earticle

영어

Employee stock options have been the representative compensation system since they were adopted in 1997 in Korea with the change into the performance culture. Recently fair valuation of employee stock options(ESOs) has become a significant issue not only because they can measure their incentive effects but also because the Accounting Standards require ESOs value to be expensed for documenting financial statements. ESOs, which are inalienable and forfeitable, exhibit different exercise patterns from standard options. Prior researches related with empirical exercise patterns of ESOs exhibit that ESOs are prematurely exercised soon after the vesting period is over and the early exercise patterns are influenced particularly by risk aversion(Huddart and Lang, 1996; Carpenter, 1998; Bettis et al., 2005; Boyd et al., 2007). Kim and Jung (2009) analyzed the Korean ESOs and showed that stock options are exercised approximately 3.15 years after being granted, and these early exercise patterns were found to be influenced by risk aversion, profitability through exercise and firm characteristics. There are ESO valuation models reflecting these ESOs features such as extended American option model(Carpenter, 1998) and Utility-maximization model(Huddart, 1994; Kulatilaka and Marcus, 1994). The one adjusted the simple American option model by adding an exogenous parameter, ‘stopping state’, in which the employees or executives automatically exercise or forfeit the option. The other adopted the employee’s utility function of CRRA(constant relative risk aversion). Employees exercise their stock options when their expected utility, influenced by their risk aversion and outside wealth as well as stopping state, is maximized. But, generally, accounting practitioner estimate the fair valuation of ESOs using just either the modified Black-Scholes model, which adjusts the option’s life to the expected life and subtracts the cancelation, or typical American option model, which can be exercised prior to maturity. The aim of this study is both to look for an ESO valuation model that can best predict the actual exercise pattern. Furthermore, we are to review whether the expected life of ESOs that are currently posted on the financial statements fits the actual exercise pattern. This analysis helps us know if accounting practitioner estimate the expected life of ESOs appropriately considering the ESOs’ features and the correlation between stock price and the timing of exercise. The process of analysis is like followings; First, we have to calibrate some unobserved parameters; stopping state in extended American option model and risk aversion, outside wealth, and stopping state in utility-maximization model according to the method of Carpenter (1998) and Bettis et al. (2005). To do this, we set the mean exercise pattern of sample the base exercise pattern, searching the best unobserved parameters showing the closest to the base exercise pattern through the grid-search method. Second, we calculate the expected exercise pattern of each firm using calibrated parameters(stopping state, risk aversion, outside wealth) and observed parameters of its own; volatility, dividend rate, vesting date, risk-free rate, expected return. Third, we evaluate which option model forecasts most accurately among models; modified Black-Scholes model, American option model, extended American option model, Utility-maximization model. Also we analyze whether the expected life of ESOs that is currently posted on the financial statements forecast properly by comparing the forecast error such as the mean error, the percentage error, the mean absolute error, and the square root of the mean squared percentage error, and by the regressions of the actual exercise variable on the model forecast. We analyzed a total of 159 exercised employee stock options for the years between 2000 and 2008. We limited the sample to ones that we can obtain the characteristics of stock option grant and exercise and the firm specifies the estimates of the characteristics of ESOs on the footnote of financial statement such as expected life of their own. The results are like followings; First, the analysis of 159 stock options in this study indicates that among many theoretical ESO models, the extended American option model appears to be the best valuation model in predicting the expected stock-to-strike ratio and the expected life of ESOs. This result is encouraging and practicable because extend American option model doesn’t assume the risk aversion which is very difficult to observe and presume. So, we can estimate the fair valuation of ESOs without using the elaborate model such as utility-maximization model. Second, the officially posted estimate on the financial statements, on the other hand, didn’t have as good a predictability as the model, and the correlation with the actual exercise period was not even close to the statistics. Consequently, proper measures should be taken in order to estimate the expected life based on the ESOs features such as early exercise and forfeiture rate in the process of fair valuation of ESOs for documenting financial statements.

한국어

임직원 스톡옵션의 공정가치평가는 재무제표작성시 스톡옵션의 공정가치를 비용화하도록 한 기업회계기준에 의해 중요한 사안이 되었다. 임직원 스톡옵션은 개인의 위험회피도와 실권에 의해 조기행사패턴을 보이는 점에서 일반적인 옵션과 다르며, 이러한 점이 공정가치평가시 반영되어야 한다. 이러한 스톡옵션의 특성을 반영한 대표적인 가치평가모형으로 효용극대화모형(Utility-Maximazation Model; Huddart, 1994)과 확장된 미국형 옵션모형(Extended American Option Model; Carpenter, 1998)이 있다. 본 논문은 이 두 모형을 중심으로 스톡옵션의 실제존속기간을 가장 잘 예측할 수 있는 임직원 스톡옵션의 평가모형은 무엇인지, 그리고 재무제표주석에 공시되는 추정존속기간이 스톡옵션의 특성을 잘 반영하여 산정되었는지 살펴보고자 하였다. 분석 결과, 임직원 스톡옵션에 대한 이론적인 모형 중 확장된 미국형 옵션모형이 다른 어떤 모형보다 더, 또한 재무제표에 제시된 실무자들의 추정치보다 더 기대주가비율과 기대존속기간에 대한 예측력 측면에서 가장 타당한 모형이라고 판단되었다