Future exchange rates and Siegel's paradox

TL;DR

This paper proposes an arbitrage-free, symmetric, and currency-invariant solution to Siegel's paradox in international finance, providing a comprehensive classification of all such exchange rate aggregators based on reciprocity functions.

Contribution

It introduces a novel approach to resolving Siegel's paradox that ensures no arbitrage, invariance under currency re-denomination, and symmetry, along with a complete classification of all solutions.

Findings

Derived a formula for no-arbitrage forward exchange rates.

Provided a complete classification of exchange rate aggregators.

Ensured invariance under currency re-denominations.

Abstract

Siegel's paradox is a fundamental question in international finance about exchange rates for futures contracts and has puzzled many scholars for over forty years. The unorthodox approach presented in this article leads to an arbitrage-free solution which is invariant under currency re-denominations and is symmetric, as explained. We will also give a complete classification of all such aggregators in the general case. The formula obtained in this setting therefore describes all the negotiated no-arbitrage forward exchange rates in terms of a reciprocity function. Keywords: Siegel's paradox, forward exchange rates, discount bias.