Just as example I did ES spot about 3900, sell put at 3635 buy protective put at 3500 with 19 dte. IB profile shows 99% for max profit about 500, 1% max loss of around 13000. However calculating for partial losses I've not found a good method of weighted outcomes for more complex cases to estimate the EV. For example 85% max gain with 4% max loss selling delta 20 puts and buying 10 delta protective put. How to estimate the outcome gain or loss for the other 11% since the distribution isn't linear? Formula method or monte carlo? I don't think IB includes such tools.
I've got daily historical data, I wonder if I should split the gap data out too since it can be significant. I've normalized it to percentage moves. It appears overall in the data set that a stdev is about 1%/day. 2020 data was more like 1.2%. monte carlo using actual movements should give a good idea of the outcome distribution, then I can weigh it by the strategy p.l at that price. Any tools that do this? I may just write one for this purpose.
i had written one like 15 years ago. I would write my own if i were you, as the input parameters are what's critical and there isn't a perfectly right answer for that. Your edge will come from those parameters.