Magazine article The CPA Journal

Valuing Employee Stock Options Using a Lattice Model

Magazine article The CPA Journal

Valuing Employee Stock Options Using a Lattice Model

Article excerpt

A recent FASB exposure draft on stock-option expensing would require the valuation of equity-based compensation awards at their grant date. Option value and the resulting expense are based upon models that capture the characteristics determining the value of a particular grant of employee options. The exposure draft discusses lattice valuation models that accommodate the often complex attributes of option plans that can change over time. The lattice model can explicitly capture expected changes in dividends and stock volatility over the expected life of the options, in contrast to the Black-Scholes option-pricing model, which uses weighted average assumptions about option characteristics. The authors' objective is to provide an overview of how lattice models work and to provide insights into how lattice models can help ascertain the costs and benefits of various option-granting strategies.


A lattice structure, such as the binomial model, incorporates assumptions about employee exercise behavior over the life of each option grant and changes in expected stock-price volatility. This results in more-accurate option values and compensation expense.

Employee stock options have distinct characteristics. For example, it is typical for a large percentage of employees to exercise their options upon vesting. Other employees hold their options and exercise based upon their assessment of the expected future movement of the stock price. Lattice models provide a framework to capture the impact of these varying exercise patterns into the calculation of the value of the option. This impact can be material.

Another advantage of the lattice structure is the ability to incorporate expected changes in volatility over the life of the option. This is particularly important to young companies that, while currently recording highly volatile returns, expect decreased volatility in the future. The lattice model allows for more precise assumptions, therefore allowing more precise estimates of option values. The lattice model uses data collected about employee exercise behavior and stock-price volatility to project an appropriate array of future exercise behaviors. This in turn allows more-accurate estimates of option values. In comparison to the Black-Scholes model, the lattice structure allows the incorporation of various early-exercise assumptions, once substantiated by an analysis of employee behavior patterns, which results in more-accurate, and often lower, option values and lower expenses.

The Logic of Lattice Models

Lattice-based option-pricing models, such as the binomial model, use estimates of expected stock-price movements over time. The expected magnitude and likelihood of stock-price movement is predicated upon the expected volatility of a security's returns. Exhibit 1 illustrates a simple two-year lattice model that depicts the expected price changes of the security, along with their probability of occurrence. Each node of the lattice reflects an expected year-end share price. These expectations are developed through analysis of the security's historical volatility and its likely future volatility.


Volatility refers to the fluctuations in share returns over time. Volatility is measured by calculating the expected standard deviation of the returns of a security. The expected future volatility then determines expected share price movements over time. In turn, these potential share price movements are a major factor in estimating option value. Exhibit 1 illustrates how the estimated standard deviation results in share price movements over time.

The most common method of estimating future volatility is to use historical volatility as a proxy. There are no hard-and-fast guidelines on how far back one should calculate historical volatility. Future volatility can also be estimated by solving for the implied volatility of a company's traded options. Interpreting implied option volatility requires caution, as option volatility is impacted by the interaction of:

* The option's expected time to expiration,

* Whether the option is trading at-the-money, and

* General economic conditions. …

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