Explaining the Smile in Currency Options: Is It Anchoring?

Abstract

An anchoring adjusted currency option pricing formula is developed in which the risk of the underlying currency is used as a starting point which gets adjusted upwards to arrive at the currency call risk. Anchoring bias implies that such adjustments are insufficient. The new formula converges to the Garman-Kohlhagen formula in the absence of anchoring bias. Anchoring bias generates the implied volatility smile if investors hold heterogeneous exchange rate expectations.