Market Delay and G-expectations

TL;DR

This paper investigates super-replication in markets with delayed information, showing that delays significantly increase costs in Black-Scholes models and linking the scaling limit of binomial models to G-expectation with volatility uncertainty.

Contribution

It introduces the impact of market delays on super-replication costs and connects binomial model limits to G-expectation, a novel approach in this context.

Findings

Super-replication prices are prohibitively costly with delays in Black-Scholes models.

Scaling limits of binomial models with delays converge to G-expectation.

Delays lead to trivial buy-and-hold strategies in continuous models.

Abstract

We study super-replication of contingent claims in markets with delayed filtration. The first result in this paper reveals that in the Black--Scholes model with constant delay the super-replication price is prohibitively costly and leads to trivial buy-and-hold strategies. Our second result says that the scaling limit of super--replication prices for binomial models with a fixed number of times of delay $H$ is equal to the $G$--expectation with volatility uncertainty interval $[0,\sigma\sqrt{H+1}]$.