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
Ciurlia, Pierangelo
;
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.File | Dimensione | Formato | |
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