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A reduced form model for ESO valuation

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  • Alexander Szimayer

Abstract

In this paper we extend a reduced form model for the valuation of employee share options (ESOs) to incorporate employee departure, and company takeover. We also allow for performance linked vesting and other exotic features specific to ESOs. We clarify the assumptions underlying the reduced form model, and discuss their implications. We analyze the probabilistic structure of the model which includes an explicit characterization of the set of equivalent martingale measures, as well as the computation of the variance optimal martingale measure and the minimal martingale measure. Moreover, we deduce an additive decomposition of the relative entropy. Particular ESO specifications are studied emphasizing different aspects of the proposed framework. In this context, we also provide strict no-arbitrage bounds for ESO prices by applying optimal stopping. Furthermore, possible limitations of the proposed model are explored by examining departures from the crucial assumptions of no-arbitrage, i.e. by considering the effects of the employee having inside information. Copyright Springer-Verlag 2004

Suggested Citation

  • Alexander Szimayer, 2004. "A reduced form model for ESO valuation," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 59(1), pages 111-128, February.
    • Handle: RePEc:spr:mathme:v:59:y:2004:i:1:p:111-128
    DOI: 10.1007/s001860300320
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    Cited by:

    1. Dai, Min & Kwok, Yue Kuen & You, Hong, 2007. "Intensity-based framework and penalty formulation of optimal stopping problems," Journal of Economic Dynamics and Control, Elsevier, vol. 31(12), pages 3860-3880, December.
    2. Kamil Kladivko & Mihail Zervos, 2017. "Valuation of Employee Stock Options (ESOs) by means of Mean-Variance Hedging," Papers 1710.00897, arXiv.org.
    3. 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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