Option Traders Biggest Mistakes: Part III

Sometimes there are good reasons to buy out of the money options. Most of the time they are low probability bets. Like buying lottery tickets.

Lottery Tickets

There are ways to buy lottery tickets that increase your chances of winning. For example, many people bet their birthdays or their kid’s birthdays. So if you bet the numbers greater than 31 you have increased your odds of winning. There are also syndicates that wait for the lottery pay off pot to be large enough and then they will buy tickets with every combination to ensure that they win.

Good Reasons to Buy Out of the Money Options

Most books talk about the probability to profit at option expiration. But that isn’t the whole story. If the stock or future underlying the option is very volatile, or there is an event that leads to high volatility, an out of the money option can make you money before expiration. Then, an out of the money option might be the best bet.

Delta

Delta is the change in the option value for a one dollar change in the price of the underlying. For the mathematicians, it is dV/dS. It is not just a mathematical relationship, it has some very important properties. For one, it is the probability that the option is in the money at expiration.

An at the money option has a delta of one half, so that tells us that there is a 50% probability that it expires in the money. Out of the money options have lower probabilities to end up at a profit.

Here is a quick and dirty way to calculate delta with the information that you can find at your broker’s website.

Volatility

The volatility is the standard deviation of the price changes for one year. That means, that a $100 stock today with a volatility of 30% has a 68% chance to be between $70 and $130 one year from now. The 68% is because the price has that chance to be within one standard deviation for a normal distribution.

What is the daily volatility? There are 252 trading days in a year. As the stock price wanders in its random walk, the price can get farther and farther away from where it is now. In our example the daily volatility is 1.89% = 30% / square root(252) So, there is a 68% chance for the stock to end the day between 98.11 and 101.89. If we are looking at an option that has 20 trading days until expiration, the volatility is 1.89% * squareroot(20) = 8.45% Our $100 stock has a 68% chance to end up between $91.55 and $108.45.

What About that $110 Call?

Say you are thinking of buying a $110 call with 20 trading days until expiration. Is this a good bet? It depends. If there is an upcoming earnings announcement and there is a lot of uncertainty about earnings, it might be a good trade because the volatility will increase and make the call more valuable.

If there is no upcoming event to increase volatility, is this a good probability trade?

Let’s look at the probability to be in the money at expiration. $10 above the current price is 1.18 standard deviations away. 86.5% of the price curve is below $110 so that leaves you 13.5% probability for the price to be above $110 at expiration.

(How did we get the 86.5%? $100 is at the center of the price distribution, so half or 50% is below $100. $10845 is one standard deviation above the center, so 84% is below that. There is 34% above the center and 34% below the center. I estimated that 0.18 above that has 2.5% of the distribution in it.)

Long odds.