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

See all articles by Tim Leung

Tim Leung

University of Washington - Department of Applied Math

Yang Zhou

University of Washington - Department of Applied Math

Date Written: December 12, 2019

Abstract

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

Leung, Tim and Zhou, Yang, A Top-Down Approach for the Multiple Exercises and Valuation of Employee Stock Options (December 12, 2019). International Journal of Theoretical and Applied Finance, Forthcoming , Available at SSRN: https://ssrn.com/abstract=3396205 or http://dx.doi.org/10.2139/ssrn.3396205

Tim Leung (Contact Author)

University of Washington - Department of Applied Math ( email )

Lewis Hall 217
Department of Applied Math
Seattle, WA 98195
United States

HOME PAGE: http://faculty.washington.edu/timleung/

Yang Zhou

University of Washington - Department of Applied Math ( email )

Lewis Hall 305
Department of Applied Math
Seattle, WA 98195-2420
United States
2065567421 (Phone)

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