# How to find the probability of touching between two dates

#### Socratic

##### Newbie
5 0
Problem is I never tried to simulate anything like that so I'll need some source to learn that form. Is there any website you know that teaches it? It might a good idea to know just for the fun of checking some crazy occurrences

Anyway now that I gave it another thought I'm inclined to be more convinced you're right. Maybe it's just a mistake on my part because by my own assumption the expression "p(A and B)" turns zero anyway because one of the terms in it sufficiently prevents it from being exemplified together with the other (even if the other doesn't exclude it alone). I mean, the expression "p(A and B)" in

p(A or B) = p(A) + p(B) - p(A and B)

turns zero since A was "hitting only between T and T+whatever." and there is no such single event combined with both it and B (=hitting before T)

##### Junior member
41 0
Consider this proposal: US Equities trade as a derivative of the USD FX. (an inverted dollar carry).

Ideas jobs production assets revenues sales (etc) are down across all sectors. Yet, as if by magic, US indexes bubble up to magnificence of past glory like a giant underlying Elliot event is just over the horizon and heading this way on a fast horse.

Bolted together a forward [currency] rate swap engine back the the day. The specs came from a well credentialed geek. Recollection is that machine could reliably peg an FX, as well as LIBOR, to the basis point, six months out.

The markets back then still had some basis in reality. Assets priced to business product events. The inverse sovereign carry trade was in the closet - so this approach may not be as affable now as it was then.

Reality check: FX Spikes are being telegraphed ..
Ann Rand suggested "We can ignore reality but we cannot ignore it's consequences".

1) The Euro Zone will change
2) That change will cause demand for USDs
3) The strong USD will deflate US equity value and collapse US equity and commodity indexes.
4) The very famous so called super committee in the US will fail to deliver a workable austerity plan.
5) Without a US austerity plan S&P will downgrade, as promised, US credit rating.
6) The rating downgrade will weaken the USD
7) US indexes, thanks to weak USD, again climb to unbelievable glory.
8) Followed by the final and largest wave of the Elliot Wave set resulting in a total collapse of the global fiat currency apparatus.

Within items 6, 7, 8 there will be opportunities for profit (and we know the date the "Super Committe" will anounce it has failed) , albeit fiat profits, but profits, nonetheless for those with nose to wheel and ear to ground. After item 8, fiat exchange tokens worthless.

Reality check fact: China just a few months back said it's pencil pushers had determined the true US GDP was more like 5 Trillion than 14 Trillion.

Accepting equities trade more as derivatives of the FX Swap Market then the solution may be as simple as forward (let's say) 3M LIBOR curve. Once the forward LIBOR is in hand it would be easy to hash a set of forward currency spreads.

With forward curve and spreads in hand, some work would need to be done with a critter called "Beta Weighted Delta". BWDs, done right, are said to prescribe the trading behaviors of equity / index pairs. IOW: When "A" expresses this vector "B" expresses that vector.

Next determine the BWD for the equities or indexes being considered paired with their sovereign FX index.

Use the forward FX curve, apply the BWD and, viola, you can forward price the market for the equities being considered.

Well, maybe, in theory, anyway!

#### scose-no-doubt

##### Veteren member
4,630 954
[1- P(T)] x [P(T1)] ?

Would that even work? Does that only work between two given strikes?

Last edited:

#### Hotch

##### Experienced member
1,410 256
Buy Hull, bit of c++, bit of stoch calc, bit of math finance, take you a month max.

##### Junior member
41 0
[1- P(T)] x [P(T1)] ?

Would that even work? Does that only work between two given strikes?
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!

##### Junior member
41 0
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

##### Veteren member
4,630 954
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

##### Established member
872 236
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)

Last edited: