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First Passage Time
October 14, 2026, 11:06 AM
Indicators
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Introduction
Most volatility tools answer the question “how far can price go?”. Traders usually care about a different one: “how long will it take to get there, and which side is likely to be reached first?”. A 5% target is not the same trade if it is typically reached in two days or in three weeks, and a stop placed 5% away matters very differently if the market tends to hit the downside first.
First Passage Time answers exactly that. On the last bar it places two thresholds, X% above and X% below the current close, and runs a Monte Carlo simulation to estimate the distribution of the time needed to touch each one for the first time, the probability that each side is touched first, and the average waiting time. Everything is expressed in minutes, hours or days according to the chart timeframe.
Theory Behind the Indicator
The “first passage time” is a classic concept from probability theory: the first moment a random process reaches a given level. For a price following a geometric Brownian motion it depends on three things: the distance to the level, the volatility and the drift.
The indicator measures volatility as the standard deviation of the log returns over the last 60 bars, and the drift as their average. Each simulated path starts at the current close and moves step by step with a lognormal shock:
price(t) = price(t-1) * exp(drift – 0.5 * sigma^2 + sigma * z)
where z is a standard normal draw. Each path stops when it has touched both thresholds or when it reaches the maximum number of periods. For every path the indicator records when the upper level was hit, when the lower level was hit, and which one came first. With 1,000 paths, the percentiles of those times describe the whole distribution, not just an average.
Because the barriers are path-dependent (what matters is the first touch, not where price ends up), there is no simple shortcut: the simulation really has to walk every path. The random numbers come from a Wichmann-Hill generator with a fixed seed, so the result is stable from tick to tick and reproducible; change the seed to draw a different sample.
Key Features at a Glance
- Monte Carlo of up to 2,000 price paths with the volatility and drift of the chart itself.
- Percentile table (10, 25, 50, 75, 90) of the first passage time for both thresholds, or a sigma view (2σ and 1σ) with a theoretical minimum.
- First hit rate: share of paths that touch the upside or the downside first, with a directional bias.
- Average time to reach each level when it is reached.
- Annualised volatility, and optional annualised drift and drift mode.
- Three drift modes: historical, zero (neutral) and 50% reduced.
- Threshold lines, gradient risk zones and labels with the median time and the first-hit probability.
- Times shown in minutes, hours or days depending on the timeframe.
How to Read the Indicator
The green line is the upside threshold and the red line the downside one. The label next to each line shows the threshold, the median time to reach it (half of the paths need less than that) and the probability that this side is touched first.
The table spreads the distribution: the 10% row is a fast scenario, the 90% row a slow one. A narrow gap between them means the timing is fairly predictable for that distance; a wide gap means patience may be needed. The First Hit row compares both sides directly: with zero drift both should be close to 50%, so any clear imbalance comes from the measured trend.
Two things are worth keeping in mind when reading those numbers. First, the drift is the average log return of the last volPeriod bars, which is simply the net change from the close volPeriod bars ago to the current one, divided by volPeriod. The Directional Bias therefore reflects that single net move, and it is very sensitive to it: on a 30-minute chart with a 5% threshold, a net fall of 0.16% over the last 60 bars is enough to move the first-hit rate from 50% to about 47.5%. Second, the table is a Monte Carlo sample. With 1,000 paths the first-hit rate carries a sampling noise of roughly ±3 points and the percentile times of around ±10 to 12%, so a different seed gives slightly different figures. The fixed seed keeps the reading stable from tick to tick; changing it shows how much of a given reading is noise.
If the table shows “Low Hit Rate”, fewer than 90% of the paths reached any threshold within the maximum number of periods. Increase maxPeriods or reduce thresholdPct.
Practical Applications
- Target and stop planning: check whether a profit target is realistic within the holding period you have in mind.
- Options and time-limited trades: compare the median time with the time left before expiry.
- Drift sensitivity: switch the drift mode to zero to see how much of the directional bias comes from the recent trend and how much from volatility alone.
- Position sizing: wide and slow distributions call for smaller size or more patience than tight and fast ones.
Keep in mind that the model assumes constant volatility and normally distributed returns. Real markets have volatility clusters and fat tails, so treat the numbers as a baseline, not as a forecast.
Indicator Configuration
- thresholdPct (default 5.0): distance of both thresholds from the current close, in percent.
