Option Pricing with Delayed Information

TL;DR

This paper investigates how delayed information impacts option pricing, providing a model that ensures no arbitrage, offers closed-form solutions, and examines effects on volatility smiles in both discrete and continuous time frameworks.

Contribution

It introduces a novel model for option pricing with delayed information, including closed-form formulas and convergence analysis, extending to continuous time and analyzing volatility smile effects.

Findings

No arbitrage conditions are established in the delayed information model.

Closed-form formulas for convex claim prices are derived.

Delayed information amplifies the volatility smile.

Abstract

We propose a model to study the effects of delayed information on option pricing. We first talk about the absence of arbitrage in our model, and then discuss super replication with delayed information in a binomial model, notably, we present a closed form formula for the price of convex contingent claims. Also, we address the convergence problem as the time-step and delay length tend to zero and introduce analogous results in the continuous time framework. Finally, we explore how delayed information exaggerates the volatility smile.