THE PRICE‐TAKER EFFECT ON THE VALUATION OF EXECUTIVE STOCK OPTIONS

• Date: 01 February 2014
• Published date: 01 February 2014
• DOI: http://doi.org/10.1111/jfir.12027

THE PRICE‐TAKER EFFECT ON THE VALUATION OF EXECUTIVE

STOCK OPTIONS

Tung‐Hsiao Yang

National Chung Hsing University

Don M. Chance

Louisiana State University

Abstract

Because of vesting requirements and the absence of liquidity, executive stock options are

valued at less, and often far less, than Black–Scholes–Merton values. We argue that this

view assumes the subtle condition that option holders are price takers and therefore

cannot influence the payoffs of their options, an assumption that clearly contradicts the

very reason for granting options. We build a model to incorporate the executive’s effort

and perception of his quality, private beliefs, and confidence to show that these options

are worth considerably more than previously believed and under some conditions even

more than Black–Scholes–Merton values.

JEL Classification: G34, M52

I. Introduction

Traditional financial models almost always assume that no investor can influence the price

of an asset by trading. Investors are said to be price takers. This assumption, so common

that it is rarely even mentioned, is second nature in models of competitive markets. The

markets for publicly traded options are generally competitive enough to support this

assumption, and as such, the Black–Scholes–Merton model and almost all of its variants

assume that all market participants are price takers.

There is a history, both in research and in practice, of using the Black–Scholes–

Merton model, with some adjustments, to value executive stock options. Thus, doing so

implicitly assumes that executives are price takers. Because the options are awarded in

part to incentivize executives, the notion that an executive is a price taker clearly belies a

critical characteristic of these options.

A significant body of published papers shows that executives value their options

at substantially less than Black–Scholes–Merton values. Such a conclusion is a natural

result of penalizing the options for their lack of liquidity. Awarding executives financial

This paper was presented at the Financial Management Association Europe, Southern Finance Association,

and Northern Finance Association meetings, and a faculty seminar at the University of Oklahoma. The authors thank

Jean Canil, Andrea Heuson, Wei‐Ling Song, Cliff Stephens, John Wald, Adam Yore, David Koslowsky, and Ivan

Brick for comments and suggestions.

The Journal of Financial Research Vol. XXXVII, No. 1 Pages 27–54 Spring 2014

27

© 2014 The Southern Finance Association and the Southwestern Finance Association

RAWLS COLLEGE OF BUSINESS, TEXAS TECH UNIVERSITY

PUBLISHED FOR THE SOUTHERN AND SOUTHWESTERN

FINANCE ASSOCIATIONS BY WILEY-BLACKWELL PUBLISHING

assets over which they have no control of the payoffs and that they cannot sell will

certainly cause the executives to value those assets at less than would other investors who

similarly have no control over the outcomes but who are free to sell at will.

Accurate valuation of executive stock options is an important issue, as it affects

our understanding of how options incentivize executives. The literature acknowledges

that the executive and the company do not hold mirror images of each other’s position.

1

The company’s cost of the option can be substantially different from the executive’s value

of the option. If an executive has a different opinion of the value of his options than the

company believes the options are worth, it will not award the proper number of options to

incentivize the executive. As noted, under traditional models of executive stock option

valuation, the option value tends to lie well below the cost to the company, but as also

noted, these models assume the executive is a price taker. Recognizing the fact that the

executive can influence the payoff of the option, it follows that the executive is likely to

have a higher opinion of the value of the option than he would if he had no influence. As

such, the company’s belief of how the executive values the option would be well below

what the executive actually believes. Failing to recognize this fact could lead the company

to award more options than necessary to incentivize the executive and therefore would

raise the cost to the company. Indeed, the large numbers of options seemingly awarded to

executives may well be driven by the belief that executives value these options at much

less than they really do.

In this article we reexamine the traditional utility‐based approach of executive

stock option valuation and remove the price‐taker assumption by incorporating the effect

of the executive’s perception of his effort, ability, and confidence on his private valuation

of the options. It shows that these factors lead executives to value options at far more than

suggested by traditional models and that under some circumstances, at more than Black–

Scholes–Merton values. We also examine how incorporation of these effects influences

the executive’s decision to exercise early.

II. Previous Research

A large body of literature exists on the valuation of executive stock options. Probably the

most widely referenced work is Hall and Murphy (2002), who model a risk‐averse

executive holding a stock option and stock in the firm. They set up an expected utility

maximization problem in which the executive determines the certainty equivalent value of

the option as the cashthat would be accepted in lieu of the option. The executiveis assumed

to be unable to sell the option, but may, after the vesting day, choose to exercise it early.

There are numerous extensions of the Hall–Murphy model, but all are generally framed

around the idea that a risk‐adverseexecutive holds an illiquid option with limited ability to

diversify within a moderateto extremely high degree of risk concentration in his portfolio.

2

1

For an excellent discussion of this distinction, see Carpenter (1998, pp. 131–32).

2

For related and different approaches, see Lambert, Larcker, and Verrecchia (1991), Carpenter (1998),

Henderson (2005), Kulatilaka and Marcus (1994), Cai and Vijh (2005), Detemple and Sundaresan (1999),

Meulbroek (2001), and Ingersoll (2006).

28 The Journal of Financial Research