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How to Value Employee Stock Options Using FINCAD® XL Version 9

FINCAD XL Version 9 now offers improved Employee Stock Option Modeling.

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Overview

Whereas Employee Stock Options (ESOs) have traditionally been used by companies to reward top levels of management, in recent years more and more companies have been issuing ESOs to a wider range of their employees. The National Bureau of Labor Statistics estimates that in March 2003, 8% or all workers in the US had access to stock options [1]. Especially in the high-technology start-up industry, most if not all employees now receive ESOs as part of an overall compensation package, but this is also the case in some larger, publically traded companies [2].

Moreover, expensing of ESOs will soon become mandatory for US public and non-public companies [3]. At the beginning of their first interim or annual reporting period after 15-Jun-2005 (for public companies) and after 15-Dec-2005 (for non-public companies), ESOs will have to be expensed; these laws will thus have effect as early as Sep-2005 for public firms. In Canada meanwhile, expensing of ESOs has been in effect since Jan-2004 [4], and internationally since Jan-2005 [5].

Broadly speaking, Employee Stock Options plans are used to compensate, retain and attract employees, and to link their interests to those of the company as a whole. They provide a way for companies to share ownership with their employees, to reward them for performance, and to keep the workforce motivated.

ESOs are contracts between a company and its employees that give the employees the right to buy a specific number of the company's shares at a fixed price within a certain period of time. The price is called the exercise or "grant" price and is usually the market price of the shares at the time the options are granted. As the share price of the company increases, employees stand to profit to a greater extent, through their ability to purchase the stock at the lower grant price, and then to sell the stock at the higher current market price.

ESOs can thus be viewed as simple call options, but with non-standard exercise provisions. Typically this involves the following features:

  • There is a "vesting period" of a few years during which the options cannot be exercised.
  • Employees who leave the company (voluntarily or not) during the vesting period forfeit their options.
  • After the vesting period, employees who leave the company (voluntarily or not) forfeit options which are out-of-the-money, and must exercise options which are in-the-money.
  • After the vesting period, employees can exercise the options at any time before the expiration date
  • At the expiration date, employees will exercise the options if they are in-the-money, otherwise they are worthless
  • Employees cannot sell their options. If they want to realise a cash benefit or diversify their portfolio, they must exercise the options and then sell the resulting stock.
  • When the options are exercised, the company issues new Treasury stock. This dilutive effect is typically very small, however, and can be offset in various ways [6].
  • Some ESOs have the additional feature that the options only come into existence if the share price reaches a certain predefined value. This "barrier" makes such ESOs similar to single barrier knock-in call options.

Because ESOs cannot be freely traded, employees tend to exercise the options early, and this must be taken into account during their valuation.

FINCAD Valuation

FINCAD allows the fair value and risk statistics of Employee Stock Options to be calculated through a generalisation of the Hull and White models [6]. The Basic Model values ESOs through the standard Black-Scholes equation, whereas the Enhanced Model uses a binomial tree. Both models are supported by functions in the FINCAD XL Version 8 and FINCAD Developer products, with additional features allowing for various time-varying parameters.

The FINCAD XL Version 9 product updates these functions by generalising the Hull and White Enhanced Model in two important ways:

  • A knock-in barrier can be specified, in which case the ESO only comes into existence if the underlying share price reaches the level of the barrier. The barrier can also be time-varying.
  • Time-varying future, or local, volatility of the underlying share price is allowed for. Companies might, for example, expect the volatility of their stock to increase during certain future periods of time.

Both features are incorporated into the binomial tree-based valuation method.

The Hull and White Basic Model [6] as discussed in Appendix B of FAS 123 [3] and implemented in FINCAD XL and FINCAD Developer is a three-step valuation procedure. The expected lifetime of the option must first be estimated, assuming the employee does not leave the company during the vesting period. This expected life is then used as the time to maturity in either the Black-Scholes model [7], or the Cox, Ross and Rubinstein binomial tree [8], to value the option. Finally, the value of the option is adjusted to allow for the possibility that the employee may leave the company during the vesting period.

Although this valuation technique is fairly simple, it suffers from at least two important drawbacks: the possibility of employees leaving the company after the vesting period is not explicitly considered; nor is the possibility that the employee may exercise the option early. Both possibilities are, however, considered in the Hull and White Enhanced Model. This accounts explicitly for the non-standard exercise strategy described above.

Firstly, options can be exercised only after the vesting period. Secondly, the possibility of employees leaving the company is captured by assuming an "employee exit rate", e, per unit time. Within any period of time t during the vesting period, a probability et exists that the option will be forfeited. The same probability exists that the option will cease to exist after the vesting period. If this happens, the option is forfeited if it is out-of-the-money, and exercised immediately if it is in-the-money.

