Analytical upper bounds for American exotic currency options with a stochastic skew model

Abstract

On the basis that most instruments traded on options markets are American-style ones, this paper develops the analytical upper and lower bounds of American cross-currency and quanto options under the stochastic skew model proposed by Carr and Wu (2007) when domestic risk free rates are higher or lower than the foreign risk free rates. The analytical bounds derived here are not only very tight and accurate for American option pricing, but also offer a quasi-closed form solution which is able to enhance evaluation and hedging efficiency in real world markets. We also acquire the analytical solutions for European cross-currency and quanto options given by applying two separate mean-reverting square-root processes to two separate time-changed Levy processes, consistent with the realistic phenomena of currency returns.