Options with Constant Underlying Elasticity in Strikes

Closed-form solutions are derived and interpreted for European options, with stochastic strike prices, that maintain constant elasticity of the strike with respect to the price of the underlying asset. We refer to such options as CUES. CUES preserve the relative shares of exercise price risk for both the buyer and writer of the option, regardless of whether the price of the underlying asset moves up or down. The relevance of the CUES concept is established through applications in two distinct fields. First, it is established that CUES-like options are embedded in private equity investments. This concept is then used in a novel application to determine the equity share of a private company corresponding to a given level of investment. Secondly, the advantages that CUES would provide over traditional executive stock option grants are considered and it is shown that CUES can provide enhanced incentive-alignment without increasing options expense to the company. JEL Classification: G130     

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.     

Valuing executive stock options: performance hurdles, early exercise and stochastic volatility

Accounting standards require companies to assess the fair value of any stock options granted to executives and employees. We develop a model for accurately valuing executive and employee stock options, focusing on performance hurdles, early exercise and uncertain volatility. We apply the model in two case studies and show that properly computed fair values can be significantly lower than traditional Black–Scholes values. We then explore the implications for pay-for-performance sensitivity and the design of effective share-based incentive schemes. We find that performance hurdles can require a much greater fraction of total compensation to be a fixed salary, if pre-existing incentive levels are to be maintained.     

Should there exist secondary markets for executive stock options?

This paper investigates the potential disadvantages of the secondary markets for executive stock options (ESOs). The benefits of such markets are evident, but they might also have negative effects for shareholders. Executives might, for example, use inside information to time their ESO selling. We investigate two personal motives of managers that can be assumed to affect their optimal selling decision, that is, managers' personal portfolio management issues and the use of inside information. We explore these motives by analyzing unique data from Finland, where there are secondary markets for ESOs. The results of the study support the traditional portfolio diversification hypothesis according to which managers tend to sell their ESOs when holding an ESO is equivalent to holding the underlying stock; that is, in such a case a manager's wealth is closely tied to the stock price of the firm. With respect to the use of inside information the results indicate that ESO selling activity is not related to future stock price behaviour, suggesting that managers do not use inside information to determine the selling time of their ESOs. These results imply that the existence of secondary markets for ESOs does not weaken the usefulness of ESOs as the management compensation, although the benefits of such markets are evident.     

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.     

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.

The association between financially expert independent directors and the accounting for employee stock options

This study investigates how the financial expertise of independent directors is associated with voluntary accounting policy decisions. As representatives of a company’s shareholders, financially-expert independent directors are more likely to cause management to pursue higher quality accounting policy decisions. The policy decision investigated involves the expense/non-expense policy choice for employee stock options as previously permitted under SFAS No. 123. Using a sample of 174 option-expensing firms and a matched control sample of 174 non-expensing firms, the results indicate a significant, positive association between the decision to expense employee stock options and the financial expertise of a company’s independent directors. Further, a significant, negative association was found between the option-expensing decision and whether the chief executive officer was the largest internal blockholder.     

Stock Option Measures and the Stock Repurchase Decision

The major purposes of this study are two fold. First, we investigate whether or not the dilutive effect from stock options on the denominator of earnings per share is associated with the incurrence of stock repurchases. We use the FASB dilution and the economic dilution as the direct dilution measures and examine their relationship with stock repurchase decision. Second, we explore which of the extant measures of stock options can better explain the incurrence of stock repurchases. Six extant measures of stock options from previous studies are used: (1) the FASB's treasury-stock EPS dilution method, (2) the economic dilution measure based on Core, Guay and Kothari (2002), (3) the number of employee stock option exercises, (4) the number of stock option grants, (5) the number of total stock options outstanding, and (6) the number of exercisable stock options.Using a pooled cross-sectional sample from 1996–2000, we find a positive association between the likelihood of stock repurchases and the FASB dilution as well as the economic dilution in EPS, respectively. Thereby providing support for the undo-dilution hypothesis. The highest incremental explanatory power is found when we add the number of stock options exercisable to the baseline model. However, further analysis does not support the option-funding hypothesis suggested by Kahle (2002). We provide two explanations for why exercisable stock options better explain the stock repurchase decision.     

What drives the dating game of executive options exercise? Evidence from Taiwan

Examining Taiwanese firms from 2002 to 2008, this paper investigates the motivations behind backdating the exercising of executive stock options. The probability of suspect exercises (backdating) is positively related to the firm’s stock return, the value of the option, tax savings, institutional ownership and the extent of CEO equity ownership and negatively related to firm‐specific risk and the use of Big Four accounting firms. Tax incentives motivate executives to backdate the exercise date, implying that the greater the potential for larger tax savings, the greater the likelihood of backdating. Backdating usually occurs in firms that have heavy ownership by the CEO, have more claims to executive stock options and are not family‐run, confirming the presence of the agency cost problem.     

