Skip to main content

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

Central European Journal of Operations Research volume 22, pages 237–262 (2014)Cite this article

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.

This is a preview of subscription content, access via your institution.

Access options

Buy single article

Instant access to the full article PDF.

USD 39.95

Price includes VAT (USA)
Tax calculation will be finalised during checkout.

Fig. 1
Fig. 2
Fig. 3
Fig. 4

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).

References

  • Aggarwal R, Samwick A (1999) The other side of the trade-off: the impact of risk on executive compensation. J Polit Econ 107:65–105

    Article  Google Scholar 

  • Aggarwal R, Samwick A (2002) The other side of the trade-off: the impact of risk on executive compensation-a reply. Dartmouth College Working Paper. http://papers.ssrn.com/sol3/papers.cfm?

  • Ammann M, Seiz R (2004) Valuing employee stock options: Does the model matter? Finan Anal J 60:21-37

    Google Scholar 

  • Anderson TW, Hsiao C (1981) Estimation of dynamic models with error components. J Am Stat Assoc 76:589–606

    Article  Google Scholar 

  • Anderson M, Muslu V (2011) Implications of estimation error in option grants for evaluating CEO pay. Working Paper. http://ssrn.com/abstract=1623467

  • Arellano M, Bond S (1991) Some tests of specification for panel data: Monte Carlo evidence and an application to employment equations. Rev Econ Stud 58:277–297

    Article  Google Scholar 

  • Armstrong CS, Vashishtha R (2012) Executive stock options, differential risk-taking incentives, and firm value. J Finan Econ 104:70–88

    Article  Google Scholar 

  • Baltagi BH (2001) Econometric analysis of panel data. Wiley, Chichester

    Google Scholar 

  • Bettis JC, Bizjak JM, Lemmon ML (2005) Exercise behavior, valuation, and the incentive effects of employee stock options. J Finan Econ 76:445–470

    Article  Google Scholar 

  • Black F, Scholes M (1973) The pricing of options and corporate liabilities. J Polit Econ 81:637–654

    Article  Google Scholar 

  • Brenner M, Sundaram RK, Yermack D (2000) Altering the terms of executive stock options. J Finan Econ 57:103–128

    Article  Google Scholar 

  • Brockman P, Martin X, Unlu E (2010) Executive compensation and the maturity structure of corporate debt. J Finan 65:1123–1161

    Article  Google Scholar 

  • Brown P, Szimayer A (2008) Valuing executive stock options: performance hurdles, early exercise and stochastic volatility. Acc Finan 48:363–389

    Article  Google Scholar 

  • Bryan S, Hwang L, Lilien S (2002) CEO stock-based compensation: an empirical analysis of incentive-intensity, relative mix and economic determinants. J Bus 73:661–693

    Article  Google Scholar 

  • Carpenter JN (1998) The exercise and valuation of executive stock options. J Finan Econ 48:127–158

    Article  Google Scholar 

  • Carr P, Linetsky V (2000) The valuation of executive stock options in an intensity-based framework. Eur Finan Rev 4:211–230

    Article  Google Scholar 

  • Chava S, Purnanandam A (2010) CEOs versus CFOs: incentives and corporate policies. J Finan Econ 97:263–278

    Article  Google Scholar 

  • Chidambaran NK, Prabhala NR (2003) Executive stock option repricing, internal governance mechanisms, and management turnover. J Finan Econ 69:153–189

    Article  Google Scholar 

  • Cohen R, Hall B, Viceira L (2000) Do executive stock options encourage risk-taking? Harvard Business School Working Paper. http://www.people.hbs.edu/lviceira/cohallvic3.pdf

  • Coles JL, Daniel ND, Naveen L (2006) Managerial incentives and risk-taking. J Finan Econ 79:431–468

    Article  Google Scholar 

  • Core J, Guay W (1999) The use of equity grants to manage optimal equity incentive levels. J Acc Econ 28:151–184

    Article  Google Scholar 

  • Core J, Guay W (2002a) Estimating the value of employee stock options portfolios and their sensitivities to price and volatility. J Acc Res 40:613–630

    Google Scholar 

  • Core J, Guay W (2002b) The other side of the trade-off: the impact of risk on executive compensation a revised comment. University of Pennsylvania Working Paper. http://papers.ssrn.com/sol3/papers.cfm?abstract_id=292955

  • Corrado CJ, Jordan BD, Miller TW, Stansfield JJ (2001) Repricing and employee stock option valuation. J Bank Finan 25:1059–1082

    Article  Google Scholar 

  • Cvitanic J, Wiener Z, Zapatero F (2008) Analytic pricing of employee stock options. Rev Finan Stud 21:683–724

    Article  Google Scholar 

  • Demsetz H, Lehn K (1985) The structure of corporate ownership: causes and consequences. J Polit Econ 93:1155–1177

    Article  Google Scholar 

  • Denis DJ, Hanouna P, Sarin A (2006) Is there a dark side to incentive compensation? J Corp Finan 12: 467–488

    Google Scholar 

  • Devers CE, Cannella AA, Reilly GP, Yoder ME (2007) Executive compensation: a multidisciplinary review of recent developments. J Manag 33:1016–1072

    Google Scholar 

  • Dong Z, Wang C, Xie F (2010) Do executive stock options induce excessive risk taking? J Bank Finan 34:2518–2529

    Article  Google Scholar 

  • Duan JC, Wei J (2005) Executive stock options and incentive effects due to systematic risk. J Bank Finan 29:1185–1211

