The main determinants of an option’s value are: volatility, time to expiration, the risk free rate of interest, strike price and the underlying stock’s price. Understanding the interplay of these variables – especially volatility and time to expiration – is crucial for making informed decisions about the value of your Employee Stock Options (ESOs). (Related: Option Valuation)

In the following example, we assume an ESO giving the right (when vested) to buy 1,000 shares of the company at a strike price of \$50, which is the stock’s closing price on the day of the option grant (making this an at-the-money option upon grant). Table 4 uses the Black-Scholes option pricing model to isolate the impact of time decay while keeping volatility constant, while Table 5 illustrates the impact of higher volatility on option prices. (You can generate option prices yourself using this nifty options calculator at the CBOE website).

As can be seen in Table 4, the greater the time to expiration, the more the option is worth. Since we assume this is an at-the-money option, its entire value consists of time value. Table 4 demonstrates two fundamental options pricing principles:

1. Time value is a very important component of options pricing. If you are awarded at-the-money ESOs with a term of 10 years, their intrinsic value is zero, but they have  a substantial amount of time value, \$23.08 per option in this case,  or over \$23,000 for ESOs that give you the right to buy 1,000 shares.
2. Option time decay is not linear in nature. The value of options declines as the expiration date approaches, a phenomenon known as time decay, but this time decay is not linear in nature and accelerates close to option expiry. An option that is far out-of-the-money will decay faster than an option that is at the money, because the probability of the former being profitable is much lower than that of the latter.

Table 4: Valuation of an ESO, assuming at-the-money, while varying time remaining (assumes non-dividend paying stock)

 Theoretical Value of ESO Across Time - 30% Assumed Volatility Stock Price \$50 \$50 \$50 \$50 Volatility 30% 30% 30% 30% Time Remaining 10 Years five years three years two years Risk-Free Rate 3% 3% 3% 3% Strike Price \$50 \$50 \$50 \$50 Fair Value \$23.08 \$15.99 \$12.10 \$9.69 Total Value \$23,080 \$15,990 \$12,100 \$9,690

Table 5 shows option prices based on the same assumptions, except that volatility is assumed to be 60% rather than 30%. This increase in volatility has a significant effect on option prices. For example, with 10 years remaining to expiration, the price of the ESO increases 53% to \$35.34, while with two years remaining, the price increases 80% to \$17.45. Figure 1 shows option prices in graphical form for the same time remaining to expiration, at 30% and 60% volatility levels.

Similar results are obtained by changing the variables to levels that prevail at present. With volatility at 10% and the risk free interest rate at 2%, the ESOs would be priced at \$11.36, \$7.04, \$5.01 and \$3.86 with time to expiration at 10, 5, 3 and 2 years respectively.

Table 5: Valuation of an ESO, assuming at-the-money, while varying volatility (assumes non-dividend paying stock)

 Theoretical Value of ESO Across Time – 60% Assumed Volatility Stock Price \$50 \$50 \$50 \$50 Volatility 60% 60% 60% 60% Time Remaining 10 Years five years three years two years Risk-Free Rate 3% 3% 3% 3% Strike Price \$50 \$50 \$50 \$50 Fair Value \$35.34 \$26.76 \$21.20 17.45 Total Value \$35,340 \$26,760 \$21,200 \$17,450

Figure 1: Fair value for an at-the-money ESO with exercise price of \$50 under different assumptions about time remaining and volatility

The key take-away from this section is that merely because your ESOs have no intrinsic value, do not make the naive assumption that they are worthless. Because of their lengthy time to expiration compared to listed options, ESOs have a significant amount of time value that should not be frittered away through early exercise.

Employee Stock Options: Risk and Reward Associated with Owning ESOs
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