effects and the impact of noise correlation on market regime transitions.

Contribution

It introduces a nonlinear extension of the Heston model with correlated noises, analyzing noise effects on market stability and regime switching.

Findings

Identification of noise-enhanced stability in the model

Demonstration of the role of noise correlation in market dynamics

Insights into noise effects on metastable state lifetimes

Abstract

We study a generalization of the Heston model, which consists of two coupled stochastic differential equations, one for the stock price and the other one for the volatility. We consider a cubic nonlinearity in the first equation and a correlation between the two Wiener processes, which model the two white noise sources. This model can be useful to describe the market dynamics characterized by different regimes corresponding to normal and extreme days. We analyze the effect of the noise on the statistical properties of the escape time with reference to the noise enhanced stability (NES) phenomenon, that is the noise induced enhancement of the lifetime of a metastable state. We observe NES effect in our model with stochastic volatility. We investigate the role of the correlation between the two noise sources on the NES effect.