Super-Replication with Fixed Transaction Costs

TL;DR

This paper investigates the high costs of super-replication in markets with fixed transaction costs, showing that it leads to trivial strategies in continuous models but deriving meaningful limits in binomial models with small costs.

Contribution

It demonstrates the impracticality of super-replication in continuous models with fixed costs and provides scaling limits in binomial models with small fixed costs.

Findings

Super-replication prices are prohibitively costly in continuous models.

Trivial buy-and-hold strategies are optimal in continuous models.

Scaling limits are derived for binomial models with small fixed costs.

Abstract

We study super--replication of contingent claims in markets with fixed transaction costs. This can be viewed as a stochastic impulse control problem with a terminal state constraint. The first result in this paper reveals that in reasonable continuous time financial market models the super--replication price is prohibitively costly and leads to trivial buy--and--hold strategies. Our second result derives nontrivial scaling limits of super--replication prices for binomial models with small fixed costs.