Executive Stock Options

Abstract

As a part of the compensation package many companies provide executives with executive stock options, which are call options with additional restrictions. They provide some financial advantages to the executives and help the company retain the service of the executives who improve the company’s earnings and management.

Until recently the values of the executive stock options were not required to be disclosed in the company?s financial reports. But recent statements from the Financial Accounting Standards Board (FASB) have made it necessary to value these executive stock options. The valuation of executive stock options is also required for investors and financial practitioners. This paper considers the award of performance-based executive stock options when the stock price at the time of stock option award exceeds a given preassigned value. It is assumed that the stock price follows a geometric Brownian motion, and that the number of stock options awarded at any time depends on the stock price at that time.

A valuation formula is derived using the method of Esscher transforms for a multiyear award plan. The closed-form formula derived is similar to the Black-Scholes formula for options and utilizes the standard bivariate normal distribution function, which is available in statistical software. In this paper the number of stock options awarded is assumed to be in a specific form, but the theory presented can be modified to suit other forms of award structure. Moreover, by suitable choice of parameters, a valuation formula is also presented for the award of fixed-value executive stock options grants; this formula is also in a closed form and involves cumulative distribution values of the standard normal random variable. Numerical illustrations of the use of the valuation formulas are presented.     

A GUIDE TO VALUING EMPLOYEE STOCK OPTIONS WITH A RELOAD FEATURE

At first glance, executive stock options with reload provisions appear to be more complicated than conventional options, and thus the valuation of such options would appear to be more difficult. But, as the authors demonstrate in this article, such reload options provide the employee with a dominant exercise strategy—namely, to exercise the option whenever it is "in-the-money." And the fact that reload options will always be exercised simplifies their valuation by eliminating a major problem—that associated with employee's risk references and uncertain early exercise—in valuing conventional options.     

American-style Indexed Executive Stock Options

This paper develops a new pricing model for American-style indexed executive stock options. We rely on a basic model framework and an indexation scheme first proposed by Johnson and Tian (2000a) in their analysis of European-style indexed options. Our derivation of the valuation formula represents an instructive example of the usefulness of the change-of-numeraire technique. In the paper's numerical section we implement the valuation formula and demonstrate that not only may the early exercise premium be significant but also that the delta of the American-style option is typically much larger than the delta of the otherwise identical (value-matched) European-style option. Vega is higher for indexed options than for conventional options but largely independent of whether the options are European- or American-style. This has important implications for the design of executive compensation contracts. We finally extend the analysis to cover the case where the option contracts are subject to delayed vesting. We show that for realistic parameter values, delayed vesting leads only to a moderate reduction in the value of the American-style indexed executive stock option.     

Pricing Contingent Claims under Interest Rate and Asset Price Risk

This paper presents a general framework for pricing contingent claims under interest rate and asset price uncertainty. The framework extends Ho and Lee's (1986) valuation framework by allowing not only future interest rates but also future asset prices to depend on the current term structure of interest rates. The approach is shown to provide risk-neutral valuation relationships that are consistent with the initial term structure of interest rates and can be applied to valuation of a broad class of assets including stock options, convertible bonds, and junk bonds.     

Valuation of a Repriceable Executive Stock Option

We introduce a path-dependent executive stock option. The exercise price might be reduced when both the firm’s stock price and a stock market index fall greatly. The repriceable executive stock option has a simple payoff that may be used for realistic executive rewards. We show the valuation formula, and compute the probability of the repriceable executive stock option expiring in-the-money. Both price and probability are important pieces of quantitative information when choosing an executive compensation package.     

How Might Companies Value ESOs?

There has been a steady growth in the use of employee equity compensation plans, and in the use of executive stock options (ESOs) in particular, along with a rise in shareholder and public perceptions that the values of compensation plans are not always fully disclosed. The IFSA of Australia recently called for separate reporting in financial statements of numbers and values of ESOs. Companies, when negotiating employment contracts, frequently agree to compensate an executive if a share option plan is subsequently not approved by shareholders. These facts suggest that reporting the value of an ESO plan is a useful and important exercise. We outline a model for the valuation of ESOs typically issued by Australian listed companies and illustrate the application of the model with a case study.     

The impact of the market portfolio on the valuation,incentives and optimality of executive stock options

This paper examines the effect on valuation and incentives of allowing executives receiving options to trade on the market portfolio. We propose a continuous time utility maximization model to value stock and option compensation from the executive's perspective. The executive may invest non-option wealth in the market and riskless asset but not in the company stock itself, leaving them subject to firm-specific risk for incentive?purposes. Since the executive is risk averse, this unhedgeable firm risk leads them to place less value on the options than their cost to the company.

By distinguishing between these two types of risks, we are able to examine the effect of stock volatility, firm-specific risk and market risk on the value to the executive. In particular, options do not give incentive to increase total risk, but rather to increase the proportion of market relative to firm-specific risk, so executives prefer high beta companies. The paper also examines the relationship between risk and incentives, and finds firm-specific risk decreases incentives whilst market risk may decrease incentives depending on other parameters. The model supports the use of stock rather than options if the company can adjust cash pay when granting stock-based compensation.     

