Employee Stock Option Exercise and Firm Cost

• Date: 01 June 2019
• DOI: http://doi.org/10.1111/jofi.12752
• Author: RICHARD STANTON,NANCY WALLACE,JENNIFER N. CARPENTER
• Published date: 01 June 2019

THE JOURNAL OF FINANCE •VOL. LXXIV, NO. 3 •JUNE 2019

Employee Stock Option Exercise and Firm Cost

JENNIFER N. CARPENTER, RICHARD STANTON, and NANCY WALLACE∗

ABSTRACT

We develop an empirical model of employee stock option exercise that is suitable for

valuation and allows for behavioral channels. We estimate exercise rates as functions

of option, stock, and employee characteristics using all employee exercises at 88

public firms, 27 of them in the S&P 500. Increasing vesting frequency from annual to

monthly reduces option value by 11% to 16%. Men exercise faster, reducing value by

2% to 4%, while top employees exercise slower, increasing value by 2% to 7%. Finally,

we develop an analytic valuation approximation that is more accurate than methods

used in practice.

EMPLOYEE STOCK OPTIONS (ESOS)ARE A major component of corporate compen-

sation and a material cost to firms. Murphy (2013) reports that options repre-

sented 21% of CEO pay in 2011, and Meridian Compensation Partners (2018)

report that 42% of their national sample use executive stock options. Despite

the overall importance of ESOs in executive compensation, their valuation re-

mains a challenge in practice as shown by the recent controversy over the

value of options granted to the CEO of IBM, which Institutional Shareholder

Services valued at more than twice the company’s valuation.1The valuation

of long-maturity American options such as ESOs is sensitive to assumptions

about how they will be exercised. Because employees face hedging constraints,

∗Jennifer Carpenter is at New York University. Richard Stanton and Nancy Wallace are at the

University of California, Berkeley.We thank two anonymous referees and the Editors, Ken Single-

ton and Stefan Nagel, for many helpful comments and suggestions. We are grateful for comments

from Daniel Abrams; Terry Adamson; Xavier Gabaix; WenxuanHou; James Lecher; Kai Li; Ulrike

Malmendier; Kevin Murphy; TerryOdean; Nicholas Reitter; Jun Yang; and David Yermack;as well

as from seminar participants at Cheung Kong Graduate School of Business, Erasmus University,

Federal Reserve Bank of New York, Fudan University, Lancaster University, McGill University,

New York University, The Ohio State University, Oxford University, Peking University, Rice Uni-

versity,the Securities and Exchange Commission, Shanghai Advanced Institute of Finance, Temple

University, Tilburg University, Tsinghua University, and the 2017 Western Finance Association

meetings. We thank Terry Adamson at AON Consulting for providing some of the data used in

this study. We also thank Xing Huang for valuable research assistance. Financial support from

the Fisher Center for Real Estate and Urban Economics and the Society of Actuaries is gratefully

acknowledged. The authors have no conflicts of interest to disclose.

1See Melin, Anders, 2017, IBM says CEO pay is $33 million. Others say it is far higher,

https://www.bloomberg.com/news/articles/2017-04-24/ibm-says-ceo-pay-is-33-million-others-say-it

-is-far-higher.

DOI: 10.1111/jofi.12752

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1176 The Journal of Finance R

standard option exercise theory does not apply.2In addition, commonly used

modifications to Black-Scholes (1973) are inadequate because they ignore key

empirical features of employee exercise patterns.

In this paper, we develop an empirical model of employee option exercise

suitable for valuation and apply it to a sample of all employee exercises at 88

publicly traded firms from 1981 to 2009. We develop a Generalized Method of

Moments (GMM)-based methodology that is robust to both heteroskedasticity

and correlation across option exercises to estimate the rate of voluntary exer-

cise as a function of the stock price path and of firm, contract, and option holder

characteristics. We show that these characteristics significantly affect exercise

behavior, in a manner consistent with both portfolio theory and results from

the behavioral literature, such as Barber and Odean (2001). Our data are pro-

vided by corporate participants in a sponsored research project funded by the

Society of Actuaries in response to regulatory calls for improved ESO valuation

methods.

