Market dynamics after large financial crash

TL;DR

This paper models market behavior after a major financial crash using stochastic differential equations, linking empirical data to potential and volatility predictions that align with observed market phenomena.

Contribution

It introduces a stochastic differential equation model with variable noise to describe post-crash market dynamics, validated against empirical data from the 1987 crash.

Findings

Model accurately predicts market behavior post-1987 crash

Estimates of potential and volatility match empirical observations

Provides a framework for understanding market recovery dynamics

Abstract

The model describing market dynamics after a large financial crash is considered in terms of the stochastic differential equation of Ito. Physically, the model presents an overdamped Brownian particle moving in the nonstationary one-dimensional potential $U$ under the influence of the variable noise intensity, depending on the particle position $x$. Based on the empirical data the approximate estimation of the Kramers-Moyal coefficients $D_{1,2}$ allow to predicate quite definitely the behavior of the potential introduced by $D_1 = - \partial U /\partial x$ and the volatility $\sim \sqrt{D_2}$. It has been shown that the presented model describes well enough the best known empirical facts relative to the large financial crash of October 1987. \