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I have a formulas for figuring out probability the price will be struck within T days. Now what I need help with is figuring out the probability price will be stuck 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 being stuck within a given time period based on the current volatility price movement of 13.0 pips.

My Test Variables

  • Period (PRD): = 14 // number of 5min bars
  • 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(n)): = 1 // can be 1,2,3,4, etc.
  • CurrentPrice (P): = 1.2300

Example Strike Prices


I created 4 strike prices based on the current Volatility (V) = 13.1, multiplied by the Multiplier (M). I want to determine the probability for each Strike Price that it will be hit (e.g. S1, S2, S3, or S4) for any given time period be it minutes, or hours.

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

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

Questions:

  1. What do I need to change in order to determine the probability of the strike price will be hit in (nth)minutes, or (nth)hours, etc???

    $$sqrt(T/365) = sqrt(M / (TS) ??????)$$

  2. sigma - what exactly is sigma I know this means SUM. Do I sum $$sigma = sum(PRD)$$ close prices from the last 14 bars 5min time period (e.g. all previous close prices from 14 bars ago (or sum of close price from 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:

Formula

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


Definition of the Functions used in the formula:


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

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

  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.
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