A note on the pricing of perpetual continuous-installment options

Abstract

A perpetual continuous-installment option is an infinite maturity option in which the premium is paid continuously instead of up-front. The holder has the right to terminate payments at any time by either exercising the option or dropping the option contract. Within the standard Black-Scholes framework, the perpetual continuous-installment option pricing problem is discussed and solved as a free boundary problem for a parabolic inhomogeneous ordinary differential equation. The closed-form solution obtained for the special case of a non-dividend paying asset gives the\npossibility to observe some analytical properties of the initial premium and the optimal boundaries for the perpetual continuous-installment call option. -