# Calculating the Probability of Touching

As a novice options trader, it is important to become familiar with option calculators. The typical calculator does the math for the Greeks (delta, gamma, theta, vega**, **rho) and provides the theoretical value for the option when you have the proper inputs: stock price; strike price; time (number days until the option expires); interest rates; dividend, if any; option type (call or put); volatility estimate for the underlying stock.

### Probability of Touching Calculator

This calculator provides such useful information that it should be used by all options traders, including very experienced ones, and it is referred to by more than one name. It could be called a "Probability of Touching Calculator" or a "Stock Price Probability Calculator." Ask your broker if they have such a calculator available for you to use.

The basic question answered by this calculator is: If I plan to own a given option position for a specific number of days, what are the chances that the stock price will touch the strike price?

**For premium sellers**: When you specify how many days you plan to hold the short position (you are not forced to hold all the way to expiration), the calculator lets you know the probability that the underlying stock price will reach the **strike price** *at least one time* during the holding period. If that probability turns out to be 15 percent, then the chances that the option will expire worthless *without ever moving into the money* is 85 percent.

NOTE: This is *not* the same as a probability that the option will expire worthless. Why? Sometimes an option moves ITM and later moves OTM, only to expire worthless. The probability of touching calculator ignores those (ITM then OTM) situations. As a good approximation, the probability of the stock price touching the strike price (at least once prior to expiration) is double the probability that it will expire worthless. Another way of stating the same theorem is: Any option is expected to touch the strike price prior to expiration is approximately double the option's Delta. NOTE: Use the Delta at the time the trade is made.

**For premium buyers**: When you specify how many days you plan to hold the long option position (you may exit prior to expiration), the calculator provides an approximate probability that the underlying stock price will reach the strike price (or any other price that you specify) at least one time during the holding period.

If you own an ITM option, then the probability of touching refers to the chance that the option will move out of the money. If you own an OTM option, then the probability of touching refers to the chance that the option will move in the money.

### Other Strategies

When you trade any options strategy with multiple legs (these are known as spreads), there is more than one option that matters. For example, in a typical butterfly spread, you own two different options.

**Example**:

Buy 1 XYZ Oct 100 call

Sell 2 XYZ Oct 105 calls

Buy 1 XYZ Oct 110 call

When the stock price moves below 100 or above 110, the spread loses much of its value and becomes worthless if expiration arrives and the stock is not priced between 100 and 110. Thus, a trader should want to know the probability that the stock price will touch *either* 100 or 110 during the anticipated holding period. The Probability of Touching Calculator provides that information. Clarification: The calculator generates the probability that the stock with touch *either* $100 or $110. For similar strategies (iron condor, for example) it is essential to know the chances that either of two different strike prices (or both prices) will be touched to effectively manage risk.

### Choosing the Holding Period

Another way to use this calculator is to decide how long to hold onto the position. By plugging a different number of "days" into the calculator, you can learn how the probability of touching changes. By making the calculation every day, based on the then-current stock price and the potential profit and loss, you can determine whether it pays to hold onto the position.