Asset Price Bubbles in market models with proportional transaction costs

TL;DR

This paper examines how proportional transaction costs influence the formation of asset price bubbles, defining fundamental value via super-replication and showing that bubbles can naturally emerge in such market models.

Contribution

It introduces a dual representation of fundamental asset value under transaction costs and demonstrates the intrinsic emergence of bubbles in the model.

Findings

Transaction costs affect bubble formation.

Fundamental value differs from ask-price in the model.

Bubbles can naturally arise due to transaction costs.

Abstract

We study asset price bubbles in market models with proportional transaction costs $\lambda\in (0,1)$ and finite time horizon $T$ in the setting of [49]. By following [28], we define the fundamental value $F$ of a risky asset $S$ as the price of a super-replicating portfolio for a position terminating in one unit of the asset and zero cash. We then obtain a dual representation for the fundamental value by using the super-replication theorem of [50]. We say that an asset price has a bubble if its fundamental value differs from the ask-price $(1+\lambda)S$. We investigate the impact of transaction costs on asset price bubbles and show that our model intrinsically includes the birth of a bubble.