# Why Cheap Options Take So Long to Decay

04/21/2010 12:01 am EST

Focus: OPTIONS

As a mentor, I see students that have knowledge ranges from borderline expert to total novice. The one thing that almost every one of my students have in common is their love of the credit spread. Another trait that many of my students share is their unwillingness to exit credit spreads when the short option becomes inexpensive. This is not because the students want to hold the trades to expiration. It is because most do not understand that there is a second component in the value of options that most option pricing models cannot calculate. This component will cause the final portion of the value of an option to take much longer to decay than the model will predict. This value exists because of the payout disparity if the option goes sour (unit risk). I like to call this value “the card game value.” Understanding this will allow traders to exit trades at an earlier date and move money into trades that will follow the standard option model.

The Card Game

Two men are going to play a card game, and they will only play it once. Here are the details:

1. There are 100 cards
2. 99 of the cards have a value of 0
3. One card has a value of 1,000

One of the men will pay the other for the chance to draw one card. If he draws a 0, he gets nothing, if he draws the 1,000, the other man must pay him \$1,000.00. Theoretically, the card game is worth 10.00 (1000 x 1/100). But, what do you think the one man should charge the other to play the game. If this game were going to be played over and over again the man would probably charge a very low number, say 11.00. He would know that over time, probabilities are in his favor and he will come out ahead in the long run (this is how Las Vegas pays for all those nice hotels!). However, this game will only be played once. The odds are the same, but if the 1,000 card is drawn, the man on the hook for the money will have no opportunity to make the money back. My guess is that it would take a lot more than \$11.00 to get someone to play this game.

This thought process is exactly what throws off the value of cheap options. Yes, the probabilities say that the option should be worth nothing, but the option will maintain a value of .10-.25 for an exceptionally long time. That is because the person who sells the cheap option is the same as the man who is selling the draw in our card game. Yes, the person would make money over time in a Vegas world, but the months have a very limited life. If the seller of the cheap option has the trade go bad on him or her, they will never see that money again. The trader will not have an unlimited number of chances to play this game. The major move has happened; the trader has lost. To make matters worse, unlike our card game, the trader has an undefined risk, meaning he or she has no idea how much they will lose if the trade goes against them. Thus, the final .25 of an option takes extra long to decay out.