• Employees are often faced with the task of valuing their

employee stock options:

a) Prior to accepting employment, when incentive

packages are offered,

b) During employment when bonuses and incentives 

are offered, 

c) In the event of a divorce or for estate planning

purposes, or

d) When an evaluation for risk and investment

management purposes is needed.

Employers also want to know the value of what they

are offering the employees. In addition, employers now 

have to expense the fair value of options for earnings

purposes and need an accurate value to determine

the impact. They need accurate values to comply

with FASB mandates.   

The question then becomes “What methods should

employees and employers use to accurately value

these employee options." And then there is the question

of whether the perceived value to the employee is

equal to the cost to the employer.

One way is to use the Black Scholes or other theoretical

valuation models. These are mathematical models,

which give theoretical prices for a particular exchange

traded option. These models incorporate such variables

as the stock price, the exercise price, the expiration

date of the option, the expected volatility, expected

dividends, and the interest rate. The models assume that

stock prices are lognormally distributed.

The Black Scholes model was created in 1973 by

Myron Scholes, Fischer Black and Bill Merton. It was

first used in the real world on the CBOE and the

Pacific Stock Exchange in 1975 and 1976 by market makers

trading listed stock options. Your writer is one of those

market makers.

In some small circles of traders and academics, it is well

known that the Black Scholes and other models are faulty

in the valuation of listed long term options as well as

employee options especially on highly volatile stocks.

Some models also seem to have problems with stock 

paying high dividends.

If we do decide to use the Black Scholes model or any

model, we must then approach these models with the

understanding that these are just useful tools and not

precise instruments. Traders, who understand the models’

inaccuracies, actually trade the options at prices that are

different from the theoretical values, especially long term

options on highly volatile stocks.
                                                      
Can these models be used to accurately value the employee

stock options? If so what adjustments have to be made

in doing so?

If the employee was certain to remain with his employer until

expiration of the options and was certain not to prematurely

exercise his options, there would be little need to make any

adjustments in assumptions when valuing employee stock

options compared to the assumptions in valuing listed stock

options. Although his inability to liquidate the options until

expiration certainly would cause a perceived discount in value.

Some claim the fact that employee stock options are not

transferable is a significant factor to be considered . My view

is that that idea is in error because of the availability of listed

option hedging, allowing effective transferability. The

non - transferable consideration is indeed a greater

consideration when employees are prohibited from hedging

with listed options. When employers prohibit hedging, the

perceived value to the employee is indeed diminished. 

However, creative employees can find ways to hedge.

For example they can write calls on positively correlated

stocks in lieu of sellings calls on the employer stock.

FASB Mehtod

The FASB recommended evaluation method is to reduce

the nominal time to expiration to the "expected" time to

expiration. Does this not fully discount the value to the

employee when hedging is restricted? My view is that it

does but if the contract terms are extremely restrictive,

a further ajustment should be made in perceived value.

Employees do regularly terminate employment prior to

expiration with the resulting loss of options value and do

prematurely exercise their employee stock options with

substantial theoretical value forfeited. Therefore, there

must be some adjustments to certain of the assumptions

made in the pricing models when calculating the expected

costs to the employer and value to the employee.

By making these adjustments, essentially you have

adjusted the expected average cost to the employer.

That expected average cost to the employer may be more

or less than the value any particular employee may ascribe

to his options.

Better Method

We will now illustrate our valuation method for employee

stock options by using an example below:

1. Assume an employee is granted options to purchase

10,000 shares of stock in ABC company as part of a

compensation package. Those options expire ten

years after the grant day and are considered non-qualified.

2. Assume that the stock closes at $50 on grant day and

the options are exercisable at $50. Usually the exercise

price equals the market price at grant.

3. Assume the annual historical volatility (defined as the

standard deviation of returns) is .45. Assume the

“implied volatility” on the two year listed LEAP calls is .40. 

LEAP calls are merely long term listed call options.

