The value of informational arbitrage

TL;DR

This paper investigates how much an investor would pay for inside information that enables arbitrage in a complete market, using an indifference valuation approach and analyzing the impact of initial information and arbitrage opportunities.

Contribution

It introduces a general framework for valuing informational arbitrage using indifference valuation and characterizes conditions for the universality of this value.

Findings

Provides new results on models with inside information.

Characterizes when the value of informational arbitrage is preference-independent.

Includes explicit examples illustrating the valuation of inside information.

Abstract

In the context of a general semimartingale model of a complete market, we aim at answering the following question: How much is an investor willing to pay for learning some inside information that allows to achieve arbitrage? If such a value exists, we call it the value of informational arbitrage. In particular, we are interested in the case where the inside information yields arbitrage opportunities but not unbounded profits with bounded risk. In the spirit of Amendinger et al. (2003, Finance Stoch.), we provide a general answer to the above question by relying on an indifference valuation approach. To this effect, we establish some new results on models with inside information and study optimal investment-consumption problems in the presence of initial information and arbitrage, also allowing for the possibility of leveraged positions. We characterize when the value of informational arbitrage is universal, in the sense that it does not depend on the preference structure. Our results are illustrated with several explicit examples.