Value Of Employee Stock Options Research Articles

Mean–variance hedging of contingent claims with random maturity

AbstractWe study the mean–variance hedging of an American‐type contingent claim that is exercised at a random time in a Markovian setting. This problem is motivated by applications in the areas of employee stock option valuation, credit risk, or equity‐linked life insurance policies with an underlying risky asset value guarantee. Our analysis is based on dynamic programming and uses PDE techniques. In particular, we prove that the complete solution to the problem can be expressed in terms of the solution to a system of one quasi‐linear parabolic PDE and two linear parabolic PDEs. Using a suitable iterative scheme involving linear parabolic PDEs and Schauder's interior estimates for parabolic PDEs, we show that each of these PDEs has a classical C1, 2 solution. Using these results, we express the claim's mean–variance hedging value that we derive as its expected discounted payoff with respect to an equivalent martingale measure that does not coincide with the minimal martingale measure, which, in the context that we consider, identifies with the minimum entropy martingale measure as well as the variance‐optimal martingale measure. Furthermore, we present a numerical study that illustrates aspects of our theoretical results.

Will I Get Paid? Employee Stock Options and Mergers and Acquisitions

AbstractWe analyze how employee compensation contracts of target firms affect merger terms and outcomes. Using unique data from merger agreements, we document that in 80.0% of all merger and acquisition (M&A) deals, at least some of the target’s employee stock options (ESOs) are canceled by the acquirer and not replaced by new equity-based grants. Contract modifications reduce the value of ESOs by 38.4% in the average M&A deal. Further, the combined merger returns are larger when employees experience greater losses. Overall, our results indicate that the benefits of reducing the number of ESOs outweigh the potential negative effects on firm value.

Use of independent valuation specialists in valuing employee stock options: evidence from IPOs

We investigate the impact of independent valuation specialists on the downward bias of pre-initial public offering employee stock option valuations. Undervalued stock price estimates underlying firms’ option grants produce option valuations that overstate earnings and provide employees with deep in the money options. We find independent stock price valuations are more likely for firms with a Big Four auditor and an audit committee accounting expert. Furthermore, valuations prepared by independent valuation specialists are less downward biased than those prepared internally. Cross-sectional results suggest the following. First, independent valuations have a stronger effect on reducing downward bias when the board is more independent, suggesting independent boards facilitate independent valuations. Second, independent valuations have a weaker effect on reducing downward bias when an accounting expert sits on the audit committee and when CEO equity ownership is greater, suggesting these factors offset the need for an independent valuation to reduce downward valuation bias.

A TOP-DOWN APPROACH FOR THE MULTIPLE EXERCISES AND VALUATION OF EMPLOYEE STOCK OPTIONS

We propose a new framework to value employee stock options (ESOs) that capture multiple exercises of different quantities over time. We also model the ESO holder’s job termination risk and incorporate its impact on the payoffs of both vested and unvested ESOs. Numerical methods based on Fourier transform and finite differences are developed and implemented to solve the associated systems of PDEs. In addition, we introduce a new valuation method based on maturity randomization that yields analytic formulae for vested and unvested ESO costs. We examine the cost impact of job termination risk, exercise intensity and various contractual features.

Use of Independent Valuation Specialists in Valuing Employee Stock Options: Evidence from IPOs

We investigate the impact of independent valuation specialists on the downward bias of pre-initial public offering employee stock option valuations. Undervalued stock price estimates underlying firms’ option grants produce option valuations that overstate earnings and provide employees with deep in the money options. We find independent stock price valuations are more likely for firms with a Big Four auditor and an audit committee accounting expert. Furthermore, valuations prepared by independent valuation specialists are less downward biased than those prepared internally. Cross-sectional results suggest the following. First, independent valuations have a stronger effect on reducing downward bias when the board is more independent, suggesting independent boards facilitate independent valuations. Second, independent valuations have a weaker effect on reducing downward bias when an accounting expert sits on the audit committee and when CEO equity ownership is greater, suggesting these factors offset the need for an independent valuation to reduce downward valuation bias.

An improved of Hull–White model for valuing Employee Stock Options (ESOs)

Employee stock options (ESOs) are call options granted by a company to its employees as a means to retain and to motivate them for working towards improvement of the company’s earning and management. ESOs have unique characteristics, such as: they have long maturity time, they are not tradable, and they can be exercised only after the vesting period. All these characteristics have significant implication on the valuation of ESOs. In this paper, we improve Hull–White ESO model using Bino-Trinomial tree method. We also modify a single psychological barrier on Hull–White model with moving psychological barriers based on empirical study that the ESO’s holders require the stock price to be at relatively high to induce voluntary exercise, yet later they will exercise at relatively low stock price near the time to maturity. Numerical experiments are given to verify the robustness of the proposed model and to analyze the sensitivity with respect to the model parameters. The ESO prices become cheaper if the holders degrade their psychological barriers.

