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.
Highlights
A reset option is a path-dependent derivative whose payoff depends on the historical prices of underlying assets
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
Summary
A reset option is a path-dependent derivative whose payoff depends on the historical prices of underlying assets. Cheng and Zhang [1] evaluated a reset option with multiple discrete reset dates They obtained a closed-form solution by using probability method. Wang and Chen [8] priced an arithmetic average reset option using the Green function method In recent years, it became more and more popular for companies to issue employee stock options with reset constraints on a lock-up period. Liao and Wang [6] formulated the price of a continuous reset option to be equal to the difference between the prices of a down-and-out barrier option with an original strike price and a down-and-in barrier option with a reset strike price Their method can’t solve the valuation of window reset options, since the method is useful only when the end of reset date is the maturity of the contract. In the last section there are conclusions and discussions
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