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.     

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.     

Accounting for Option–based Compensation: The Economic Cost Approach

The intrinsic value approach amortizes over the life of the option, the difference between the stock price on the date of the grant and the exercise price of the option. The fair market value approach amortizes over the life of the option, the market value of stock options on the date of the grant. These approaches do not reflect the changes in the option–based compensation cost after the grant date. This paper proposes an economic cost approach that not only adjusts for the changes in the value of the options during its life but also records the issuance of the stock at fair market value on the exercise date.     

Stock price decreases prior to executive stock option grants

This study examines abnormal stock price changes prior to executive stock option grants. Executives have the incentive and opportunity to manage the timing of their communications of inside information to the market during the period just prior to the date of their stock-option grant so as to reduce the exercise price of their options. Executives benefit from temporary stock price decreases before the grant date and by stock price increases after the grant date. Executive stock option grants create a unique opportunity for insiders to profit by manipulating the timing of information flowing to the market without engaging in insider trading. Using data on 783 stock-option grants to chief executive officers, we find a statistically significant abnormal decrease in stock prices during the 10-day period immediately preceding the grant date.     

On the Upper Bound of a Call Option

Using only a weak set of assumptions, Merton (1973) shows that the upper bound of a European or American call option on a non-dividend paying stock is the underlying stock price: a result which is often extended to options on dividend paying stocks. In this short technical piece we show that the underlying stock price is in fact not the least upper bound of either a European or an American call option on a stock that pays one or more known dividends prior to maturity. Based on Merton's (1973) original framework, new upper bounds are established which depend on the size(s) of the dividend(s) compared to the size of the strike. JEL Classification: G12, G13     

THE DESIGN OF MULTI-YEAR STOCK OPTION PLANS

Despite the explosion in the corporate use of stock options, the incentives created by stock options are not well understood by either the boards who grant them or the executives who are meant to be motivated by them. A major source of confusion stems from the corporate practice of using multi-year stock option plans. Such multi-year grants create subtle, potentially important links between current performance and future grants that can significantly dilute incentives for better performance.
For example, so-called "fixed value" plans provide very weak, even perverse, incentives ex ante since the value of future option grants is completely insulated from current performance. Under such plans, an executive's reward for superior performance is to receive fewer options, and to receive more options for substandard performance. In contrast, the fixed number plan creates an intrinsic link between changes in this year's stock price and changes in the value of future option grants.
The author also reports the findings of new empirical research that shows that stock option plans, taken as a whole, have a pay-to-performance correlation that is eight times stronger than that of salary and bonus. But, consistent with the analysis above, fixed value option plans have pay-to-performance that is only six times that of salary and bonus, as compared to ten times for fixed number plans.     

Perpetual American options in incomplete markets: the infinitely divisible case

We consider the exercise of a number of American options in an incomplete market. In this paper we are interested in the case where the options are infinitely divisible. We make the simplifying assumptions that the options have infinite maturity, and the holder has exponential utility. Our contribution is to solve this problem explicitly and we show that, except at the initial time when it may be advantageous to exercise a positive fraction of his holdings, it is never optimal for the holder to exercise a tranche of options. Instead, the process of option exercises is continuous; however, it is singular with respect to calendar time. Exercise takes place when the stock price reaches a convex boundary which we identify.     

Executive stock options and incentive effects due to systematic risk

Existing research on executive stock options mainly focuses on total risk when studying risk incentives. In this study, we use a GARCH option pricing framework to show that the incentive effects of executive stock options depend on the composition of risk. Controlling for total risk, the value of executive stock options increases with systematic risk and this effect is stronger when the total risk is low. Thus, when firms grant standard or non-indexed options, CEOs will have incentives to increase systematic risk even when the total risk remains constant. In contrast, indexed options will provide CEOs with incentives to reduce systematic risk. We therefore conclude that an optimal mix of indexed and non-indexed option grants will provide CEOs with incentives to take the desired level of systematic risk.     

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     

Ironing out the kinks in executive compensation: Linking incentive pay to average stock prices

Traditional stock option grant is the most common form of incentive pay in executive compensation. Applying a principal-agent analysis, we find this common practice suboptimal and firms are better off linking incentive pay to average stock prices. Among other benefits, averaging reduces volatility by about 42%, making the incentive pay more attractive to risk-averse executives. Holding the cost of the option grant to the firm constant, Asian stock options are more cost effective than traditional stock options and provide stronger incentives to increase stock price. More importantly, the improvement is achieved with little impact on the option grant’s risk incentives (after adjusting for option cost). Finally, averaging also improves the value and incentive effects of indexed stock options.     

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 Pricing of Options on Assets with Stochastic Volatilities

One option-pricing problem that has hitherto been unsolved is the pricing of a European call on an asset that has a stochastic volatility. This paper examines this problem. The option price is determined in series form for the case in which the stochastic volatility is independent of the stock price. Numerical solutions are also produced for the case in which the volatility is correlated with the stock price. It is found that the Black-Scholes price frequently overprices options and that the degree of overpricing increases with the time to maturity.     