IRC Section 162(m) and the law of unintended consequences

In 1993, Section 162(m) of the U.S. Internal Revenue Code was passed into law with the intent to reign in outsized executive compensation by eliminating the tax-deductibility of executive compensation above $1 million unless the excess compensation was performance-based. An unintended consequence of the legislation was that executives' total compensation actually increased in the post-1993 period, largely due to a dramatic increase in employee stock options. Employee stock options have unintended consequences of their own. The economic value of stock options may be influenced by executive decision-making when the options are valued using the Black-Scholes model or some variant thereof. Our findings suggests an unintended consequence that executives used their discretion to positively impact the performance-based component of their compensation through actions increasing share price volatility and reducing dividend yields, assumptions implicit in option valuation models.     

Valuation and incentive effects of hurdle rate executive stock options

Traditional executive stock options are often criticized for inherently weak links between pay and performance. Hurdle rate executive stock options represent a viable improvement. However, valuing these options presents extraordinary analytic difficulties. With a constant dividend yield the strike price becomes a path-dependent function of the stock price and exact analytic valuation is intractable. To solve this problem, we apply the Monte Carlo valuation approach developed by Longstaff and Schwartz (Rev Financ Stud 4:113–147, 2001) to estimate the value of path-dependent American options. We also extend the methodology to incorporate the theoretical framework by Ingersoll (J Bus 79:453–487, 2006) to permit subjective valuation influenced by an executive’s risk aversion.

Exercises of Executive Stock Options on the Vesting Date

We investigate the motives for executives to exercise executive stock options on the options’ vesting date versus a later early exercise. We find that executives frequently exercise on the vesting date, executives with a greater need for portfolio diversification and riskier underlying stocks are more likely to exercise their options on the vesting date versus a later early exercise, and private information appears less relevant to vesting date exercises.     

An IFRS 2 and FASB 123 (R) Compatible Model for the Valuation of Employee Stock Options

In this paper, we show how employee stock options can be valued under the new reporting standards IFRS 2 and FASB 123 (revised) for share-based payments. Both standards require companies to expense employee stock options at fair value. We propose a new valuation model, referred to as Enhanced American model, that complies with the new standards and produces fair values often lower than those generated by traditional models such as the Black–Scholes model or the adjusted Black–Scholes model. We also provide a sensitivity analysis of model input parameters and analyze the impact of the parameters on the fair value of the option. The valuation of employee stock options requires an accurate estimation of the exercise behavior. We show how the exercise behavior can be modeled in a binomial tree and demonstrate the relevance of the input parameters in the calibration of the model to an estimated expected life of the option. JEL Classification G13, G30     

Long memory options: LM evidence and simulations

This paper demonstrates the impact of the observed financial market persistence or long term memory on European option valuation by simple simulation. Many empirical researchers have observed the non-Fickian degrees of persistence in the financial markets different from the Fickian neutral independence (i.i.d.) of the returns innovations assumption of Black–Scholes’ geometric Brownian motion assumption. Moreover, Elliott and van der Hoek [Elliott, R.J., van der Hoek, J., 2003. A general fractional white noise theory and applications to finance. Math. Finance 13, 301–330] provide a theoretical framework for incorporating these findings into the Black–Scholes risk-neutral valuation framework. This paper provides the first graphical demonstration why and how such long term memory phenomena change European option values and provides thereby a basis for informed long term memory arbitrage. By using a simple mono-fractal fractional Brownian motion, it is easy to incorporate the various degrees of persistence into the Black–Scholes pricing formula. Long memory options are of considerable importance in corporate remuneration packages, since stock options are written on a company’s own shares for long expiration periods. It makes a significant difference in the valuation when an option is “blue” or when it is “red.” For a proper valuation of such stock options, the degrees of persistence of the companies’ share markets must be precisely measured and properly incorporated in the warrant valuation, otherwise substantial pricing errors may result.     

A jump to default extended CEV model: an application of Bessel processes

We develop a flexible and analytically tractable framework which unifies the valuation of corporate liabilities, credit derivatives, and equity derivatives. We assume that the stock price follows a diffusion, punctuated by a possible jump to zero (default). To capture the positive link between default and equity volatility, we assume that the hazard rate of default is an increasing affine function of the instantaneous variance of returns on the underlying stock. To capture the negative link between volatility and stock price, we assume a constant elasticity of variance (CEV) specification for the instantaneous stock volatility prior to default. We show that deterministic changes of time and scale reduce our stock price process to a standard Bessel process with killing. This reduction permits the development of completely explicit closed form solutions for risk-neutral survival probabilities, CDS spreads, corporate bond values, and European-style equity options. Furthermore, our valuation model is sufficiently flexible so that it can be calibrated to exactly match arbitrarily given term structures of CDS spreads, interest rates, dividend yields, and at-the-money implied volatilities.     

