TITLE:
A Simple Method to Price Window Reset Options
AUTHORS:
Yi-Long Hsiao
KEYWORDS:
Window Reset Option; Black-Scholes PDE; Boundary Integral Method; Green’s Function
JOURNAL NAME:
Journal of Mathematical Finance,
Vol.3 No.1,
February
28,
2013
ABSTRACT:
A window reset option is a kind of reset options with continuous reset constraints. The issue is very important for applying to employee stock options in finance or reservation options on truck-only toll lanes in traffic management. Our contribution of this study is that we proposed an accurate and simple method to price window reset options. The option price is formulated as the solution of a boundary value problem of the Black-Scholes PDE. The problem is then transformed into an initial-boundary value problem of the heat equation. Then Green’s function is applied to solve the heat equation problem. Finally, the option price is calculated numerically. A numerical example and some discussions are presented in this paper.