Steven Smith

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Options Forum: The End of Days

Steven Smith

-- W.

This is a great question that goes right to the heart of options pricing and valuation. The most commonly used method is the Black-Scholes, which considers five factors (price of the underlying security, strike price, time or expiration date of option, interest rates and expected or implied volatility) in calculating an option's theoretical price.

The reader makes a great point that calendar days certainly have a relationship to an option's value, but its impact actually becomes part of the implied volatility formula, not the time remaining. It's the number of days that an option is available to trade that is a more important factor in putting a time value on an option's price.

To put it simply: If you can never trade an option, it doesn't matter how much time is remaining -- for all practical purposes, it would be worthless. This is why many option traders choose to plug in trading days or work with 22-day months when pricing options; the days that an option can't be bought or sold are essentially worthless in terms of time value.

The market's close on Friday takes one day away from the option's trade availability. What if the decision had been to close for five days? Would you be willing to pay more or less for a decaying asset if you couldn't trade it during that time?

This doesn't mean that the possible events that the reader mentions can't occur, but they're the exception rather than the rule. They are unknown quantities, and as such their probability and impact would become part of the option's implied volatility calculus. But given that about 85% of all options expire worthless, most traders will use the general guideline that one less day of trading is one less day the stock price can change.

Obviously, an extraordinary act such as Sept. 11 creates an environment of uncertainty that pumps up the volatility and increases an option's price. We still feel the impact of that day in various forms, from a change in the terror alert code to other geopolitical events. But again, assessing the likelihood of all possible future events falls under the realm of implied volatility.

Given that Friday's close is already known and due to an event that should have no direct impact on a security's price, the odds lean toward activity resuming on Monday where it left off Thursday. All else being equal, for the purposes of pricing options, we have essentially traveled forward one day in time. Obviously, the longer the life span of an option the more likely a price-changing event will occur; this will be reflected in an option's valuation.

This also brings up some issues surrounding the expensing of employee stock options. No company can honestly say they have no value, but there is a legitimate complaint that applying the Black-Scholes pricing model (which was developed to reflect an option's value on a continuous basis within a dynamic trading environment) to a static employee option, which comes with trading restrictions, and binding it to one specific moment in time (its issuance date), may not accurately reflect its ultimate value at a later date.

Bringing this back around, then, consider an example of XYZ Corp. currently trading at $50. Which of these three do you think is more valuable? 1) an exchange-traded $50 call with two years until expiration, 2) an employee stock option with an exercise price of $50 that vests and can be exercised in 12 months, but expires after two years, or 3) an employee stock option with a $50 exercise price that doesn't vest for 23 more months, and can be exercised in the 24th and final month of its life span?

I think we'd all agree that the exchange-traded option, which can be bought and sold at any time during the two-year period, is more valuable than the one that vests in 12 months and has a full year in which it can be exercised or "traded," which in turn is more valuable than the one that can be exercised or traded only during the last month of the option's two-year life span.

If you don't think this is true, ask some of the "paper millionaires" from the bubble days who watched the value of their stock options evaporate and could do nothing about it because they were still in the lock-up period and restricted from exercising or trading their options for a period of time. The stocks had huge price moves, which the related exchange-traded options reflected with high implied volatilities. But for those holding company-issued stock options, it was as if those days never existed.