- volPeriod (default 60): bars used to measure volatility and drift.
- numSims (default 1000): number of simulated paths (500 to 2000). More paths give smoother results and more calculation time.
- maxPeriods (default 1000): maximum length of each path, in bars.
- showZones (default 1): gradient risk zones between the close and each threshold.
- showLabels (default 1): labels at the end of the threshold lines.
- distType (default 0): 0 shows the percentile table, 1 the sigma table with the theoretical minimum.
- driftMode (default 0): 0 historical drift, 1 zero drift, 2 drift reduced by 50%.
- showDiag (default 0): adds the annualised drift and the drift mode to the table.
- projBars (default 25): length of the threshold lines and zones to the right, in bars.
- labelSize (default 2): label size, from 0 (tiny) to 4 (huge).
- labelShift (default 12): distance in bars between the end of the lines and the centre of the labels.
- seed (default 1): seed of the random generator. The same seed always gives the same result.
- dashX / dashY (defaults -90 / -20): position of the table in pixels from the top-right corner. If the table touches the price scale, make dashX more negative.
The Code
//---------------------------------------------------------------
// PRC_First Passage Time
// version = 0
// 14.10.2026
// Iván González @ www.prorealcode.com
// Author: Henrique Centieiro
// Sharing ProRealTime knowledge
//--------------------------------------------------------------------//
defparam drawonlastbaronly = true
//----------------------------------------------
// === INPUTS ===
//----------------------------------------------
thresholdPct = 5.0 // Threshold % above and below the current price
volPeriod = 60 // Volatility lookback period (bars)
numSims = 1000 // Monte Carlo simulations (500-2000)
maxPeriods = 1000 // Maximum periods simulated per path (100-5000)
showZones = 1 // 1 = gradient risk zones
showLabels = 1 // 1 = labels at the end of the threshold lines
distType = 0 // 0 = Percentile table, 1 = Sigma table
driftMode = 0 // 0 = Historical drift, 1 = Zero (neutral), 2 = 50% reduced
showDiag = 0 // 1 = show annualised drift and drift mode
projBars = 25 // Length of the projection to the right (bars)
labelSize = 2 // Label size: 0 tiny, 1 small, 2 normal, 3 large, 4 huge
labelShift = 12 // Bars between the end of the lines and the centre of the labels
seed = 1 // Seed of the random generator (same seed = same result)
// Table position, in pixels from the top-right corner of the window
dashX = -90 // right edge of the table
dashY = -20 // centre of the first row
//----------------------------------------------
// === RETURNS, VOLATILITY AND DRIFT ===
//----------------------------------------------
IF barindex > 0 THEN
ret = log(close / close[1])
ELSE
ret = 0
ENDIF
volat = std[volPeriod](ret)
driftRaw = average[volPeriod](ret)
IF driftMode = 1 THEN
drift = 0
ELSIF driftMode = 2 THEN
drift = driftRaw * 0.5
ELSE
drift = driftRaw
ENDIF