How Do Quasi‐Random Option Grants Affect CEO Risk‐Taking?

We examine how an increase in stock option grants affects CEO risk‐taking. The overall net effect of option grants is theoretically ambiguous for risk‐averse CEOs. To overcome the endogeneity of option grants, we exploit institutional features of multiyear compensation plans, which generate two distinct types of variation in the timing of when large increases in new at‐the‐money options are granted. We find that, given average grant levels during our sample period, a 10% increase in new options granted leads to a 2.8% to 4.2% increase in equity volatility. This increase in risk is driven largely by increased leverage.     

Informed Trading in Stock and Option Markets

We investigate the contribution of option markets to price discovery, using a modification of Hasbrouck's (1995) "information share" approach. Based on five years of stock and options data for 60 firms, we estimate the option market's contribution to price discovery to be about 17% on average. Option market price discovery is related to trading volume and spreads in both markets, and stock volatility. Price discovery across option strike prices is related to leverage, trading volume, and spreads. Our results are consistent with theoretical arguments that informed investors trade in both stock and option markets, suggesting an important informational role for options.     

Too much of a good incentive? The case of executive stock options

Using a utility-maximization framework, I show that the incentive to increase stock price does not always increase as more options are granted. Keeping the total cost of his compensation fixed, granting more options creates greater incentives to increase stock price only if option wealth does not exceed a certain fraction of total wealth. Beyond this critical level, granting more options actually reduces incentive effects and becomes counterproductive. In addition, stock options also create incentive to reduce (increase) idiosyncratic (systematic) risk. These incentive effects are sensitive to the choice of exercise price.     

Parisian options with jumps: a maturity–excursion randomization approach

This paper introduces an analytically tractable method for the pricing of European and American Parisian options in a flexible jump–diffusion model. Our contribution is threefold. First, using a double Laplace–Carson transform with respect to the option maturity and the Parisian (excursion) time, we obtain closed-form solutions for different types of Parisian contracts. Our approach allows us also to analytically disentangle contributions of the jump and diffusion components for Parisian options in the excursion region. Second, we provide numerical examples and quantify the impact of jumps on the option price and the Greeks. Finally, we study the non-monotonic effects of volatility and jump intensity close to the excursion barrier, which are important for shareholders’ investment policy decisions in a levered firm.     

Employee Stock Options and Investment

Exercises of employee stock options generate substantial cash inflows to the firm. These cash inflows substitute for costly external finance in those states of the world in which the demand for investment is high. Using the fact that the proceeds from option exercises exhibit a distinct nonlinearity around the point where options fall out of the money, we estimate that firms increase investment by $0.34 for each dollar received from the exercise of stock options. Firms that face higher external financing costs allocate more of the proceeds from option exercises to investment.     

What determines stock option contract design?

We analyze the factors that drive exercise price policy for executive option plans (ESOPs) and their scope in a country where firms are not subject to the tax and accounting considerations that seem to have led to the dominance of at-the-money options in the US Our “unbounded” data for Finland provide us with an excellent opportunity to investigate whether contract design is consistent with compensation theory. Our findings are largely consistent with predictions from the optimal contracting literature. The size of the plan is negatively related to Tobin's Q and firm size and positively related to proxies for monitoring costs, which also influence the probability of launching premium ESOPs. Our results also show that the premium (out-of-the-moneyness) is negatively related to prior stock returns and cash flow-to-assets, which may be an indication of high-water mark contracting, or alternatively, of managerial power. Finally, we also find some support for a positive relation between the premium and the length of the vesting period when maturity is fixed, which indicates an effort to keep the incentives for management from falling over time.     

Valuing employee reload options under the time vesting requirement

Upon the exercise of an employee stock option, the embedded reload provision entitles the holder to receive additional units of new options from the employer. The number of units of new options received is equal to the number of shares tendered as payment of strike and the new strike is set at the prevailing stock price. The reload provision may be subject to a time vesting requirement, that is, after each exercise, the employee is prohibited from exercising the reload until the end of a vesting period. In this paper, we construct an efficient numerical algorithm that computes the market value of the employee reload options under a time vesting requirement. Also, we explore the analytic properties of the price functions and optimal exercise policies of the employee reload options.     

Over-the-Counter Option Market Dividend Protection and “Biases” in the Black-Scholes Model: A Note

Most options are traded over-the-counter (OTC) and are dividend “protected;” the exercise price decreases on the ex date by an amount equal to the dividend. This protection completely inhibits the early exercise of American call options. Nevertheless, OTC-protected options have market values which differ systematically from Black-Scholes values for European options on non-dividend paying stocks. The pricing difference is related to both the variance of the underlying stock return and to time until expiration of the option, but it is quite small in dollar amount.