A perpetual continuous-installment option is an infinite ma- turity 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 prob- lem for a parabolic inhomogeneous ordinary differential equation. The closed-form solution obtained for the special case of a non-dividend pay- ing asset gives the possibility to observe some analytical properties of the initial premium and the optimal boundaries for the perpetual continuous- installment call option.
A note on the pricing of perpetual continuous-installment options
PIERANGELO CIURLIA
Primo
;
2009-01-01
Abstract
A perpetual continuous-installment option is an infinite ma- turity 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 prob- lem for a parabolic inhomogeneous ordinary differential equation. The closed-form solution obtained for the special case of a non-dividend pay- ing asset gives the possibility to observe some analytical properties of the initial premium and the optimal boundaries for the perpetual continuous- installment call option.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