Using the estimated exercise function, we value a range of options and find

that vesting structure has a large effect on the option cost to firms: increasing

vesting-date frequency from annual to monthly reduces option value by as much

as 16% for typical option holders. In addition, men exercise options significantly

faster than women, resulting in a 2% to 4% lower option value. Higher ranked

option holders exercise more slowly than lower ranked option holders, implying

that the options of top employees are typically worth 2% to 7% more than those

of lower ranked employees. Top employees are less responsive to the passage of

vesting dates and the stock price reaching a new high. Consistent with theory,

employees with greater wealth tend to exercise more slowly, and employees

with greater option risk tend to exercise faster. Consistent with both standard

option theory and utility maximization, the rate of voluntary option exercise is

positively related to the level of the stock price and the imminence of a dividend.

However, the exercise rate is also higher when the stock price is in the 90th

percentile of its distribution over the past year, which may reflect behavioral

effects.

We compare option values calculated using our model and Black-Scholes-

based methods commonly used in practice. Even when their inputs are es-

timated perfectly, we find that the Black-Scholes-based approximations have

significant biases, which vary systematically with firm characteristics.3Given

the practical appeal of a Black-Scholes-based approximation, however, we de-

velop an alternative Black-Scholes approximation to our model that matches

the correct option values more closely than existing methods. It is easy to

2For example, employees systematically exercise options on nondividend-paying stocks well

before expiration, and this substantially reduces their cost to firms.

3Moreover, for dividend-paying firms, it is possible for the true (American) option value to be so

large that the (European) Black-Scholes formula cannot give the correct result. To illustrate the

problem, a 10-year American call option with strike price $100 on a stock with S=100, r=0.05,

σ=0.3, and a dividend rate d=0.06 has value $24.59. With the same parameters and varying the

expiration date, the highest possible European option value is $18.72, which occurs at an option

maturity of 7.44 years.

Employee Stock Option Exercise and Firm Cost 1177

implement analytically without the need for additional data, can serve as the

basis for a new accounting valuation method, and can also be used in corporate

finance research on executive and employee compensation.

The paper proceeds as follows. Section Ibriefly summarizes prior literature

in this area. Section II describes our valuation and estimation methodology and

develops an empirical model of employee exercise that is both flexible enough

to capture observed exercise behavior and suitable as a basis for option valua-

tion. Section III describes the sample of proprietary data on employee options.

Section IV presents estimation results for the empirical exercise function. Sec-

tion Vanalyzes the impact of the estimated exercise factor effects on employee

option cost and the approximation errors of current valuation methods, and

develops a new analytic approximation method. Section VI concludes.

I. Previous Literature

The principles of employee option valuation and the need to study exercise

behavior are well understood. One approach taken in the literature is to model

the exercise decision theoretically. The employee chooses an option exercise

policy as part of a greater utility maximization problem that includes other

decisions such as portfolio, consumption, and effort choice, and this typically

leads to some early exercise for the purpose of diversification. Papers that

develop utility-maximizing models and calculate the implied cost of options

to shareholders include Huddart (1994), Detemple and Sundaresan (1999),

Ingersoll (2006), Leung and Sircar (2009), Grasselli and Henderson (2009),

and Carpenter, Stanton, and Wallace (2010).

Combining theory and data, papers such as Carpenter (1998) and Bettis,

Bizjak, and Lemmon (2005) calibrate utility-maximizing models to mean exer-

cise times and stock prices in the data, and then infer option value. However,

these papers provide no formal estimation and the approach relies on the va-

lidity of the utility-maximizing models used. Huddart and Lang (1996), Heath,

Huddart, and Lang (1999), and Klein and Maug (2011) provide more flexible

empirical descriptions of option exercise patterns, but do not go as far as op-

tion valuation. Armstrong, Jagolinzer, and Larcker (2007) perform a valuation

based on a hazard model of the exercise of option grants, but this specification

is inappropriate for valuation because employees exercise random fractions of

outstanding option grants.

A number of analytic methods for approximating employee option value have

also been proposed. FAS 123R permits using the Black-Scholes formula with

the expiration date replaced by the option’s expected life, and SAB 110 permits

using Black-Scholes with expiration replaced by the average of the contractual

vesting date and expiration date. Jennergren and N¨

aslund (1993), Carr and

Linetsky (2000), and Cvitani´

c, Wiener, and Zapatero (2008) derive analytic for-

mulas for option value assuming exogenously specified exercise boundaries and

stopping rates. Hull and White (2004) propose a model in which exercise oc-

curs when the stock price reaches an exogenously specified multiple of the stock