The CTRW in finance: Direct and inverse problems with some generalizations and extensions

TL;DR

This paper explores the application of continuous time random walk models to finance, addressing both direct and inverse problems, and introduces generalizations including non-Markovian dynamics to better capture correlated financial returns.

Contribution

It presents new results on overnight effects and extends the CTRW framework to include non-Markovian, correlated return increments in financial modeling.

Findings

Enhanced CTRW model incorporating overnight effects

Generalized formalism for non-Markovian, correlated returns

Improved understanding of financial distribution dynamics

Abstract

We study financial distributions within the framework of the continuous time random walk (CTRW). We review earlier approaches and present new results related to overnight effects as well as the generalization of the formalism which embodies a non-Markovian formulation of the CTRW aimed to account for correlated increments of the return.