Pricing European continuous-installment strangle options

This paper investigates the valuation of European continuous-installment strangle options written on dividend-paying underlying assets in the standard Black-Scholes framework. In this pricing problem, the premium of the strangle option is paid continuously instead of up-front. Since the holder of this option has the right to surrender installment payments at any time, the valuation of installment strangle option can be formulated as an optimal stopping problem with two surrender boundaries. Based on the Mellin transform approaches, we derive the integral equation representations for the value function and the two optimal surrender boundaries. By using the recursive integration method, we obtain efficiently the numerical solution for the integral equations and illustrate the optimal surrender boundaries with respect to the significant parameters.