A Top-Down Approach for the Multiple Exercises and Valuation of Employee Stock Options

We propose a new framework to value employee stock options (ESOs) that captures multiple exercises of different quantities over time. We also model the ESO holder's job termination risk and incorporate its impact on the payoffs of both vested and unvested ESOs. Numerical methods based on Fourier transform and finite differences are developed and implemented to solve the associated systems of PDEs. In addition, we introduce a new valuation method based on maturity randomization that yields analytic formulae for vested and unvested ESO costs. We examine the cost impact of job termination risk, exercise intensity, and various contractual features.

Accounting for Employee Stock Options: Accelerating Convergence

Hull and White (2004) have developed a lattice pricing model that makes explicit reference to parameters that are not available in Black Scholes (1973) yet are important for the valuation of Employee Stock Options (ESOs). Cvitanic, Wiener and Zapatero (2008) point out that a key weakness of the lattice approach, when applied to valuing ESOs, is the sluggish convergence not generally experienced in trees configured to estimate plain vanilla options. Cvitanic, Wiener and Zapatero (2008) propose a very useful closed form solution which may or may not be endorsed by a whole host of regulatory and professional bodies. In this paper, we propose a small refinement to Hull and White (2004), based on insights developed by Boyle and Lau (1994) which ensures faster convergence in lattice estimation when barriers occur. Our model provides estimates consistent with Cvitanic, Wiener and Zapatero (2008). The proposed model should also neatly fit into the rubric currently prescribed by the American Financial Accounting Standards Board (FASB) and endorsed by the Securities and Exchange Commission (SEC). We also apply a number of truncation techniques to the lattice which removes the zero region of the tree. We truncate the ESO lattice above the early exercise boundary, peculiar to Hull White (2004), and dynamically specify the lattice array to spare memory and reduce estimation time.

American GARCH Employee Stock Option Valuation

We implement a new and flexible simulation based approach for the fair value of Employee Stock Option (ESO) plans to value American options in order to consider the common ESO characteristics of vesting period, departure risk and voluntary suboptimal early exercise. We introduce GARCH effects on the underlying asset and we analyze the price bias with respect to the constant volatility case. We also find a significant bias if we value the ESO using a short-memory GARCH model instead of a long-memory one. We also develop a sensitivity analysis with respect to changes in several ESO characteristics. We compare this valuation with FAS 123 method using the implicit expected life of the ESO revealing a FAS overvaluation. Finally, we value a real ESO plan providing the confidence intervals for the estimated ESO prices.

Valuing Employee Stock Options with Exogenous and Endogenous Early Exercise

This paper examines how forfeiture, vesting, and early exercise affect the value of employee stock options. The forfeiture and exogenous exercise of the options are modeled as two Poisson processes with constant intensity. Rational exercise by the employee due to the option's American feature is modeled as endogenous exercise. The Crank-Nicholson numerical method is used to solve for the resulting value of employee stock options. Results are consistent with the findings that the employee stock options are worth substantially less than the Black-Scholes formula value. The model demonstrates that the option holder would rationally exercise the option early even when the underlying stock pays no dividend. The model also provides results on the expected time to exercise of employee stock options and the expected exercise price relative to strike price. The method used in this paper is proposed as an alternative to the Black-Scholes formula for measuring fair market value of employee stock options for accounting and regulation purposes.

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 employee stock options using the exercise multiple approach and life tables

Employee stock options (ESOs) are common in performance-based employee remuneration. Financial reporting standards such as IFRS2 and AASB2 require public corporations to report on the cost of providing ESOs, and mandate the incorporation of voluntary and involuntary early exercise. In this paper we extend the exercise multiple approach of Hull and White (2004) and decompose the attrition unadjusted voluntary exercise ESO into a gap call option and two partial-time barrier options. We use exit probabilities obtained from empirically determined multiple decrement or life tables to model involuntary early exercise or forfeiture. We provide a new analytic valuation formula which expresses the ESO value in terms of a portfolio of exotic European bivariate power options and which correctly accounts for both voluntary exercise and employee attrition. Recent approaches seek to model employee attrition using a constant hazard rate. Our approach uses an empirically driven actuarial method for incorporating employee attrition in the valuation.

External competition and internal governance on stock options plans: Evidence from Taiwan

This study is to investigate the influences that external product market competition and internal corporate governance mechanisms have on managerial incentives. In this study, the values of employee stock options are used to measure managerial incentives. The findings show that excessively large boards, CEO duality, cross-holding, and a pyramidal structure achieve a positive correlation with managerial incentives. In addition, the presence of independent directors also increases the stock options values of managers. The independent directors possible overlook governance functions to increase managerial incentives, and they focus more on equity incentives. Furthermore, the relationship between product market competition and managerial incentives is nonlinear, which implies that in less competitive markets, an increase in competition stimulates firms to increase their managerial incentives. By contrast, in highly competitive markets, an increase in competition stimulates firms to decrease their managerial incentives.

