Employee Stock Options, Equity Valuation, and the Valuation of Option Grants Using a Warrant-Pricing Model

We investigate the use of a warrant‐pricing approach to incorporate employee stock options (ESOs) into equity valuation and to account for the dilutive effect of ESOs in the valuation of option grants for financial reporting purposes. Our valuation approach accounts for the jointly determined nature of ESO and shareholder values. The empirical results show that our stock price estimate exhibits lower prediction errors and higher explanatory powers for actual share price than does the traditional stock price estimate. We use our valuation approach to assess the implications of dilution on the fair‐value estimates of ESO grants. We find that the fair value is overstated by 6% if we ignore the dilutive feature of ESOs. Furthermore, this bias is larger for firms that are heavy users of ESOs, small, and R&D intensive, and for firms that have a broad‐based ESO compensation plan.     

Valuing Employee Share Options: Four Australian Case Studies

We take four case studies to illustrate three issues: how ESOs are valued; how the valuation depends on assumptions; and how US proposals to account for ESOs would affect a company's financial profile. We adopt the Black-Scholes options model to value ESOs issued by Brambles Industries, Coles Myer, Tabcorp Holdings and Westpac Banking Corporation. Under the FASB's proposal, after-tax profit is lower and shareholders' funds and assets are higher beginning with the grant date. At the end of the amortisation period, assets and shareholders' funds would be the same as under current practice, but the fair value of the ESOs on their grant date would have been transferred from unappropriated profits to issued capital.     

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.     

Managing Employee Stock Option Expense: A Fair Value Approach

Owing to special characteristics, classic option pricing models are not well suited to the valuation of employee stock options (ESOs). This paper attempts to conduct a more general fair value estimation based on attaching performance targets to option vesting. Considering a setting that includes factors such as options that may be exercised early at employee discretion, employee exit rates and firm default risk, this paper presents a sensitivity analysis and empirical tests of option value. The results highlight the importance of considering the characteristics of ESOs in the design of performance‐vested option plans so as to provide the most attractive incentives for employees.     

Valuation of Callable Warrants

A simple valuation model for callable warrants is derived and tested. The model is expressed in closed form except for one term which can be evaluated numerically. Predictions of 78 warrant prices are compared to market prices and the average error is -.224 percent. By contrast, the Black-Scholes model applied to the same warrants produces an average error of 31.44 percent. Thus the callability feature cannot safely be ignored in determining warrant values.     

Implied volatility skews and stock return skewness and kurtosis implied by stock option prices

The Black-Scholes* option pricing model is commonly applied to value a wide range of option contracts. However, the model often inconsistently prices deep in-the-money and deep out-of-the-money options. Options professionals refer to this well-known phenomenon as a volatility ‘skew’ or ‘smile’. In this paper, we examine an extension of the Black-Scholes model developed by Corrado and Su that suggests skewness and kurtosis in the option-implied distributions of stock returns as the source of volatility skews. Adapting their methodology, we estimate option-implied coefficients of skewness and kurtosis for four actively traded stock options. We find significantly nonnormal skewness and kurtosis in the option-implied distributions of stock returns.     

ESO compensation: The roles of default risk, employee sentiment, and insider information

This paper derives a pricing model for employee stock options (ESO) that includes default risk and considers employee sentiment. Using ESO data from 1992 to 2004, the study finds that the average executive's subjective value is about 55% of the Black-Scholes value. Only employees who over-estimate firm returns (or insiders who know that the firm is under-valued) by about 10% per annum will prefer ESOs over cash compensation. Our model also shows that work incentives offered by ESOs may be far lower than those implied by Black-Scholes but that ESOs may induce less risk-taking behavior, contrary to typical moral hazard arguments. Findings may impact relevant accounting regulations as well as compensation decisions.     

Arbitrage,Continuous Trading,and Margin Requirements

This paper studies the impact that margin requirements have on both the existence of arbitrage opportunities and the valuation of call options. In the context of the Black-Scholes economy, margin restrictions are shown to exclude continuous-trading arbitrage opportunities and, with two additional hypotheses, still to allow the Black-Scholes call model to apply. The Black-Scholes economy consists of a continuously traded stock with a price process that follows a geometric Brownian motion and a continuously traded bond with a price process that is deterministic.     

