Using Lattice Models to Value Employee Stock Options under SFAS 123(R)
Folami, Lookman Buky, Arora, Tarun, Alli, Kasim L., The CPA Journal
SFAS 123(R) requires that employee stock options (ESO) be measured at fair value. While either the BlackScholes or the lattice option-pricing model is acceptable under the standard, the lattice model is better suited to the unique characteristics of ESOs.
The use of a lattice model has broad implications. Auditors and corporate executives must understand the variables that are used to calculate the fair value of ESOs. They must also understand how changes in the required variables drive ESOs' fair value and the resulting effect on total compensation expense. Finally, the additional record-keeping responsbilities created by implementing SFAS 123(R) require significant changes on the part of corporate finance executives for modeling resources, data requirements, and record-keeping capabilities. If the existing information systems of a company cannot provide the information necessary to value ESOs, some modifications to the information system may be necessary to meet the requirements for applying the lattice model. Implementing the lattice model within the SFAS 123(R) framework presents certain practical implications that are discussed by way of an example, below.
Description of Lattice Models
Lattice models are option-pricing models that involve constructing a binomial tree representing different paths that might be followed by the underlying asset during the life of the option. In the case of ESOs, the underlying asset is the company stock. The fair value of the option is then derived by backward induction through the binomial tree.
The lattice model of stock valuation divides time into discrete bits and models prices at these points in time. The period of time covered by the lattice is broken down into individual time periods (month, quarter, or annual) and the model predicts possible stock prices at the end of each time period. In the lattice model, stock prices will move either up or down at the end of each period. A probability of occurrence is assigned to each possible up or down position. As shown in Exhibit 1, in a short period of time a stock price can either rise by the up-move factor (u), or decline by the down-move factor (d).
In Exhibit 1, S^sub 0^ represents the initial stock price at time zero (i.e., the grant date). S^sub u^ is the stock price in the next time segment, assuming the price rose by the up-move factor of u. S^sub d^ is the stock price in the next time segment, assuming the stock price fell by the down-move factor d. By generalizing a one-period binomial tree one can construct a multi-period stock-price tree. Each node represents a probable stock price in that time period. Therefore, the more we divide total time into smaller pieces over the life of the option, the bigger the lattice gets (as more possible stock prices are modeled), and the more accurate the model can be. This is depicted in Exhibit 2.
By following the logic depicted in Exhibit 2, one can build a stock-price tree for the option's contractual life. The next step is to estimate the fair value of an ESO. To do this, one builds another tree, starting with the option payoff at the terminal nodes in the future, when the option matures, and discounting the option back to the present time.
Implementation of Valuation Procedures
The actual implementation of the valuation procedure for ESOs within a lattice model entails three steps:
* Determining the input variables and assumptions for the model;
* Using the lattice model to value the option; and
* Recording the valuation.
The assumptions used in the model should reflect external and internal information that is available on the grant date. These assumptions must be reasonable and supportable, and must not represent the biases of a particular party. Applying the lattice model requires inputs for the minimum set of substantive characteristics specified in SFAS 123(R). The interplay of these inputs is illustrated using the case study described below. …