# Probability of Touching Both Sides

Options Jive

Options involve risk and are not suitable for all investors. Please read Characteristics and Risks of Standardized Options before deciding to invest in options.

Our research studies have taught us that you can be profitable selling premium using strategies such as short Strangles in the SPY (the S&P 500 ETF). You may become doubtful if one of your strikes is tested and even more so if both are tested. What are the theoretical chances of both sides of a Strangle being tested and how does that compare to the actual results?

The Probability of Touch for any particular strike is approximately twice the Delta of the Strike Price. The probability of two strikes being touched is product of their respective probabilities of touch. The formula then would be P(A & B) = P(A) X P(B). That means for a Strangle composed of a 30 Delta Call and a 30 Delta Put the chance of both being touched would be 36%.

A table based upon the results of SPY Strangles from 2005 to the present was displayed. The table compared the theoretical probability of a touch, the actual probability of a touch according to our study results and the percentage differential of the two for Strangles composed of a Put and Call with a Delta of 45, 40, 35, 30, 25, 20 and 16 (1 Standard Deviation). The table showed that the difference between the theoretical and actual probabilities of touching both sides increased as the Deltas decreased. Wider Strangles had a smaller chance of touching both sides. An additional table showed that it was extremely rare that SPY has touched both strikes of strangles that composed of a Put and Call with a Delta of 10 and there were no occurrences if the Delta was 5 or less.

Tom noted, “The takeaway from here is just that the way derivatives are priced, they are priced in such a way that the buyer has unlimited potential and the seller has limited profitability. Because of that we see an opportunity between theoretical and actual.”

Watch this segment of Options Jive with Tom Sosnoff and Tony Battista for a ground breaking segment comparing the theoretical probability of touch on both sides versus the actual results.