    Article  Google Scholar 

  • Dybvig PH, Loewenstein M (2003) Employee reload options: pricing, hedging, and optimal exercise. Rev Finan Stud 16:145–171

    Google Scholar 

  • Frydman C, Saks R (2010) Executive compensation: a new view from a long-term perspective, 1936–2005. Rev Finan Stud 23:2099–2138

    Article  Google Scholar 

  • Fu X, Ligon JA (2010) Exercised of executive stock options on the vesting date. Finan Manag 39:1097–1125

    Article  Google Scholar 

  • Goergen M, Renneboog L (2011) Managerial compensation. J Corp Finan 17:1068–1077

    Article  Google Scholar 

  • Guay W (1999) The sensitivity of CEO wealth to equity risk: an analysis of the magnitude and determinants. J Finan Econ 53:43–71

    Article  Google Scholar 

  • Hall BJ, Murphy KJ (2003) The trouble with stock options. J Econ Perspect 17:49–70

    Article  Google Scholar 

  • Hemmer T, Kim O, Verrecchia RE (1999) Introducing convexity into optimal compensation contracts. J Acc Econ 28:307–327

    Article  Google Scholar 

  • Himmelberg C, Hubbard R, Palia D (1999) Understanding the determinants of managerial ownership and the link between ownership and performance. J Finan Econ 53:353–384

    Article  Google Scholar 

  • Huddart S (1994) Employee stock options. J Acc Econ 18:207–231

    Article  Google Scholar 

  • Huddart S, Lang M (1996) Employee stock option exercises an empirical analysis. J Acc Econ 21:5–43

    Article  Google Scholar 

  • Hull JC, White A (2004) How to value employee stock options. Finan Anal J 60:114–119

    Article  Google Scholar 

  • Jennergren LP, Näslund B (1993) A comment on valuation of executive stock options and the FASB proposal. Acc Rev 68:179–183

    Google Scholar 

  • Jin L (2002) CEO compensation, diversification and incentives. J Finan Econ 66:29–63

    Article  Google Scholar 

  • Johnson SA, Tian YS (2000) The value and incentive effects of nontraditional executive stock option plans. J Finan Econ 57:3–34

    Article  Google Scholar 

  • Kaplan SN (2012) Executive compensation and corporate governance in the U.S.: perceptions, facts and challenges. Working Paper. http://ssrn.com/abstract=2134208

  • Kaplan SN, Minton BA (2012) How has CEO turnover changed? Int Rev Finan 12:57–87

    Article  Google Scholar 

  • Knopf JD, Nam J, Thornton JH (2002) The volatility and price sensitivities of managerial stock option portfolios and corporate hedging. J Finan 57:801–813

    Article  Google Scholar 

  • Kulatilaka N, Marcus AJ (1994) Valuing employee stock options. Finan Anal J 50:46–56

    Article  Google Scholar 

  • León A, Vaello-Sebastiá A (2009) American GARCH employee stock option valuation. J Bank Finan 33:1129–1143

    Article  Google Scholar 

  • Leung T, Sircar R (2009) Accounting for risk aversion, vesting, job termination risk and multiple exercises in valuation of employee stock options. Math Finan 19:99–128

    Article  Google Scholar 

  • Lewellen K (2006) Financing decisions when managers are risk averse. J Finan Econ 82:551–589

    Article  Google Scholar 

  • Low A (2009) Managerial risk-taking behavior and equity-based compensation. J Finan Econ 92:470–490

    Article  Google Scholar 

  • Marquardt C (2002) The cost of employee stock options grants: an empirical analysis. J Acc Res 40:1191–1217

    Article  Google Scholar 

  • O’Connor ML, Rafferty M (2010) Incentive effects of executive compensation and the valuation of firm assets. J Corp Finan 16:431–442

    Article  Google Scholar 

  • Rajgopal S, Shevlin T (2002) Empirical evidence on the relation between stock option compensation and risk taking. J Acc Econ 33:145–171

    Article  Google Scholar 

  • Sanders WMG, Hambrick DC (2007) Swinging for the fences: the effets of CEO stock options on company risk taking and performance. Acad Manag J 50:1055–1078

    Article  Google Scholar 

  • Sircar R, Xiong W (2007) A general framework for valuing executive stock options. J Econ Dyn Control 31:2317–2349

    Article  Google Scholar 

  • Tian YS (2004) Too much of a good incentive? The case of executive stock options. J Bank Finan 28:1225–1245

    Article  Google Scholar 

  • Tong Z (2010) CEO risk incentives and corporate cash holdings. J Bus Finan Acc 37:1248–1280

    Article  Google Scholar 

  • Williams MA, Rao RP (2006) CEO stock options and equity risk incentives. J Bus Finan Acc 33:26–44

    Article  Google Scholar 

Download references

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.

Author information

Authors and Affiliations

  1. Departamento de Métodos Cuantitativos para la Economía, Facultad de Economía y Empresa, Universidad de Murcia, 30100 , Murcia, Spain

    Susana Álvarez-Díez

  2. Departamento de Organización de Empresas y Finanzas, Facultad de Economía y Empresa, Universidad de Murcia, 30100 , Murcia, Spain

    J. Samuel Baixauli-Soler & María Belda-Ruiz

Authors
  1. Susana Álvarez-Díez
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J. Samuel Baixauli-Soler
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. María Belda-Ruiz
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to María Belda-Ruiz.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

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

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10100-013-0287-6

Keywords

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