Option Probabilities and More

by Jay Pestrichelli on July 18th, 2012

From time to time we discuss strategies on this blog that include option driven probabilities. The question has come up how we calculate those probabilities; so today we’ll explain where that data comes from.

Any reputable brokerage that trades options will have an option chain that allows you to see probabilities. These probabilities are derived from the rates of changes that options go through as the price of the underlying moves. The probability itself represents the chance that the option will expire either ITM or OTM.

For example, here’s a quick look at put chain on GE that shows the probability of closing out-of-the-money.
Based on the option chain, we can see that the probability that the August 20 Put will close out-of-the-money is 37.98%. That means that according to the option pricing, there is a 38% chance that GE will end up higher than \$20 at August expiration. At the time, GE is trading at 19.71. So draw from that what you will, but there is less than a 40% chance that GE rises 0.29 in the next month.

The calculation comes from a series of equations that are based on the rate of change of the options prices. These rates of change are what create a set of data points know as “the Greeks”.  These are Greek letters representing a characteristic of the option price movements and are know as Delta, Gamma, Theta, Vega, & Rho.

• Delta is the rate of change of an option price relative to the rate of change of the underlying. For example, if a stock moves \$1 and the option moves \$0.50, it is said that this option has a Delta of 50.
• Gamma is the rate of change of Delta. Yes, that is a rate of change of a rate of change. A second derivative for you calculus fans out there. Think of this one as how you move in a car. Speed is the rate of change of your position (Delta) and acceleration is the rate of change of your speed (Gamma).  Delta changes as the underlying moves and Gamma helps you understand by how much Delta changes.
• Theta is the rate of change of an option price relative to the passing of one day. An option with a Theta of -0.05 is expected to decline each day by 5 cents.
• Vega is the rate of change of an option price relative to the change in volatility of the underlying asset. Vega represents the amount that an option price changes in reaction to a 1% change in the underlying’s volatility. The higher the Vega, the more the option price will move as the underlying gets more volatile
• Rho is the rate of change of an option price relative to the change in risk-free interest rates. These days its not all that relative since interest rates are locked in through 2014 according to the Fed. But when they do change, they will have in impact on option prices.

While all this information is good to be aware of, you don’t need to be a math master to use the Buy and Hedge method of investing. That would be like becoming an actuary before ever buying life insurance.  However, knowing the forces that will impact the change of an option’s price is something to be aware of and to help explain why things happen.

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