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Are we using the wrong letters? An analysis of executive stock option Greeks

Abstract

Greek letters, in particular delta and vega based on the Black–Scholes model (BS), have been widely used to estimate the sensitivity of CEO wealth to changes in stock price (delta) and stock return volatility (vega) and to evaluate the executive stock options (ESOs) granted on the basis of performance and risk. However, the BS model does not take into account the main features of ESOs and therefore the delta and vega values it produces are not valid. The Cvitanic–Wiener–Zapatero model (CWZ) is an alternative model to Black–Scholes for valuing ESOs. It has a closed formula and considers the main features of ESOs. We carry out a sensitivity analysis to show that research on option-based compensation and its risk-taking effects is not robust in ESO pricing models. The sensitivity analysis consists of comparing the impact of the common parameters of the BS and CWZ models, as well as the effect of the specific parameters of the CWZ model, on the sensitivity of CEO wealth to stock price and stock volatility. Additionally, using panel data methodology, we develop an empirical analysis to illustrate the influence of stock return volatility and different corporate policies on both CEO wealth sensitivities.

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Notes

  1. Reloading is the practice of granting more stock options to executives as a result of exercising the initial options that they have in their compensation packages (Dybvig and Loewenstein 2003). On the other hand, resetting refers to the practice of altering the terms of previously granted stock options prior maturity date. The most common instance of such resetting is the “repricing” of ESOs (Chidambaran and Prabhala 2003), that is, firms lower the exercise prices of ESOs when declining stock prices have moved ESOs out-of-the-money (Brenner et al. 2000; Corrado et al. 2001) due to after such drop, ESOs lose much of their value and their incentive effects (Sircar and Xiong 2007).

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Acknowledgments

We gratefully acknowledge the helpful advice and comments from participants in the 50th Meeting of the Euroworking Group on Financial Modeling held at Rome, in the 7th Finance Conference of the Portuguese Finance Network held at Aveiro, in the 4th International Finance and Banking Society Conference held at Valencia, in the 4th Workshop on Risk Management and Insurance Research held at Carmona and the seminar participants at Centre for Economics and Finance at the University of Porto. Also, we thank anonymous reviewers for their suggestions. Fundación Cajamurcia (Spain) and the Spanish Government (project ECO 2008-02846 and FPU program of the Ministry of Education) supported this research.

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Correspondence to María Belda-Ruiz.

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Álvarez-Díez, S., Baixauli-Soler, J.S. & Belda-Ruiz, M. Are we using the wrong letters? An analysis of executive stock option Greeks. Cent Eur J Oper Res 22, 237–262 (2014). https://doi.org/10.1007/s10100-013-0287-6

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Keywords

  • Executive stock options
  • Delta
  • Vega
  • Risk-taking
  • Stock return volatility