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.

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

// 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

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

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.

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.