There is a formula for calculating the expected move of an underlying such as a stock or futures contract based upon its price, implied volatility (IV) and the number of days to expiration (DTE). However this calculation does not factor in volatility skew.
The probability of touching a given strike price is approximately double the probability that the underlying price will expire beyond that strike (based on the concept of stock returns behaving according to Brownian Motion). The study we ran uses historical strangles to examine probability of touch as it relates to the strike prices of 1 standard deviation strangles.
A 10 year study was conducted in SPY (S&P 500 ETF). Every trading day a 1 Standard Deviation Strangle (16 Delta Call and Put) was sold in the expiration cycle closest to 45 DTE. We then tested how often SPY touched the Call strike or Put strike before expiration. A table of the expected probability of touch and actual probability of touch (over 10 years) of SPY 16 Delta Puts and Calls was displayed. The table showed that the calls had been tested more often than the puts. Tom and TP noted that this in essence is why Karen The Supertrader was so successful. The next table displayed added the expected and actual numbers for the puts and calls expiring in-the-money (ITM). The final table showed the percentage of trades that were profitable despite one leg of the strangle expiring ITM. That table factored in the premium collected which helps our probability of profit (POP).
For more on the concept of Probability of Touch we recommend the Market Measures from September 15th, 2015 “Probability of Touch”.
For more on the concept of Brownian Motion and stock returns we suggest these segments:
The Skinny on Options Math from May 16th, 2013 “Brownian Motion"
From Theory to Practice from March 11, 2016 “Geometric Brownian Motion Part 1”
From Theory to Practice from March 18, 2016 “Geometric Brownian Motion Part 2
Watch this segment of “Market Measures” with Tom Sosnoff and Tom Preston for a better understanding of probabilities as they relate to options expiring ITM and being "tested" prior to expiration.
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