On a general class of free boundary problems for European-style installment options with continuous payment plan
The aim of this paper is to provide an integral equation approach to pricing European-style installment options with continuous payment plan and general monotonic payoff function. The holder's ability to halt installment payments by dropping the option contract leads to a free boundary separating the region where it is advantageous to hold from that in which early stopping is optimal. In order to obtain a solution to this free boundary problem the author uses the incomplete Fourier transform. By inverting the solution of the transformed problem a recursive integral equation for the free boundary along with an analytic representation of the option price are derived. Based on these results it is proposed a unified framework to deal with monotonic payoff functions and continuous payment plans. Applications to the valuation of European vanilla continuous installment call options are presented and an explicit pricing formula is obtained for time-varying payment schedules.
scientific article; zbMATH DE number 5989657