Pricing of a reload employee stock option under severance risk

Since employee stock option grants have some features that do not fulfill the Black-Scholes assumptions, we use a severance incorporating model to capture its main properties that specify the price and reload condition. Generally, the employee is exposed to various severance risks such as termination with cause or without cause. Departure from a firm with or without cause means that the option would be forfeited or exercised immediately, respectively, which gives significant influence to the optimal decision of executing the reload. To compute the reload, we determine the boundary constraint as a free boundary condition and reveal the main features of the impact of severance risk on reload.