Foreign equity lookback options with guarantees

Abstract

A foreign equity lookback option plays a vital role in hedging foreign exchange rate and asset price risks. Despite its importance, valuing the foreign equity lookback option is problematic because its path dependence and stochastic exchange rate complicate calculating the expected payoff. This paper delivers a unified closed-form pricing formula for the foreign equity lookback call (or put) with fixed (or floating) strike by relying on the extreme-or-nothing formulas that facilitate computing expectations. In addition, it admits valuing the options systematically with the guarantees of exchange rate and equity extremes. Numerical experiments validate the prices obtained from the analytical pricing formula. © 2022 Elsevier Inc.