A market-induced mechanism for stock pinning

Abstract

We propose a model to describe stock pinning on option expiration dates. We argue that if the open interest on a particular contract is unusually large, delta-hedging in aggregate by floor market-makers can impact the stock price and drive it to the strike price of the option. We derive a stochastic differential equation for the stock price which has a singular drift that accounts for the price-impact of delta-hedging. According to this model, the stock price has a finite probability of pinning at a strike. We calculate analytically and numerically this probability in terms of the volatility of the stock, the time-to-maturity, the open interest for the option under consideration and a ‘price elasticity’ constant that models price impact.     

The Timing of Option Repricing

We investigate whether executive stock option repricings are systematically timed to coincide with favorable movements in the company's stock price. For a sample of 236 repricing events, we observe sharp increases in stock price in the 20‐day period following the repricing date. In addition, repricing dates tend to either precede the release of good news or follow the release of bad news in the quarterly earnings announcements. Since information about stock option repricing is not generally released to the public around the repricing date, these findings suggest that CEOs opportunistically manage the timing of the option repricing date.     

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.     

Underwater Options and the Dynamics of Executive Pay-to-Performance Sensitivities

We empirically analyze the dynamics of executives' pay‐to‐performance sensitivities. Option pay‐to‐performance sensitivities become weaker as options fall underwater, often leading to pressures to reprice options or restore pay‐to‐performance sensitivity in other ways. Building a detailed data set on executives' portfolios of stock and options, we find that the responsiveness of pay‐to‐performance sensitivities (created by all executive holdings of stock and options) to changes in stock price is large. The elasticity of pay‐to‐performance sensitivities with respect to stock price decreases is about 0.7 and is larger for high‐option executives and for executives with high percentages of options already underwater. The dominant mechanism through which companies offset declines in option pay‐to‐performance sensitivities is larger option grants following stock price declines; on average, these larger grants restore approximately 40% of the stock‐price‐induced pay‐to‐performance sensitivity declines. Option repricings are inconsequential in this regard, despite the attention they have attracted. In looking at positive returns, we find the reverse: higher returns both directly increase pay‐to‐performance sensitivities and lead to larger option grants, which raise pay‐to‐performance sensitivities further. Thus, option grants to executives tend to be largest following large stock price increases or large stock price decreases.     

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.     

Information-based stock trading and managerial incentives: evidence from China's stock market

This paper uses stock price informativeness, or information-based stock trading, to help explain the pay–performance sensitivity (PPS) of chief executive officer (CEO) compensation in China's listed firms. We argue that higher stock price informativeness, which we measure by the probability of informed trading, helps and encourages shareholders to incentivize the top management team based on stock market performance. The regression results support our argument and show that a higher level of stock price informativeness is associated with higher CEO PPSs. Moreover, the impact of stock price informativeness on CEO incentives is stronger for privately controlled listed firms than it is for state-controlled listed firms. The results also hold when information asymmetry is approximated by the accuracy and dispersion of the earnings forecasts made by financial analysts.     

The Effect of Executive Stock Option Plans on Stockholders and Bondholders

Executive stock option plans have asymmetric payoffs that could induce managers to take on more risk. Evidence from traded call options and stock return data supports this notion. Implicit share price variance, computed from the Black-Scholes option pricing model, and stock return variance increase after the approval of an executive stock option plan. The event is accompanied by a significant positive stock and a negative bond market reaction. This evidence is consistent with the notion that executive stock options may induce a wealth transfer from bondholders to stockholders.     

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.     

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.     

Do executive stock option grants have value implications for firm performance?

Consistent with predictions of agency theory, we find direct evidence that executive stock option grants have value implications for firm performance. This inference is drawn from evaluation of various motivations for the use of such grants in executive compensation: value enhancement, risk taking, tax benefit, signaling and cash conservation. We find consistent evidence for the value enhancement motivation to reduce agency costs. As well, they signal for positive price sensitive information. Our results reject the tax benefit and cash conservation motivations. This finding is robust after controlling for the endogenous character of executive stock option grants and other equity-based grants. JEL Classification G32 • J33 • M52     

Estimating the Value of Employee Stock Option Portfolios and Their Sensitivities to Price and Volatility

The costs associated with compiling data on employee stock option portfolios is a substantial obstacle in investigating the impact of stock options on managerial incentives, accounting choice, financing decisions, and the valuation of equity. We present an accurate method of estimating option portfolio value and the sensitivities of option portfolio value to stock price and stock-return volatility that is easily implemented using data from only the current year's proxy statement or annual report. This method can be applied to either executive stock option portfolios or to firm-wide option plans. In broad samples of actual and simulated CEO option portfolios, we show that these proxies capture more than 99% of the variation in option portfolio value and sensitivities. Sensitivity analysis indicates that the degree of bias in these proxies varies with option portfolio characteristics, and is most severe in samples of CEOs with a large proportion of out-of-the-money options. However, the proxies' explanatory power remains above 95% in all subsamples.     