Finally, the possibility of early exercise is captured through an "exercise multiple", M > 1. Options are then assumed to be exercised prior to maturity if they have vested, and if the stock price is at least M times the exercise price. Both the exit rate and the exercise multiple must be estimated from historical data. This heuristic exercise strategy is based upon observed employee behaviour; it is not necessarily the optimal financial strategy.

FINCAD uses a Cox, Ross and Rubinstein binomial tree [8] to calculate the fair value and risk statistics of ESOs within this Enhanced Model. The relevant equations describing the backward induction through the tree are described in Hull and White [6], with the two important generalisations mentioned above: we allow for the existence of a knock-in barrier and a time-varying volatility.

As is well-known, valuing options with barriers on a binomial tree has systematic problems which leads to very slow convergence properties. Even for ESOs without a knock-in barrier, such issues exist due to the exercise multiple M: the quantity (M x strike price) is itself an effective barrier in the binomial tree. There are various ways to deal with this problem, and the FINCAD functions use the method described in [9], for both the barrier itself and the effective barrier (M x strike price). The convergence properties of the resulting valuation method are very good.

Example

Suppose today is 14-Feb-2005 and we have 200 Employee Stock Options that we wish to value. Specifically, the options are written on underlying stock with a price of $37, they vest in 3 years (14-Feb-2008) and expire in 10 years (14-Feb-2015). Suppose further that:

The exercise price for the first 4 years after the options vest is $40, and for the remaining 3 years of the lifetime of the options it is $45;

The options will only come into existence (knock-in) if the underlying share price reaches $55 during the next 7 years or, failing that, if it reaches $60 during the final 3 years of the lifetime of the options.

The volatility of the underlying stock is expected to increase in the future, such that the volatility for the next 6 years is 15%, the volatility for the following 2 years is 20% and the volatility for the remaining 2 years of the lifetime of the options is 25%;

We expect 1% of employees who are issued the ESOs to leave the company every year, both during and after the vesting period;

From an analysis of historical data, employees tend to exercise options with these parameters once the underlying share price reaches double the exercise price (once it reaches $80 in the first 4 years after vesting, or once it reaches $90 for the remaining 3 years);

The continuously compounded risk-free interest rate and dividend yield of the stock are both 5% per annum.

We will value the ESOs using the FINCAD generalisation of the Hull and White Enhanced Model, using a binomial tree with 200 time steps. This gives the fair value of each ESO as $3.76, resulting in a total liability to the company of $751.56.

Example using aaESO_HW_enhanced2_p in FINCAD XL Version 9:

[1] Bureau of Labor Statistics (2004), National Compensation Survey: Employee Benefits in Private Industry in the United States, March 2003, Summary 04-02. Available on the Internet at http://www.bls.gov/ncs/ebs/sp/ebsm0001.pdf

[2] National Center for Employee Ownership (2005), Employee Stock Options Fact Sheet. Retrieved September 30, 2005 from http://www.nceo.org/library/optionfact.html.

[3] Financial Accounting Standards Board (revised 2004). Statement of Accounting Standards 123, Accounting for Stock-Based Compensation.

[4] The Canadian Institute of Chartered Accountants (2004). Handbook, Section 3870.

[5] International Accounting Standards Board (2004). IFRS 2, Share-based Payment.

[6] Hull, J. C. and White, A. (2004), 'How to Value Employee Stock Options', Financial Analysts Journal, 60, 1 114-119; Hull, J. C. and White, A. (2004) 'Accounting for Employee Stock Options: A Practical Approach to Handling the Valuation Issues', Journal of Derivatives Accounting, 1, 1 3-9.

[7] Black, F. and Scholes, M. (1973) 'The Pricing of Options and Corporate Liabilities', Journal of Political Economy, 81, 3 637-659.

[8] Cox, J. C., Ross, S. A. and Rubinstein, M. (1979) 'Option Pricing: A Simplified Approach', Journal of Financial Economics, 7, 3 229-264.

[9] Derman, E., Kani, I., Ergener, D. and Bardhan, I. (1995) 'Enhanced Numerical Methods for Options with Barriers', Financial Analysts Journal, 51, 6, 65-74.

Disclaimer

Your use of the information in this article is at your own risk. The information in this article is provided on an "as is" basis and without any representation, obligation, or warranty from FINCAD of any kind, whether express or implied. We hope that such information will assist you, but it should not be used or relied upon as a substitute for your own independent research.

For more information or a customized demonstration of the software, contact a FINCAD Representative.