I just came across a blog post. I believe the answer is a correct approximation: http://tastytradenetwork.squarespace.com/tt/blog/probability-of-touching-both-sides I modified the question in the post to: What is the combined probability of the stock moving up to touch the short call strike but not touching the short put strike price? **Same delta values of 0.3 for the call and 0.3 for the put.
Unfortunately those probabilities are based on hindsight, so they’re worth absolutely nothing until you can prove that they were reliable and actually useful for predicting future price movements in the past.
Nobody can know as these delta values are all based on implied volatility and they can differ from the actual resulting volatility. I have seen the underlying breaking through these delta levels and actually reaching 0.1 delta levels and I have even seen underlyings breaking through 0.1 delta levels as well. Just ask James Cordier and most recently the meme stocks GME. Basically anything can happen and this is why short vol. is so lucrative...
Delta does not mean much to me, it is a merely a crutch used by traders to pray and hope that a stock will/won't reach this particular strike. I saw stocks crashing through 10 delta like a stone too many times and guess what, delta value changes in a second. When I look to sell OTM strike I pay attention to two things. 1. The difference between implied and historic volatility, implied obviously should be above. 2. Distance in % from the current price.
Yes, I am not using delta to trade. I am trying to understand how exotic options are priced and I believe the delta is key in it’s pricing.
I understand how unreliable deltas are for the purpose of trading. However, I am just trying relate math probabilities with derivatives and exotic options. I am trying understand probabilities using options or exotic. It is just an idea not a trading idea.
I understand your point about it been mostly useless . However, I just wanted to know how to solve a similar question using the logic explained in the blog post. I actually just want to learn the math that’s all, the explanation might be useful to me later, maybe in something else.
Whatever you read on the internet is written by someone like you and me. It is someone’s personal opinion and I don’t think that you should base your decisions on it.