How to find the probability of touching between two dates

[Cadavre]

Cadavre: It seems very complicated to do back-testing ... probabilistic answer to such a question, much like the link referred to above purports to do.

Trading systems that consume BT models are usually unaware of the date (market is open or it is closed). TS world limited to current tick - B tick W tick - your post hints requirement for hard dates (easier to time trades to ECB counterfeiting and rumors that the fast but not too bright HFT admins think non-existent retail traders follow )

Back testing equities is not so much complicated (the number of parameters - aka model - rendered for trading system - trying to count - depending on number of dynamic floors and stops - can be as few as a dozen - maybe less) as it is tedious. Even single share modeling will score 10 Thousand prospective models before the money model is rendered and in the background ya got a tad of FIFO cost averaging to contend with.

It would not be unusual for a back test modeling machine to score monte carlo - CAGR - awa total returns to rank rendered scenario performance.

Speaking of BT-ing options (were we?) Have seen an EOD history for every SPX option ever all the way back to whenever . CSV format packed to zip file is about 45 MBs - datz one big multi-GB CSV that Excel ain't never gonna eat - ref: OPTSUM(?) / AMIBROKER(?). Liked that data cause the underlying "last" was timestamped to the option's.

 

[scose-no-doubt]

Option probabilities rate the likely hood, based on tick at moment probability is calibrated, that the market will price the option in / out money before expiration.

Next tick could change everything.

A less than precise probability surface: 18 day 105 SPY OTM PUT (S=109.43):

Pegging the probability of the above PUT's moneyness on a given date at a given spot is not the problem.

To payoff the market has to deliver spot - or so we been told!

Hahah yeh I kind of mis-read the thread but I meant to respond to Shakone and Socratic. I was tired as hell lol.

In retrospect I meant to write [1-P(A)] x [[P(B) -P(A)]] and to ask whether that would be a possible solution but I was also going to ask whether it would be possible use the delta of two options with strikes at the (approximate) values that you're considering for A and B to work something out. Obviously what actually came out was a convoluted and messy mish-mash lol.

 

[Joey25]

I'm trying to figure out how to calculate the probability of a stock touching a certain price target specifically between two dates I choose, without it being touched before.

For example, suppose I want to find the probability of a stock price touching some out the money target next week between Wednesday to Friday, without ever touching that target anywhere between now to Wednesday. How do I do it?

Anyone has an idea?

Why not draw a binomial tree diagram with the probabilities of going up or down each day being linked to the risk-free rate and the magnitude by the vol of the underlying? You can then highlight the paths which satisfy your criteria and add up their probabilites.

Alternatively, if 2^n is huge:

The satisfying paths may be along the lines of <= 4Ups in 6 days, in which case you use the binomial distribution to work out the probability of {4U, 2D} multiplied by the 6_C_4 combinations that satisfy that condition plus {3U, 3D} x 6_C_3 etc.


Then you can use Bayes' Theorem to work out the probability that a path that hit the target over the entire period (e.g. 10 days) took a satisfying path in the original 6 days:

P( did not hit after 6 days | did hit after 10) =

P( did hit after 10 | did not hit after 6) x P(did not hit after 6 days) / P(did hit after 10)*


*Note that P(did hit after 10) is a total probability and can be further broken down into:

P( did hit after 10 | did not hit after 6) x P(did not hit after 6 days) + P( did hit after 10 | did hit after 6) x P(did hit after 6 days)