A Matrix-Based Lattice Model to Value Employee Stock Options

Abstract

According to the Revised FAS Statement No. 123 issued on December 16, 2004, (FAS123R) the accounting treatment of employee stock options (ESOs) for U.S. companies will be radically different in the near future. Although, FAS 123R does not specify a particular valuation technique as preferable, it recognizes that "lattice" models may be better suited than "closed-form" models (such as variants of the Black-Scholes model) to accommodate various unique features of ESOs.

In light of such recent regulatory changes, our paper makes two contributions. First, we develop a reduced form lattice-based ESO valuation model that incorporates employees' expected early exercise rule through an estimated early exercise "matrix." This matrix provides the likelihood of early exercise of a vested and exercisable option at a particular node on the lattice, as a function of the ESO's remaining vested life and the option's in the moneyness at that particular node. Since our early exercise matrix is estimated from data on exercise decisions concerning past grants by the company's employees, it either directly or indirectly takes into consideration the various factors that could affect early exercise according to FAS123R.

Second, our paper provides a detailed methodology of the manner in which the early exercise matrix can be estimated and our reduced form model implemented, given sufficiently detailed data. To demonstrate the manner in which the early exercise matrix can be estimated and incorporated into the valuation model, we rely on a rich ESO dataset that has hitherto never been made public. The dataset contains the complete history of all ESOs awarded by two major technology companies (henceforth referred to as Companies A and B).

Keywords: FAS 123(R), Employee Stock Option Valuation, Lattice Binomial, Calibrated

JEL Classification: G13, M52, M41 , M44, J33