Estimating In-The-Money Probability using IV and Standard Deviation

I've studied stock (and VIX)'s implied volatility changes with time before. It was based on the book by Dan Passarelli: Trading Option Greeks. This is a great book about Option Greeks and volatility. My post on the Effect of Prices, Time, Volatility on Option Greeks was also based on this book. It's these types of studies that lead me to the understanding of estimation of ITM probability of stocks.


Recently, I also researched for methods to calculate the ITM probability of options since the supertrader Karen uses it in her naked option selling strategy. If we find a formula to estimate the ITM probability, we can implement it in ThinkScript in our backtests of the supertrader's strategy.

ITM Probability Estimation Using Standard Deviation

Due to lack of ITM probability data in ThinkScript, the ITM probability can be estimated using the standard deviation of a normal distribution as shown below, according to http://en.wikipedia.org/wiki/Standard_deviation.

ITM Probability	SD Multiples
0.27%	3
4.55%	2
5%	1.960
10%	1.645
20%	1.282
30%	1.050
31.73%	1

Stock Price Strikes/Points for Corresponding ITM Probability

In a recent TastyTrade video, the relationship between stock price changes and SD, IV, expiration days is presented in a formula:

Stock Price Change Percentage = SD Multiple x IV / Square Root of (365/DTE).

Putting all the pieces of the above information together, we should be able to estimate the stock prices for any ITM probability:

Stock Price of a certain ITM Probability = Current Price x ( 1 + Stock Price Change Percentage)

It means we can calculate the call/put selling strikes and adjustment points using the above formula for Karen's strategy. Since all of these parameters are available in TOS software, it's possible for us to implement in TS. I'll update it once I get a chance to code it. We should be able to present these prices in stock price charts to provide good visual display as well.

Update

Based on Vince's comment below, I have updated the above table which included probability on both sides. For the strategy of selling naked options, the single sided probability should be used. Therefore, the following table is the right one.

ITM Probability	SD Multiples
0.13%	3
2.28%	2
2.50%	1.960
5%	1.645   (Sold put strike)
10%	1.282   (Sold call strike)
15%	1.050
15.87%	1
30%	0.52     (Adjustment point)

Vince also kindly shared the following web site that gives us the SD multiple (Z) in a graphical representation: http://www.mathsisfun.com/data/standard-normal-distribution-table.html. In this dynamic graph, you can select "Up to Z" button at top left side first, and move curve to a probability value of interests, then read the SD multiple (Z).