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.
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/standardnormaldistributiontable.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).
Thanks Charles for your diligence and hard work. Just a minor clarification. You meant
ReplyDelete5% ITM prob "sell PUT strike" and not "Call".
I have joined the Yahoo group (id: mtambacfe)
Appreciate your initiative. Vince
Thank you, Vince for the correction. You're right. I updated the table.
DeleteCharles
Charles: You have a great suggestion about % change calculation. Perhaps, the onesided probabilities would be more appropriate for the situation on hand as shown below:
ReplyDeleteITM prob Price% Ch Z (SD X) IV (365/D)^(0.5) DTE
0.10% 16.66 3 15 2.70 50
2.30% 11.10 2 15 2.70 50
5.00% 9.10 1.64 15 2.70 50
10.00% 7.11 1.28 15 2.70 50
15.90% 5.55 1 15 2.70 50
20.00% 4.66 0.84 15 2.70 50
30.00% 2.89 0.52 15 2.70 50
0.10% 16.66 3 15 2.70 50
2.30% 11.10 2 15 2.70 50
5.00% 9.10 1.64 15 2.70 50
10.00% 7.11 1.28 15 2.70 50
15.90% 5.55 1 15 2.70 50
20.00% 4.66 0.84 15 2.70 50
30.00% 2.89 0.52 15 2.70 50
Thanks for starting a valid conversation.
Vince
Hi Vince,
DeleteExcellent points. It's my oversight to use the doublesided probability. I'll update it and share your info shortly.
Thanks a lot.
Charles