## Need help figuring out probability that an instrument will strike a price in a given

Hello,

I have a formulas for figuring out probability the price of will reach a strike price within T days. Now what I need help with is figuring out the probability price will strike a strike price with in a given (T) minutes, or (T) hours, instead of just days, how would I go about solving this for minutes or hours, given the prior price movement (volatility is 13.0), over a period of 14 bars each bar is 5 minute bars. How do this using the formula below to determine the probability of the price striking a strike price given the current volatility price movement of 13.0 pips.

Point
(PT) = 10,000
Volatility
(V) = 13.1 // based on past 14 bars price has movement of 13.0 pips over period of 14, 5 minutes bars
Multiplier
(M) = 1 // can be 1,2,3,4, etc.
CurrentPrice
(P) = 1.2300

// will have 4 instrument strike prices based on the Volatility (V) = 13.1, multiplied by the Multiplier (M), that I want to determine the probability of the
current instrument's price
(P) hitting a single
strike price
(be it S1, S2, S3, or S4)

StrikePrice0 (S1) = 1.23131 // equal (P + ((V * M(1)) / PT))
StrikePrice1 (S2) = 1.23262 // equal (P + ((V * M(2)) / PT))
StrikePrice2 (S3) = 1.23393 // equal (P + ((V * M(3)) / PT))
StrikePrice3 (S4) = 1.23524 // equal (P + ((V * M(4)) / PT))

Minutes (M) = (14 * 5) = 70 minutes // 14 bars @ 5 minute intervals

Questions
:
1. what do I change this to in order to determine the probability of the above will happen in minutes, or hours, etc from now???
sqrt(T/365) = sqrt(M / (TS) ??????)
2. sigma - what exactly is sigma I know this is a SUM of close prices, are the sum of price from the previous time period (e.g. all previous close prices from 14 bars ago (70 minutes bars))??????? Or what exactly???

============== This work for days, need to change the formula to work for minutes, hours, seconds what ever the case may be?? ============
The probability "X" that the stock will touch or exceed the strike price S, within T days:

Z = ln(S/P) / (sigma * sqrt(T/365))
X = CNDF(Z)
================================================== ==============

ln() = natural logarithm = log to the base e
Z = Zscore = size of price move from P to S, in standard deviations
CNDF() = Cumulative Normal Distribution Function

Here are some other
summations
I would I will need to test for when I get the formula to work, going to create more
summations
for minutes, and hours for my test cases.

1. The first term is the probability that the instrument will touch or exceed the strike price within 1 day (T=1).
2. The second term is the probability that the instrument DOES NOT touch or exceed the strike price within 1 day, times the probability that the instrument touches or exceeds the strike price within 2 days.
3. The third term is the probability that the instrument DOES NOT touch or exceed within 2 days, times the probability that the instrument does touch or exceed within 3 days.