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     

Valuing reload options

Over the past quarter century, the use of stock options as pay for performance has grown enormously. Option grants now account for 32% of CEO pay—more than twice that of salaries. In addition options are now being granted to many more employees than before. During this same time period, there have been numerous innovations in the features on compensation options. One of these features is the reload—the grant of new options to replace shares tendered in the payment of the exercise. Within the past year, the long-delayed FASB requirement that options be expensed for financial reporting has finally become a fact. It is incumbent upon financial researchers to provide methods to achieve the goal of valuing options, not only to serve the accounting needs, but also to provide ways of determining their true costs and incentive effects. This paper analyzes the various forms of reload options and provides simple Black-Scholes like formulas for evaluating them. JEL Classification G13     

The Subjective Valuation of Indexed Stock Options and Their Incentive Effects

We analyze the potential role of indexed stock options in future pay‐for‐performance executive compensation contracts. We present a unified framework for index‐linked stock options, discuss their incentive effects, argue that indexation schemes based on the capital‐asset pricing model (CAPM) are the most suitable for executive compensation, and derive a subjective pricing model for the class of CAPM‐based indexed stock options. Contrary to earlier work, executives would not be motivated to take on investment projects with high idiosyncratic risk once their lack of wealth diversification and degree of risk aversion are factored into the analysis.     

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.     

Do Newly Listed Derivatives Affect the Market Risk Premium in a Thin Stock Market?

This study examines the effects on the stock market unitaryrisk premium and volatility associated with the listing of stockand stock index derivatives in Switzerland. Based on a univariateGARCH (1,1) specification of the stock index variance and atime-varying unitary risk premium representation, we can rejectthe hypothesis that stock and stock index derivatives listingsdo not affect the total risk premium. Contrarily to previousempirical evidence, we find that derivatives listings affectboth the conditional market returns’ variance and theunitary risk premium through structural shocks. The gradualmarket completion hypothesis is further corroborated in that,cumulatively, the three stock and stock index options futuresderivatives listings reduced the unitary risk premium whilethe marginal impact of each successive listing decayed. JELClassification: G12, G14.     

Optimal exercise of executive stock options

Valuing executive stock options is a challenging problem, because the standard risk-neutral valuation of those options is not appropriate; the executive is not allowed to trade the stock of the firm, so is not operating in a complete market. As this paper shows, an executive holding many American-style call options on his firm’s stock will optimally exercise the options bit by bit, whereas a risk-neutral valuation of the options would assume that all are exercised at the same time. Comparative statics of the optimal exercise policy show many surprising features.      

Options trades,short sales and real earnings management

We study the link between measures of stock options’ volatility and firms’ real earnings management (RM). We hypothesise that RM causes uncertainty in the value of a firm’s common stock and, as a result, increases the volatility spread and skew of the firm’s options. Spread and skew proxy for investors’ uncertainty in the value of the options underlying a stock. Consistent with our hypothesis, we find an association between a firm’s use of RM, and the volatility spread and skew in the firm’s options, more precisely in its put options. We also study the link between short selling and the extent of RM but do not find a consistent relationship between the two.     

Partial differential equations for Asian option prices

In this article, we consider fixed and floating strike European style Asian call and put options. For such options, there is no convenient closed-form formula for the prices. Previously, Rogers and Shi, Vecer, and Dubois and Lelièvre have derived partial differential equations with one state variable, with the stock price as numeraire, for the option prices. In this paper, we derive a whole family of partial differential equations, each with one state variable with the stock price as numeraire, from which Asian options can be priced. Any one of these partial differential equations can be transformed into any other. This family includes four partial differential equations which have a particularly simple form including the three found by Rogers and Shi, Vecer, and Dubois and Lelièvre. Our analysis includes the case of a dividend yield; we also include the case of in progress Asian options with floating strike, whereby we discuss the new equation proposed by Vecer, which uses the average asset as numeraire. We perform an error analysis on the four special partial differential equations and Vecer’s new equation and find that their truncation errors are all of the same order. We also perform numerical comparisons of the five partial differential equations and conclude, as expected, that Vecer’s equations and that of Dubois and Lelièvre do better when the volatility is low but that with higher volatilities the performance of all five equations is similar. Vecer’s equations are unique in possessing a certain martingale property and as they perform numerically well or better than the others, must be considered the preferred choice.     

Leverage, volatility and executive stock options

This paper studies how an optimal wage contract can be implemented using stock options, and derives the properties of the optimal contract with stock options. Specifically, we show how the exercise price and the size of the option grant should change in response to changes in exogenous parameters. First, for a fixed exercise price of executive stock options, the size of the option grant decreases in the riskiness of a desired investment policy, decreases in the volatility of return from the risky project, and increases in leverage. Second, for a fixed size of the option grant, the optimal exercise price of managerial stock options increases in the riskiness of a desired investment policy, increases in the volatility of return from the risky project, and decreases in leverage. Several empirical predictions are drawn from these conclusions regarding the pay-performance sensitivity of management compensation.     

Do executive stock options induce excessive risk taking?

We examine whether executive stock options can induce excessive risk taking by managers in firms’ security issue decisions. We find that CEOs whose wealth is more sensitive to stock return volatility due to their option holdings are more likely to choose debt over equity as a capital-raising vehicle. More importantly, the pattern holds not only in firms that are underlevered relative to their optimal capital structure but also in overlevered firms. This evidence is inconsistent with executive stock options aligning the interests of managers and shareholders; rather, it supports the hypothesis that stock options sometimes make managers take on too much risk and in the process pursue suboptimal capital structure policies.