// chart timeframe in minutes (GetTimeFrame returns seconds)
tfMin = GetTimeFrame / 60
IF tfMin <= 0 THEN
tfMin = 1
ENDIF
//----------------------------------------------
// === EVERYTHING BELOW RUNS ON THE LAST BAR ===
//----------------------------------------------
IF islastbarupdate AND barindex > volPeriod AND volat > 0 THEN
curPrice = close
upThr = curPrice * (1 + thresholdPct / 100)
dnThr = curPrice * (1 - thresholdPct / 100)
driftComp = drift - 0.5 * volat * volat
// --- histograms of the first passage time of each barrier (periods 1..maxPeriods)
FOR t = 0 TO maxPeriods DO
$upH[t] = 0
$dnH[t] = 0
NEXT
// --- Wichmann-Hill random generator: three small congruential generators,
// exact in floating point, period close to 7e12
s1 = 1 + ((seed * 7919) MOD 30268)
s2 = 1 + ((seed * 104729) MOD 30306)
s3 = 1 + ((seed * 1299709) MOD 30322)
upFirst = 0
dnFirst = 0
upSum = 0
dnSum = 0
upCnt = 0
dnCnt = 0
FOR sim = 1 TO numSims DO
simP = curPrice
upHit = 0
dnHit = 0
upTime = 0
dnTime = 0
per = 1
WHILE per <= maxPeriods AND (upHit = 0 OR dnHit = 0) DO
s1 = (171 * s1) MOD 30269
s2 = (172 * s2) MOD 30307
s3 = (170 * s3) MOD 30323
uu = s1 / 30269 + s2 / 30307 + s3 / 30323
u1 = uu - floor(uu)
s1 = (171 * s1) MOD 30269
s2 = (172 * s2) MOD 30307
s3 = (170 * s3) MOD 30323
uu = s1 / 30269 + s2 / 30307 + s3 / 30323
u2 = uu - floor(uu)
IF u1 < 0.0001 THEN
u1 = 0.0001
ENDIF
// Box-Muller normal draw (COS works in degrees in ProBuilder)
zz = sqrt(-2 * log(u1)) * cos(360 * u2)
simP = simP * exp(driftComp + volat * zz)
IF upHit = 0 AND simP >= upThr THEN
upHit = 1
upTime = per
ENDIF
IF dnHit = 0 AND simP <= dnThr THEN
dnHit = 1
dnTime = per
ENDIF
per = per + 1
WEND
// which barrier was hit first (a tie counts for neither)
IF upHit = 1 AND dnHit = 1 THEN
IF upTime < dnTime THEN
upFirst = upFirst + 1
ELSIF dnTime < upTime THEN
dnFirst = dnFirst + 1
ENDIF
ELSIF upHit = 1 THEN
upFirst = upFirst + 1
ELSIF dnHit = 1 THEN
dnFirst = dnFirst + 1
ENDIF
IF upHit = 1 THEN
$upH[upTime] = $upH[upTime] + 1
upSum = upSum + upTime
upCnt = upCnt + 1
ENDIF
IF dnHit = 1 THEN
$dnH[dnTime] = $dnH[dnTime] + 1
dnSum = dnSum + dnTime
dnCnt = dnCnt + 1
ENDIF
NEXT
upMeanOk = 0
upMean = 0
IF upCnt > 0 THEN
upMeanOk = 1
upMean = upSum / upCnt
ENDIF
dnMeanOk = 0
dnMean = 0
IF dnCnt > 0 THEN
dnMeanOk = 1
dnMean = dnSum / dnCnt
ENDIF
//----------------------------------------------
// === PERCENTILES OF THE FIRST PASSAGE TIMES ===
// Sorted sample read at index floor(n * pct / 100); with integer times the
// sorted sample is the histogram, so the value at that index is the first
// time whose cumulative count goes past it.
// Slots: 0..4 upside rows, 5..9 downside rows, 10/11 upside/downside median
//----------------------------------------------
IF distType = 0 THEN
nRows = 5
$pctL[0] = 10
$pctL[1] = 25
$pctL[2] = 50
$pctL[3] = 75
$pctL[4] = 90
ELSE
nRows = 2
$pctL[0] = 2.28
$pctL[1] = 15.87
ENDIF
FOR k = 0 TO nRows - 1 DO
$qPct[k] = $pctL[k]
$qPct[k + 5] = $pctL[k]
NEXT
$qPct[10] = 50
$qPct[11] = 50