4. Assume the stock pays no dividends.

5. Assume the risk free interest rate is 3.0 % for three

month  U.S. government bills and 4.3% for 10 year

U.S. government bonds.

6. Assume that the employee’s options contract has

standard provisions relating to vesting, penalties upon

early termination after vesting and the provision that the

options themselves are not transferable.

7. Assume that there are no contractual restrictions on the

employee hedging his stock options by writing listed call

options or selling stock futures or buying puts.

To calculate the employee stock options value, we can 

find an appropriate options calculator at www.cboe.com or

www.numa.com or www.hoadley.net and input the

appropriate adjusted assumptions.

Those appropriate adjusted assumptions follow:

1.Stock price $50 (no adjustment necessary).Options

 exercise price $50 (no adjustment necessary).

2.Volatility.  Historical volatility equals .45 but the

adjusted volatility equals .37. To get this new volatility,

we used the implied volatility of the longest LEAP (.40)

and reduce that by 5 % to 7 % to get the proper assumed

volatility for the just granted employee options (Why we

use implied only and reduce the implied volatility further

is beyond the scope of this article). If the stock, whose 

options are subject to valuation has no listed options or no

listed LEAP’s, one can find a similar stock (in terms of

industry and historical volatility) that does, and use that

“implied volatility”.

3.Time to expiration is reduced by 37% to incorporate

the expectations of early terminations and premature

exercises. This reduction could be more or less, depending

on the employees' expectations of longevity at the company

and their awareness of hedging strategies to avoid early

exercise. On grant day we can assume an expected expiration

time of 6.3 years (i.e.10 yrs reduced by 37%). After vesting,

the expiration day discount is reduced to 22% or less.  

4.No dividends (no adjustment necessary)

5.Assume an interest rate of 3.8% (reduced from 4.3%)

---------------------------------------------------------

So what would be the value of the employee stock options

at the time of grant using the above accurate method.

CBOE gives $216,525.00 and Numa gives $218,100.00,

which for our purpose are equal.

Had we not made the corrected assumptions on volatility

and time remaining and used the historical volatility of .45

and the full 10 years to expiration, the prices would have

been CBOE $309,582.00 and Numa $310,800.00.

So there is quite a difference in pre-adjusted

and post- adjusted values.

It also must be mentioned that employees consider there

to be additional value to these employee options due to

the fact that employees receive the options without having

to report the ESOs as income for tax purposes when

granted.

The amount of additional value that is ascribed to the options

because of this factor depends on the tax bracket of the

employee and is not meant to be calculated here.

In addition it should be mentioned that the cost to the

employer in granting employee options should be considered

less than the above adjusted calculations in view of the fact

that they pay out no cash. However, the amount of that

lower cost is quite difficult to calculate. So we will not try

to calculate that amount.

Finally, this method of calculating the options value is

consistent with FASB (Financing Accounting Standards Board)

Section 123. It merely gives a more accurate calculation of

volatility and time remaining than using “historical volatility”

and using the full term to expiration.

In summary, we have demonstrated a method to calculate the

value of employee stock options. If we were to consider the

specific aspects of a particular employee options contract

(for example a prohibition on hedging) and the specifics of

each individual’s attitudes and expectations of longevity at

the company, we would surely be able to get more precise

values. That however is not the purpose of this paper.

John Olagues    olagues@hotmail.com  

See

http://www.wiley.com/WileyCDA/WileyTitle/productCd-0470471921,descCd-google_preview.html

  http://www.brighttalk.com/dcemail_redirect/webcast/5847

http://www.brighttalk.com/webcasts/8004/attend The author, JOHN OLAGUES, is a former member of the Chicago Board Options Exchange and the Pacific Stock Exchange for over ten years. He offers a unique view of employee stock options from a trader’s standpoint rather than from the standpoint of an accountant, compensation planner or academic. To contact JOHN OLAGUES email olagues@hotmail.com and  see www.optionsforemployees.com.