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.     

Option pricing model with sentiment

In this paper, we develop a closed-form option pricing model with the stock sentiment and option sentiment. First, the model shows that the price of call option is amplified by bullish stock sentiment, and is reduced by stock bearish sentiment, and the price of put option is in the opposite situation. Second, the price of call option is more sensitive to bullish stock sentiment; the price of put option is more sensitive to bearish stock sentiment. Third, the price of call option increases substantially with respect to the stock sentiment and the option sentiment. The price of put option decreases substantially with respect to the stock sentiment, increases substantially with respect to the option sentiment. Fourth, our models also reveal that the option volatility smile is steeper (flatter) when the stock sentiment becomes more bearish (bullish). Finally, stock sentiment and option sentiment lead to the option price deviating from the rational price. The model could offer a partial explanation of some option anomalies: option price bubbles and option volatility smile.     

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.     

Executive incentives and payout policy: Empirical evidence from Europe

We investigate how corporate payout policy is influenced by executive incentives, i.e. stock and option holdings, stock option deltas and stock-based pay-performance sensitivity for 1,650 publicly listed firms from the UK, Germany, France, Italy, the Netherlands and Spain, over the period from 2002 to 2009. Our results show that executive stock option holdings and stock option deltas are associated with lower dividend payments in our sample of European countries, where we do not observe any presence of dividend protection for executive stock options. We find that this relationship is mainly driven by exercisable stock options and by options that are in the money. Additionally, we observe that executive stock option holdings and stock option deltas have a negative impact on total payout, suggesting that executives do not substitute share repurchases for dividends. Furthermore, the fraction of share repurchases in total payout increases as executive stock option holdings and stock option deltas increase. Finally, our results show that executive share ownership and stock-based pay-performance sensitivity may mitigate agency conflicts by significantly increasing the level of total payout.     

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.     

Is there price discovery in equity options?

We use tick-by-tick quote data for 39 liquid US stocks and options on them, and we focus on events when the two markets disagree about the stock price in the sense that the option-implied stock price obtained from the put-call parity relation is inconsistent with the actual stock price. Option market quotes adjust to eliminate the disagreement, while the stock market quotes behave normally, as if there were no disagreement. The disagreement events are typically precipitated by stock price movements and display signed option volume in the direction that tends to eliminate the disagreements. These results show that option price quotes do not contain economically significant information about future stock prices beyond what is already reflected in current stock prices, i.e., no economically significant price discovery occurs in the option market. We also find no option market price discovery using a much larger sample of disagreement events based on a weaker definition of a disagreement, which verifies that the findings for the primary sample are not due to unusual or unrepresentative market behavior during the put-call parity violations.     

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.     

A generalization of reset options pricing formulae with stochastic interest rates

A generalization of reset call options with predetermined dates is derived in the case of time-dependent volatility and time-dependent interest rate by applying martingale method and change of nume?aire or change of probability measure. An analytical pricing formula for the reset call option is also obtained when the interest rate follows an extended Vasicek’s model. Numerical results show that the correlated coefficient between the stock price and interest rate is almost unacted on the price of reset call option with short maturity and Monte Carlo method is inefficient. Monte Carlo method should be only used if there is no closed-formed solution for option pricing.     

Market pricing of executive stock options and implied risk preferences

When managers get to trade in options received as compensation, their trading prices reveal several aspects of subjective option pricing and risk preferences. Two subjective pricing models are fitted to show that executive stock option prices incorporate a subjective discount. It depends positively on implied volatility and negatively on option moneyness. Further, risk preferences are estimated using the semiparametric model of Aït-Sahalia and Lo (2000). The results suggest that relative risk aversion is just above 1 for a certain stock price range. This level of risk aversion is low but reasonable, and it may be explained by the typical manager being wealthy and having low marginal utility. Related to risk aversion, it is found that marginal rate of substitution increases considerably in states with low stock prices.