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A Top-Down Approach For The Multiple Exercises And Valuation Of Employee Stock Options

Author

Listed:
  • TIM LEUNG

    (Department of Applied Mathematics, University of Washington, Seattle, WA 98195, USA)

  • YANG ZHOU

    (Department of Applied Mathematics, University of Washington, Seattle, WA 98195, USA)

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.

Suggested Citation

  • Tim Leung & Yang Zhou, 2020. "A Top-Down Approach For The Multiple Exercises And Valuation Of Employee Stock Options," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 23(02), pages 1-29, March.
    • Handle: RePEc:wsi:ijtafx:v:23:y:2020:i:02:n:s0219024920500041
    DOI: 10.1142/S0219024920500041
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    References listed on IDEAS

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    1. Carmona, Julio & León, Angel & Vaello-Sebastià, Antoni, 2011. "Pricing executive stock options under employment shocks," Journal of Economic Dynamics and Control, Elsevier, vol. 35(1), pages 97-114, January.
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    12. Tim Leung & Haohua Wan, 2015. "ESO Valuation with Job Termination Risk and Jumps in Stock Price," Papers 1504.08073, arXiv.org.
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