A Top-Down Approach for the Multiple Exercises and Valuation of Employee Stock Options
International Journal of Theoretical and Applied Finance, Forthcoming
26 Pages Posted: 13 Jun 2019 Last revised: 13 Apr 2020
Date Written: December 12, 2019
We propose a new framework to value employee stock options (ESOs) that captures multiple exercises of different quantities over time. We also model the ESO holder's job termination risk and incorporate its impact on the payoffs of both vested and unvested ESOs. Numerical methods based on Fourier transform and finite differences are developed and implemented to solve the associated systems of PDEs. In addition, we introduce a new valuation method based on maturity randomization that yields analytic formulae for vested and unvested ESO costs. We examine the cost impact of job termination risk, exercise intensity, and various contractual features.
Keywords: employee stock option, Fourier transform, maturity randomization, implied maturity
JEL Classification: C63, G13, J33
Suggested Citation: Suggested Citation