FOR k = 0 TO 11 DO
$qOk[k] = 0
$qVal[k] = 0
IF k < nRows OR (k >= 5 AND k < 5 + nRows) OR k >= 10 THEN
IF k < 5 OR k = 10 THEN
nVal = upCnt
ELSE
nVal = dnCnt
ENDIF
IF $qPct[k] < 1 THEN
needN = 10
ELSE
needN = 5
ENDIF
IF nVal >= needN THEN
idx = floor(nVal * $qPct[k] / 100)
idx = min(max(idx, 0), nVal - 1)
cum = 0
tq = 0
WHILE cum <= idx AND tq < maxPeriods DO
tq = tq + 1
IF k < 5 OR k = 10 THEN
cum = cum + $upH[tq]
ELSE
cum = cum + $dnH[tq]
ENDIF
WEND
$qOk[k] = 1
$qVal[k] = tq
ENDIF
ENDIF
NEXT
//----------------------------------------------
// === TIME FORMAT (minutes / hours / days) ===
// Slots 0..11 as above, 12/13 theoretical minimum, 14/15 average time
//----------------------------------------------
theo = (thresholdPct / 100) / (volat * 3)
$qOk[12] = 1
$qVal[12] = theo
$qOk[13] = 1
$qVal[13] = theo
$qOk[14] = upMeanOk
$qVal[14] = upMean
$qOk[15] = dnMeanOk
$qVal[15] = dnMean
FOR k = 0 TO 15 DO
IF $qOk[k] = 0 THEN
$fU[k] = 0 - 1
$fN[k] = 0
ELSE
totMin = $qVal[k] * tfMin
IF totMin < 120 THEN
$fU[k] = 0
$fN[k] = round(totMin)
ELSIF totMin < 5760 THEN
$fU[k] = 1
$fN[k] = round(totMin / 60 * 10) / 10
ELSE
$fU[k] = 2
$fN[k] = round(totMin / 1440 * 10) / 10
ENDIF
ENDIF
NEXT
totalFirst = upFirst + dnFirst
IF totalFirst > 0 THEN
upRate = upFirst / totalFirst * 100
dnRate = dnFirst / totalFirst * 100
ELSE
upRate = 0
dnRate = 0
ENDIF
//----------------------------------------------
// === THRESHOLD LINES ===
//----------------------------------------------
DRAWSEGMENT(barindex - 3, upThr, barindex + projBars, upThr) COLOURED(76, 175, 80, 178) STYLE(line, 2)
DRAWSEGMENT(barindex - 3, dnThr, barindex + projBars, dnThr) COLOURED(242, 54, 69, 178) STYLE(line, 2)
//----------------------------------------------
// === GRADIENT RISK ZONES (10 layers each side) ===
//----------------------------------------------
IF showZones = 1 THEN
layH = (upThr - close) / 10
dlayH = (close - dnThr) / 10
FOR i = 0 TO 9 DO
ratio = i / 9
zr = round(220 * (1 - ratio) + 190 * ratio)
zg = round(190 * (1 - ratio) + 210 * ratio)
zTr = 90 + round(i * 0.7)
za = round(255 * (100 - zTr) / 100)
DRAWRECTANGLE(barindex, close + layH * i, barindex + projBars, close + layH * (i + 1)) COLOURED(zr, zg, 255, 0) FILLCOLOR(zr, zg, 255, za)
DRAWRECTANGLE(barindex, close - dlayH * i, barindex + projBars, close - dlayH * (i + 1)) COLOURED(zr, zg, 255, 0) FILLCOLOR(zr, zg, 255, za)
NEXT
ENDIF
//----------------------------------------------
// === LABELS (threshold, median time, probability of being hit first) ===
//----------------------------------------------
IF showLabels = 1 THEN
lblX = barindex + projBars + labelShift
thrTxt = round(thresholdPct * 10) / 10
upProb = round(upRate * 10) / 10
dnProb = round(dnRate * 10) / 10
uMed = $fN[10]
dMed = $fN[11]
FOR side = 0 TO 1 DO
IF side = 0 THEN
lu = $fU[10]
ly = upThr
lr = 76
lg = 175
lb = 80
ELSE
lu = $fU[11]
ly = dnThr
lr = 242
lg = 54
lb = 69
ENDIF
IF labelSize = 0 THEN
lfs = 8
ELSIF labelSize = 1 THEN
lfs = 10
ELSIF labelSize = 3 THEN
