Chance of Employee Stock Options Being Worthless at Expiration .: Knowledge Base

The matrix below illustrates the probabilities of particular

employee stock options being worthless at expiration.

That is, if you believe the widely used pricing models,

including the Black Scholes model, to be accurate.

This matrix assumes that at the time of calculation the

stock price equals the options exercise price. The matrix

also assumes that the expected return is 7% annually.

If the stock prices are below the strike prices

(i.e. underwater) when the calculations are made,

then the probabilities of the employee stock options

being worthless at expiration day are of course greater.

Time to expiration	Expected Volatilities				Probabilities of Employee Options being worthless at expiration
	A	B	C	D	A	B	C	D
10 years	80	50	30	20 *	.83	.68	.31	.25
7 years	80	50	30	20 *	.78	.63	.36	.29
5 years	80	50	30	20 *	.73	.60	.40	.31
3 years	80	50	30	20 *	.70	.57	.44	.35
1 year	80	50	30	20 *	.62	.54	.47	.40

For example:

If the expected volatility is .50 with 3 years expected time to

expiration, the probability is approximately 57% that the

options will be worthless on expiration day because that is

the probability that the stock will be out of the money. If the

assumed volatility is .30 with one year to expiration, the

probability is approximately 47% that the options will be

worthless at expiration day.

As can be seen, the higher the volatility, the greater the

probability of the stock being below the strike price and

the options worthless at expiration.

If one believes that the probabilities are different, then

he does not believe the accuracy of the models. Your writer

happens to think that the probabilities are substantially

different and the market itself thinks the probabilities are

different (That's why there is such a phenomena as the

The Financial Accounting Standards Board and the SEC

believe that those probabilities are accurate, since they

accept the models as accurate.

The results do seem to make employees concerned about

the future value of their options as they should well be.

Those probabilities, although somewhat inaccurate,

should encourage employees and executives to reduce

risks by hedging with listed options (even early in

the options' life).

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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.