ESO Valuation with Job Termination Risk and Jumps in Stock Price

Employee stock options (ESOs) are American-style call options that can be terminated early in the case of employment shock. This paper studies an ESO valuation framework that accounts for job termination risk and jumps in the company stock price. Under general Levy stock price dynamics, we show that a higher job termination risk induces the ESO holder to voluntarily accelerate exercise, which in turn reduces the cost to the company. The holder's optimal exercise boundary and ESO cost are determined by solving an inhomogeneous partial integro-differential variational inequality. We apply the Fourier transform to simplify the variational inequality and develop accurate numerical methods. Furthermore, when the stock price follows a geometric Brownian motion, we provide closed-form formulas for both the vested and unvested perpetual ESOs. Our model is also applied to evaluate the probabilities of understating ESO expenses and contract termination.

Credit‐Implied Equity Volatility—Long‐Term Forecasts and Alternative Fear Gauges

This study discusses how to compute and forecast long‐term stock return volatilities, typically with a five‐year horizon or longer, using credit derivatives, and how such volatilities can be used in different areas ranging from the valuation of employee stock options and other long‐term derivatives to the construction of market‐based fear gauges in selected countries or market segments. In the empirical part of the paper I focus on the European financial sector and find the credit‐implied volatilities and fear gauges to behave well. The forecasting accuracy of the credit‐implied volatilities is found to be better than that of horizon‐matched historical volatilities. © 2014 The Authors. Journal of Futures Markets Published by Wiley Periodicals, Inc. Jrl Fut Mark 35:753–775, 2015

The Effect of Using a Lattice Model to Estimate Reported Option Values

Statement of Financial Accounting Standards 123R suggests that lattice valuation models may improve the estimates of reported employee stock option values relative to the more commonly used Black–Scholes (BS) model. However, lattice model critics have expressed concerns that managers may use lattice models' flexibility to opportunistically understate option values. In this study, we investigate a sample of firms that recently adopted a lattice model to value employee stock options to provide evidence on this issue by identifying the determinants of lattice model adoption and examining the effect of lattice model use on reported option values. We report three main results. First, we find that firms are more likely to adopt a lattice model when it is more likely to produce lower values than the BS model and when managers have incentives to lower stock option expense. Second, we find that firms adopting a lattice model increase understatement of reported option values more than firms that continue to use the BS model and that the incremental understatement is due to use of the lattice model. Third, we conduct several tests to examine whether the valuation effect of lattice model use is consistent with efforts to correct for documented shortcomings in the BS model and find no evidence that this is the case. Taken together, the evidence in this study suggests that firms adopt and implement lattice models primarily to lower reported option values.

Employee Stock Option Valuation under Levy Models

Employee stock options (ESOs) are American-style call options that can be terminated early due to employment shock. This paper studies an ESO valuation framework that accounts for job termination risk and jumps in the company stock price. Under general Levy stock price dynamics, we show that a higher job termination risk induces the ESO holder to voluntarily accelerate exercise, which in turn reduces the cost to the company. The holder's optimal exercise boundary and ESO cost are determined by solving an inhomogeneous partial integro-differential variational inequality (PIDVI). We apply Fourier transform to simplify the variational inequality and develop accurate numerical methods. Furthermore, when the stock price follows a geometric Brownian motion, we provide closed-form formulas for both the vested and unvested perpetual ESOs. Our model is also applied to evaluate the probabilities of ESO cost exceedance and contract termination.

An Alternative Method Of Accounting For Stock Options

<p>Currently, the grant date fair value of employee stock options is expensed over the vesting period. Our study introduces a new valuation approach for stock options and examines the impact of this change on earning per share (EPS) for a sample of firms over the period 2002-2011. The new valuation approach provides data useful to the Financial Accounting Standards Board (FASB) as it determines whether to revise the current option accounting rules. Under the proposed approach, options are valued at their intrinsic value on the grant date (i.e., the opportunity cost or the economic promise associated with the difference between the exercise price of the option and the market price of the stock at each measurement date) and further revalued each reporting date until the options are exercised.</p>

Non-marketability and the value of employee stock options

We adapt the Benninga et al. (2005) framework to value employee stock options (ESOs). The model quantifies non-diversification effects, is computationally simple, and provides an endogenous explanation of ESO early-exercise. Using a proprietary dataset of ESO exercise events we measure the non-marketability ESO discount. We find that the ESO value on the grant date is approximately 45% of a similar plain vanilla Black–Scholes value. The model is aligned with empirical findings of ESOs, gives an exercise boundary of ESOs and can serve as an approximation to the fair value estimation of share-based employee and executive compensation. Using the model we give a numerical measure of non-diversification in an imperfect market.

Pricing Employee Stock Options under Stochastic Volatility

We employ a refined tree method to value employee stock options (ESOs) in the stochastic volatility model of Heston. Our setting covers risk-averse employees maximizing expected utility where we in particular focus on subjective option valuation, personal market beliefs and stochastic volatility. We formulate theoretical results on ESO valuation independently of a specific pricing model and utilize a recombining tree algorithm to value the American-style derivatives. We focus on the utility functions employed to numerically determine subjective option values and their impact on the valuation. We perform sensitivity analysis for various parameters, where we in particular examine the impact of the vesting period and an exercise constraint. We state market, objective and subjective ESO values and discuss their impact on possible contract designs.