A Matrix-Based Lattice Model to Value Employee Stock Options

40 Pages Posted: 22 Jan 2006

See all articles by Mukesh Bajaj

Mukesh Bajaj

LECG, LLC; University of California, Berkeley - Haas School of Business

Sumon C. Mazumdar

Law and Economics Consulting Group (LECG), LLC; University of California, Berkeley - Haas School of Business

Rahul Surana

Law and Economics Consulting Group (LECG), Inc.

Sanjay C. Unni

LECG, LLC; University of California, Berkeley - Haas School of Business

Date Written: March 27, 2006

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

Suggested Citation

Bajaj, Mukesh and Mazumdar, Sumon C. and Surana, Rahul and Unni, Sanjay C., A Matrix-Based Lattice Model to Value Employee Stock Options (March 27, 2006). Available at SSRN: https://ssrn.com/abstract=877472 or http://dx.doi.org/10.2139/ssrn.877472

Mukesh Bajaj

LECG, LLC ( email )

2000 Powell Street, Suite 600
Emeryville, CA 94608
United States
510-450-6736 (Phone)

University of California, Berkeley - Haas School of Business

545 Student Services Building, #1900
2220 Piedmont Avenue
Berkeley, CA 94720
United States

Sumon C. Mazumdar

Law and Economics Consulting Group (LECG), LLC ( email )

2000 Powell Street, Suite 600
Emeryville, CA 94608
United States
510-450-5493 (Phone)

University of California, Berkeley - Haas School of Business

Finance Department
Berkeley, CA 94720
United States

Rahul Surana (Contact Author)

Law and Economics Consulting Group (LECG), Inc. ( email )

Suite 600
2000 Powell Street
Emeryville, CA 94608
United States

Sanjay C. Unni

LECG, LLC ( email )

2000 Powell Street, Suite 600
Emeryville, CA 94608
United States

University of California, Berkeley - Haas School of Business

545 Student Services Building, #1900
2220 Piedmont Avenue
Berkeley, CA 94720
United States

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