Maturity and exercise price of executive stock options

Using a simple three-period model in which a manager can gather information before making an investment decision, this paper studies optimal contracts with various stock options. In particular, we show how the exercise price of executive stock options is related to a base salary, the size of the option grant, leverage, and the riskiness of a desired investment policy. The optimal exercise price increases in the size of grant and the base salary and decreases in leverage and the riskiness of a desired investment policy. Other things equal, the optimal exercise price of European options with a longer maturity should increase more for an increase in the base salary and the size of grant and decrease more for an increase in leverage than the one with a shorter maturity. The optimal exercise price of American options is determined by the optimal exercise prices of European options with different maturities. Given the fixed exercise price, the size of the option grant does not decrease in the face value of debt.     

Optimal exercise of executive stock options and implications for firm cost

This paper conducts a comprehensive study of the optimal exercise policy for an executive stock option and its implications for option cost, average life, and alternative valuation concepts. The paper is the first to provide analytical results for an executive with general concave utility. Wealthier or less risk-averse executives exercise later and create greater option cost. However, option cost can decline with volatility. We show when there exists a single exercise boundary, yet demonstrate the possibility of a split continuation region. We also show that, for constant relative risk averse utility, the option value does not converge to the Black and Scholes value as the correlation between the stock and the market portfolio converges to one. We compare our model's option cost with the modified Black and Scholes approximation typically used in practice and show that the approximation error can be large or small, positive or negative, depending on firm characteristics.     

Risk-taking incentives of executive stock options and the asset substitution problem

Various theoretical models show that managerial compensation schemes can reduce the distortionary effects of financial leverage. There is mixed evidence as to whether highly levered firms offer less stock‐based compensation, a common prediction of such models. Both the theoretical and empirical research, however, have overlooked the leverage provided by executive stock options. In principle, adjusting the exercise prices of executive stock options can mitigate the risk incentive effects of financial leverage. We show that the near‐universal practice of setting option exercise prices near the prevailing stock price at the date of grant effectively undoes most of the effects of financial leverage. In a large cross‐sectional sample of Canadian option‐granting firms, we find evidence that executives' incentives to take equity risk are negatively rather than positively related to the leverage of their employers.     

EARLY EXERCISE OF AMERICAN INDEX OPTIONS

We show that exercise of American call options on stock indexes frequently occurs before expiration and attribute this early exercise to the “wild card” option that results from the cash settlement exercise process. The wild card represents an “implied option” to sell the index option at the fixed settlement price; it is therefore a put option on the index call option. We derive a simple one-period valuation model using compound option pricing. Analysis of observed early exercise demonstrates that the wild card feature is a factor influencing early exercise of index options.     

Employee Reload Options: Pricing, Hedging, and Optimal Exercise

Reload options, call options granting new options on exercise,are popularly used in compensation. Although the compound optionfeature may seem complicated, there is a distribution-free dominantpolicy of exercising reload options whenever they are in themoney. The optimal policy implies general formulas for numericalvaluation. Simpler formulas for valuation and hedging followfrom Black–Scholes assumptions with or without continuousdividends. Time vesting affects the optimal policy, but numericalresults indicate that it is nearly optimal to exercise in themoney whenever feasible. The results suggest that reload optionsproduce similar incentives as employee stock options and sharegrants.     

Dividend taxes and stock volatility

How do dividend taxes affect stock volatility? If a risk-averse executive faces price risk through his incentive contract, changes in stock volatility due to dividend taxes may increase agency costs and therefore decrease overall welfare. In this paper, I use a decrease in dividend taxes as a natural experiment to identify their effect on the firm’s idiosyncratic stock return volatility. Stock volatility decreased after the tax cut for firms at which executives have larger sensitivity to stock price in their incentive compensation package relative to firms at which executives have a smaller sensitivity. Therefore, with risk-averse executives and risk-neutral shareholders, dividend taxes may exacerbate agency costs. The increase in agency costs will decrease shareholder welfare, which can be partially offset by the use of options in the employment contract.     

Financial crisis and bank executive incentive compensation

We study the executive compensation structure in 14 of the largest U.S. financial institutions during 2000–2008. We focus on the CEO's purchases and sales of their bank's stock, their salary and bonus, and the capital losses these CEOs incur due to the dramatic share price declines in 2008. We consider three measures of risk-taking by these banks. Our results are mostly consistent with and supportive of the findings of Bebchuk, Cohen and Spamann (2010), that is, managerial incentives matter — incentives generated by executive compensation programs are correlated with excessive risk-taking by banks. Also, our results are generally not supportive of the conclusions of Fahlenbrach and Stulz (2011) that the poor performance of banks during the crisis was the result of unforeseen risk. We recommend that bank executive incentive compensation should only consist of restricted stock and restricted stock options — restricted in the sense that the executive cannot sell the shares or exercise the options for two to four years after their last day in office. The above incentive compensation proposal logically leads to a complementary proposal regarding a bank's capital structure, namely, banks should be financed with considerably more equity than they are being financed currently.