A TOP-DOWN APPROACH FOR THE MULTIPLE EXERCISES AND VALUATION OF EMPLOYEE STOCK OPTIONS

Tim Leung and Yang Zhou ()
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Yang Zhou: Department of Applied Mathematics, University of Washington, Seattle, WA 98195, USA

International Journal of Theoretical and Applied Finance (IJTAF), 2020, vol. 23, issue 02, 1-29

Abstract: We propose a new framework to value employee stock options (ESOs) that capture 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 options; jump process; maturity randomization; Fourier transform (search for similar items in EconPapers)
Date: 2020
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Working Paper: A Top-Down Approach for the Multiple Exercises and Valuation of Employee Stock Options (2019)
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Persistent link: https://EconPapers.repec.org/RePEc:wsi:ijtafx:v:23:y:2020:i:02:n:s0219024920500041

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DOI: 10.1142/S0219024920500041

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