Finance, Politics, and the Accounting for Stock Options

The politics of option accounting crosses party lines, reflecting both the interests of the affected constituencies and the desire for power over standard setting. House Bill HR-3574, which mandates an assumption of zero stock price volatility, runs counter to the recently passed Financial Accounting Standards Board (FASB) rule requiring fair-value expensing of stock options. For any option issued at or out of the money, where strike prices are normally set, expense recognition is zero under this bill's mandated assumption.
Besides excessive use of stock options, the lack of a "final peace" in the option accounting war appears to have encouraged another questionable corporate practice. This article examines a sample of "six-and-one restructurings," exchanges of options in which expensing of re-priced (deep out-of-the-money) options can be avoided if employees wait at least six months and one day before receiving new options. The authors found that market-adjusted stock prices tend to decrease during the six-month period before the strike price is reset. This result provides one more reason why companies should be required to use fair-value option pricing models to expense options.     

On the Relative Pricing of Long‐Maturity Index Options and Collateralized Debt Obligations

We investigate a structural model of market and firm‐level dynamics in order to jointly price long‐dated S&P 500 index options and CDO tranches of corporate debt. We identify market dynamics from index option prices and idiosyncratic dynamics from the term structure of credit spreads. We find that all tranches can be well priced out‐of‐sample before the crisis. During the crisis, however, our model can capture senior tranche prices only if we allow for the possibility of a catastrophic jump. Thus, senior tranches are nonredundant assets that provide a unique window into the pricing of catastrophic risk.     

Valuing employee stock options under SFAS 123R using the Black–Scholes–Merton and lattice model approaches

In 2004, the Financial Accounting Standards Board (FASB) issued Statement of Financial Accounting Standard No. 123 (revised 2004), Share-Based Payments (SFAS 123R), requiring all entities to recognize as expense the fair value of stock options issued to employees for services provided. Because employee stock options cannot be traded publicly, their fair value must be estimated using a model, with the Black–Scholes–Merton (BSM) and lattice models being the most appropriate alternatives.This teaching note provides an overview of employee stock options, followed by a discussion of the BSM and lattice valuation models, including their application and limitations. A project which has been used in financial accounting courses is also presented. The conceptual discussion coupled with illustrated examples will help students enhance their understanding of fair value estimation of and accounting for employee stock options under the recently adopted SFAS 123R.     

ON USING THE BLACK-SCHOLES MODEL TO VALUE WARRANTS

In this paper ad hoc procedures that employ the Black-Scholes model in the valuation of warrants are examined. Findings indicate that the Black-Scholes model unadjusted for either dividends or dilution undervalues out-of-the-money warrants with short expirations. An adjustment for dilution improves the valuation for longer-term warrants of firms that do not pay dividends. For dividend-paying firms, findings suggest that it is better to adjust for dividends than for dilution when warrants are in the money or have expirations exceeding four years.     

An Empirical Analysis of the Pricing of Bank Issued Options versus Options Exchange Options

Since 1998, large investment banks have become active as issuers of options, generally referred to as call warrants or bank‐issued options. This has led to an interesting situation in the Netherlands, where simultaneously call warrants are traded on the stock exchange, and long‐term call options are traded on the options exchange. Both entitle their holders to buy shares of common stock. We start with a direct comparison between call warrants and call options, written on the same stock and with the same exercise price, but where the call option has a longer time to maturity. In 13 out of 16 cases we find that the call warrants are priced higher, which is a clear violation of basic option pricing rules. In the second part of the analysis we use option pricing models to compare the pricing of call warrants and call options. If implied standard deviations from options are used to price the call warrants, we find that the call warrants are strongly overpriced during the first five trading days. The average overpricing is between 25 and 30%. Only a small part of the overpricing can be explained by rational arguments such as transaction costs. We suggest that the overvaluation can be explained by a combination of an active financial marketing by the banks and the framing effect.     

Revisiting the incentive effects of executive stock options

We develop a multiperiod framework to evaluate the incentive effects of executive stock options (ESOs). For a given increase in the grant-date firm stock price (and a concurrent increase in return volatility), the increment of total value at the vesting date acts as a proxy for the incentive effects of ESOs. If the option is attached to the existing contract without adjusting cash compensation, we suggest that a firm should not always fix the strike price to the grant-date stock price; instead, the strike price should vary with the length of the vesting period. We also show that, compared with at-the-money options, restricted stock generates greater incentives to increase stock prices in some scenarios, especially when equity-based awards are vested early. If the vesting period is long, the firm could grant options instead of restricted stock to maximize incentives.     

