Pricing generalized capped exchange options

The article makes two contributions to the literature. The first contribution is to derive a closed-form solution of Taiwanese capped options. We also provide the properties of Taiwanese capped options and the phenomenon of delta jump at monitoring dates. When the interest rate changes dramatically, instead of deriving the pricing formulas for derivatives separately, the second contribution is to provide the closed-form solution of generalized capped exchange options with stochastic barriers under the Hull and White framework. Special cases of generalized capped exchange options with stochastic barriers are abundant. They include capped (floored) options, capped (floored) options with exponential barriers, capped (floored) options with related assets or indices as triggers and capped (floored) options with related assets or indices as triggers and other related assets as barriers.