Pricing Bounds on Quanto Options

Abstract

This article proposes model-independent pricing bounds on quanto options and the corresponding replicating strategies, which are static strategies with portfolios consisting of plain vanilla options on the foreign asset and on the FX rate. Because they are model-independently derived, one can make profit without risk if quanto options are priced outside the bounds. Additionally, the pricing bounds can be improved if liquid quanto contracts, such as quanto forward contracts, are used for replication. Numerical examples compare our pricing bounds with the Black pricing formula and the same formula with an ad-hoc adjustment. It is found that prices produced by the Black formula with and without ad-hoc adjustments may be outside the model-independent pricing bounds, and that the pricing bounds with quanto forward contracts are substantially improved.