The relation between corporate governance and CEOs’ equity grants

We investigate whether the firm’s corporate governance affects the value of equity grants for its CEO. Consistent with the managerial power view, we find that more poorly-governed firms grant higher values of stock options and restricted stock to their CEOs after controlling for the economic determinants of these grants. We show that the negative relation between governance strength and equity grants is not likely to be attributable to omitted economic factors or substitution effects between governance strength and equity incentives. As further evidence consistent with the managerial power view, we show that firms with poorer governance in the pre-Enron era cut back more on using employee stock options (ESOs) for their CEOs in the post-Enron era, a period when the accounting and outrage costs of ESOs increased, consistent with poorly-governed firms taking more advantage of opaque ESO accounting rules than better-governed firms. We show that the association between governance strength and abnormal equity grants is less negative in the post-Enron period than it was in the pre-Enron period, consistent with firms making more efficient equity-granting decisions after the corporate governance changes mandated by the Sarbanes–Oxley Act of 2002 and the major US stock exchanges took effect.     

Is warrant really a derivative? Evidence from the Chinese warrant market

This paper studies the Chinese warrant market that has been developing since August 2005. Empirical evidence shows that the market prices of warrants are much higher systematically than the Black-Scholes prices with historical volatility. The prices of a warrant and its underlying asset do not support the monotonicity, perfect correlation and option redundancy properties. The cumulated delta-hedged gains for almost all expired warrants are negative. The negative gains are mainly driven by the volatility risk, and the trading values of the warrants for puts and the market risk for calls. The investors are trading some other risks in addition to the underlying risks.     

The Value Relevance of Equity Method Fair Value Disclosures

We assess the valuation implications of the fair value disclosures made for publicly traded securities accounted for under the equity method. We test the association between investors' stock price metrics and fair value disclosures while controlling for book values on a sample of 172 investor firm-years during 1993–1997. Our results indicate that the information in the fair value disclosures is incremental to the information provided by both an investment's equity method book value and equity method reported income. This suggests that there is nothing unique about investments in publicly traded common stock that involve significant influence that makes the fair value disclosures irrelevant for firm valuation.     

Repricing and employee stock option valuation

A repricing occurs when the issuing firm resets the strike price of an employee stock option (ESO). ESO repricings occur most frequently following a significant decline in the underlying stock price. Typically, the strike price is reset to the new stock price. We develop a new model for valuing ESOs with a repricing feature. Our valuation model is developed within a utility-maximizing framework that accounts for potentially multiple repricings, employee risk aversion, employee non-option wealth, the non-tradeability of ESOs, and the early exercise feature of ESOs. Simulations suggest that these factors can significantly affect ESO value.     

What determines early exercise of employee stock options in Australia?

Employee stock options (ESOs) are a popular way of remunerating employees. We analyse factors at the firm and option level affecting the employee's decision to exercise ESOs before they mature. Exercises over the period 1998–2004 are analysed and the key factor influencing early exercise is found to be dividends. Exercises frequently occur well before maturity, but in most cases little time value is sacrificed. Our findings have implications for the ‘fair’ valuation of ESOs in companies’ financial statements, as required by the relevant Australian accounting standard, AASB 2.     

SKEWNESS AND KURTOSIS IN S&P 500 INDEX RETURNS IMPLIED BY OPTION PRICES

The Black-Scholes (1973) model frequently misprices deep-in-the-money and deep-out-of-the-money options. Practitioners popularly refer to these strike price biases as volatility smiles. In this paper we examine a method to extend the Black-Scholes model to account for biases induced by nonnormal skewness and kurtosis in stock return distributions. The method adapts a Gram-Charlier series expansion of the normal density function to provide skewness and kurtosis adjustment terms for the Black-Scholes formula. Using this method, we estimate option-implied coefficients of skewness and kurtosis in S&P 500 stock index returns. We find significant nonnormal skewness and kurtosis implied by option prices.