Employee Stock Option Valuation
The Hull-White model for Employee Stock Option (ESO) Valuation model uses a binomial or trinomial lattice as recommended by FASB 123R.
Lattice models are based on the same underlying option pricing theory as the Black-Scholes model. But they extend Black-Scholes by taking into account the impact of events -- such as early exercise of options by employees, or employee exit rates after vesting -- which occur during the term of the option.
This contrasts with the Black-Scholes model which values an option based on the expected pay-off at only one point in time: the option's expiry. Black-Scholes cannot therefore take these time-dependent factors, which are an essential part of ESOs, into account.
The Hull-White model is an enhancement of the basic lattice model. The major advantage it has over the the basic model is the way it handles the early exercise behaviour of employees. It does this by defining the conditions under which employees are expected to exercise their options after vesting in terms of the stock price reaching a specified multiple of the exercise price. The exercise multiple is a statistic readily available in most companies and Hull and White have argued that it provides a much sounder theoretical and practical basis for ESO valuation than trying to estimate the expected life (ie time until exercise) of an option.
Another significant advantage of the Hull-white model is that it explicitly recognizes the valuation impact of employees leaving the company following the vesting period by estimating whether their options are likely to be exercised or forfeited.
The Hull-White model is very widely used. In fact it has become a de facto standard for IFRS 2 and FASB 123R compliant ESO valuation due to it's strong theoretical basis and the ease of estimating the various inputs required. The Hoadley Finance Add-in for Excel implements the Hull-White model in the ESO2 function, and builds on this model for the ESO3, ESO4, ESO5, ESOIndexed, and ESOForwardStart functions.
For more information on the Hull-White model please refer to these original papers available for download: