Lattice Model vs. Black-Scholes Model

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Apr25

Lattice Model vs. Black-Scholes Model

Linda Chan

Know More: Benefits 2.0, Benefits

Most companies in the United States have used the Black-Scholes model to measure the value of employee stock options. Black-Scholes does not allow for modifications that reflect the specific characteristics of the security being valued, such as illiquidity, exercise probability, and vesting period. Black-Scholes measures employee exercise behavior by using the expected rather the contractual term of the option detailed in a company’s stock option plan. The lattice model is a binominal model that analyzes the fair value of stock options at the grant date by estimating the prices of the underlying stock at points in time up to and including the option’s expiration date. There are two possible outcomes over a single period over time. One outcome is that the underlying security will increase. The other outcome is that the security will decrease. Each outcome is probability weighted, and the option value is based on the security value at the end of the period. The lattice model reduces the value of a pool of options which may be overstated by Black-Scholes because it takes into account employee turnovers and early exercises. However, reasons for early exercise behavior may not be reliable since they involve personal drivers such as divorce, college tuition, investment decisions, and real estate purchase.

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