Consideration of early exercise in the valuation of employee stock options

Employee options serve as an instrument for recruiting and retaining staff. According to IFRS 2, all employee options generally have to be recognised in the income statement and allocated over the vesting period. As part of this, an option valuation is necessary.

The expected term is a key input for the valuation, as employee stock options regularly have significantly longer potential terms than standard stock options. At the same time, the exercise behaviour of employees is sub­optimal. A call option should never be exercised early (except before dividend payments). However, empirical studies show that the majority of employees tend to exercise granted options early. One reason for this is the lack of marketability. As a result, employees can only realise cash inflows by exercising them. On the other hand, early exercise is encouraged by increased risk aversion, a lack of diversification and the risk that the options will expire due to termination or can no longer be exercised in the next exercise period. The integration of early exercise into the valuation of employee options leads to a discount in value due to the lower time value.

This article provides an overview of how early exercise can be taken into account in the valuation of employee options.

In principle, various models can be used to valuate options. The Black-Scholes model, the binomial model and the Monte Carlo simulation are explained below:

The model is often applied in practice because of its ease of use. This is a single-period model with a closed-form solution. However, the standard Black-Scholes model is only applicable to simple, less complex options. For example, it can only be used for the valuation of European options. These, in contrast to American options which can also be exercised during their term, may only be exercised at the end of their term. In addition, this model assumes constant volatility. Empirical studies show, however, that implied volatility depends on whether an option has an intrinsic value or on how far it is from it ("volatility smile"). Furthermore, volatility is often path-dependent. Lower volatility is observed in the case of rising prices, and higher volatility in the case of falling prices.

In contrast to the Black-Scholes model, the binomial model (also called Cox-Ross-Rubenstein model) can incorporate changes in the input parameters during the option term. This is an iterative procedure in which, in the first step, a decision tree (a binomial tree) is built to model out the development of the market value of the shares underlying the option based on volatility and the risk-free rate of interest. The time steps (decision nodes) may be freely chosen. In the second step, the option value is determined recursively and condensed into a discounted expected value on the basis of the intrinsic values at the individual decision nodes. In contrast to the Black-Scholes model, American options can also be valued or volatilities that change over time can be taken into account.

The general rule is: The more decision nodes between the commitment and exercise dates, the more meaning­ful the results. However, the workload involved in the modelling of each intermediate step also increases accordingly.

Monte Carlo simulation is a stochastic method based on a large number of random experiments. Monte Carlo simulations are particularly suitable for pricing options whose value depends on several uncertainty factors. The uncertainty factors are then mapped via stochastic processes or distributions. In the case of company or share values, for example, it is assumed that they follow a geometric Brownian motion. If different parameters are simulated at the same time (e.g. revenue and costs or share price and benchmark index), it is essential to consider possible correlations.

In practice, the consideration of early exercise in the valuation of employee options is largely dependent on the valuation model. 

While in the Black-Scholes model the expected time to maturity can be used instead of the contractual option term, in the binomial model and in the Monte Carlo simulation it is also possible to model the exercise depending on the path, e.g. depending on certain exercise levels and strategies. Empirical evidence suggests that the threshold for early exercise is between twice and three times the strike. When modeling, it should be noted that the vesting period defines the lower limit for the expected time to maturity, as exercise before vesting is not possible. However, modeling a path-dependent exercise behavior entails additional complexity.

When taking exercise behavior into account, it may also make sense to make divergent assumptions for different groups of employees. For example, empirical evidence shows that the time to exercise depends on the gender of the beneficiary and their position in the company. Women and employees in higher hierarchical levels generally hold their options for longer. In addition, share prices in the top 10% of recent years and upcoming dividends favor the exercise of options. In order to determine the expected maturity, evaluations of the exercise behavior (e.g. by hierarchy) should be carried out and the valuation individually adjusted to the underlying commitment if there is a sufficiently large history and number of employees.

Taking into account the early exercise possibility when valuing employee options makes economic sense and is in line with IFRS 2. Even if the calibration of the Black-Scholes model based on the expected time to maturity to take into account early exercise is considered justifiable, early exercise should preferably be modeled using the binomial model or the Monte Carlo simulation, as correlations between the exercise and the development of the share price and other factors can be taken into account explicitly. In conclusion, it can be stated that there is scope for discretion when integrating early exercise into the valuation, which has a direct impact on the expense to be recognized in the income statement because of the valuation.