TY - JOUR
T1 - A Matrix-Based Lattice Model to Value Employee Stock Options
JF - The Journal of Derivatives
SP - 9
LP - 26
DO - 10.3905/jod.2006.650161
VL - 14
IS - 1
AU - Bajaj, Mukesh
AU - Mazumdar, Sumon C.
AU - Surana, Rahul
AU - Unni, Sanjay
Y1 - 2006/08/31
UR - http://jod.pm-research.com/content/14/1/9.abstract
N2 - New accounting standards require U.S. companies that give out employee stock options (ESOs) to expense them at fair values as of the grant date. But valuing ESOs is a difficult problem, due to a variety of factors including long vesting periods, nontradability, and „suboptimal” exercise by the holders. In this article, Bajaj, et al develop a valuation algorithm based on combining a binomial lattice with a model for early exercise probabilities. The approach is supported by an empirical analysis of historical exercise behavior for two ESO-granting firms. A dataset covering millions of options awarded over more than 15 years is used to calibrate the early exercise probability matrix. This yields some interesting results, both expected (e.g., early exercise increases with option moneyness) and unexpected (e.g., the effect of time to expiration on exercise probability is clearly nonlinear). The analysis shows that the features of ESOs not taken into account when using the Black–Scholes model for valuation can be quite large–more than 50% of the BS value for one of the companies.
ER -