Information, no-arbitrage and completeness for asset price models with a change point

TL;DR

This paper analyzes continuous asset price models with a change point, examining their properties under various filtrations, and characterizes conditions for no-arbitrage and market completeness.

Contribution

It introduces a general framework for models with a change point, providing martingale representation and no-arbitrage conditions under minimal assumptions.

Findings

Martingale representation results for models with a change point

Characterization of no-arbitrage conditions (NA1 and NFLVR)

Analysis of model behavior across different filtrations

Abstract

We consider a general class of continuous asset price models where the drift and the volatility functions, as well as the driving Brownian motions, change at a random time $\tau$. Under minimal assumptions on the random time and on the driving Brownian motions, we study the behavior of the model in all the filtrations which naturally arise in this setting, establishing martingale representation results and characterizing the validity of the NA1 and NFLVR no-arbitrage conditions.