lfs = 14
ELSIF labelSize = 4 THEN
lfs = 18
ELSE
lfs = 12
ENDIF
IF side = 0 THEN
IF lu = 0 THEN
IF lfs = 8 THEN
DRAWTEXT("↑ #thrTxt#% 50%: #uMed#m Prob: #upProb#%", lblX, ly, sansserif, bold, 8) COLOURED(lr, lg, lb, 230)
ELSIF lfs = 10 THEN
DRAWTEXT("↑ #thrTxt#% 50%: #uMed#m Prob: #upProb#%", lblX, ly, sansserif, bold, 10) COLOURED(lr, lg, lb, 230)
ELSIF lfs = 14 THEN
DRAWTEXT("↑ #thrTxt#% 50%: #uMed#m Prob: #upProb#%", lblX, ly, sansserif, bold, 14) COLOURED(lr, lg, lb, 230)
ELSIF lfs = 18 THEN
DRAWTEXT("↑ #thrTxt#% 50%: #uMed#m Prob: #upProb#%", lblX, ly, sansserif, bold, 18) COLOURED(lr, lg, lb, 230)
ELSE
DRAWTEXT("↑ #thrTxt#% 50%: #uMed#m Prob: #upProb#%", lblX, ly, sansserif, bold, 12) COLOURED(lr, lg, lb, 230)
ENDIF
ELSIF lu = 1 THEN
IF lfs = 8 THEN
DRAWTEXT("↑ #thrTxt#% 50%: #uMed#h Prob: #upProb#%", lblX, ly, sansserif, bold, 8) COLOURED(lr, lg, lb, 230)
ELSIF lfs = 10 THEN
DRAWTEXT("↑ #thrTxt#% 50%: #uMed#h Prob: #upProb#%", lblX, ly, sansserif, bold, 10) COLOURED(lr, lg, lb, 230)
ELSIF lfs = 14 THEN
DRAWTEXT("↑ #thrTxt#% 50%: #uMed#h Prob: #upProb#%", lblX, ly, sansserif, bold, 14) COLOURED(lr, lg, lb, 230)
ELSIF lfs = 18 THEN
DRAWTEXT("↑ #thrTxt#% 50%: #uMed#h Prob: #upProb#%", lblX, ly, sansserif, bold, 18) COLOURED(lr, lg, lb, 230)
ELSE
DRAWTEXT("↑ #thrTxt#% 50%: #uMed#h Prob: #upProb#%", lblX, ly, sansserif, bold, 12) COLOURED(lr, lg, lb, 230)
ENDIF
ELSIF lu = 2 THEN
IF lfs = 8 THEN
DRAWTEXT("↑ #thrTxt#% 50%: #uMed#d Prob: #upProb#%", lblX, ly, sansserif, bold, 8) COLOURED(lr, lg, lb, 230)
ELSIF lfs = 10 THEN
DRAWTEXT("↑ #thrTxt#% 50%: #uMed#d Prob: #upProb#%", lblX, ly, sansserif, bold, 10) COLOURED(lr, lg, lb, 230)
ELSIF lfs = 14 THEN
DRAWTEXT("↑ #thrTxt#% 50%: #uMed#d Prob: #upProb#%", lblX, ly, sansserif, bold, 14) COLOURED(lr, lg, lb, 230)
ELSIF lfs = 18 THEN
DRAWTEXT("↑ #thrTxt#% 50%: #uMed#d Prob: #upProb#%", lblX, ly, sansserif, bold, 18) COLOURED(lr, lg, lb, 230)
ELSE
DRAWTEXT("↑ #thrTxt#% 50%: #uMed#d Prob: #upProb#%", lblX, ly, sansserif, bold, 12) COLOURED(lr, lg, lb, 230)
ENDIF
ELSE
IF lfs = 8 THEN
DRAWTEXT("↑ #thrTxt#% 50%: N/A Prob: #upProb#%", lblX, ly, sansserif, bold, 8) COLOURED(lr, lg, lb, 230)
ELSIF lfs = 10 THEN
DRAWTEXT("↑ #thrTxt#% 50%: N/A Prob: #upProb#%", lblX, ly, sansserif, bold, 10) COLOURED(lr, lg, lb, 230)
ELSIF lfs = 14 THEN
DRAWTEXT("↑ #thrTxt#% 50%: N/A Prob: #upProb#%", lblX, ly, sansserif, bold, 14) COLOURED(lr, lg, lb, 230)
ELSIF lfs = 18 THEN
DRAWTEXT("↑ #thrTxt#% 50%: N/A Prob: #upProb#%", lblX, ly, sansserif, bold, 18) COLOURED(lr, lg, lb, 230)
ELSE
DRAWTEXT("↑ #thrTxt#% 50%: N/A Prob: #upProb#%", lblX, ly, sansserif, bold, 12) COLOURED(lr, lg, lb, 230)
ENDIF
ENDIF
ELSE
IF lu = 0 THEN
IF lfs = 8 THEN
DRAWTEXT("↓ #thrTxt#% 50%: #dMed#m Prob: #dnProb#%", lblX, ly, sansserif, bold, 8) COLOURED(lr, lg, lb, 230)
ELSIF lfs = 10 THEN
DRAWTEXT("↓ #thrTxt#% 50%: #dMed#m Prob: #dnProb#%", lblX, ly, sansserif, bold, 10) COLOURED(lr, lg, lb, 230)
ELSIF lfs = 14 THEN
DRAWTEXT("↓ #thrTxt#% 50%: #dMed#m Prob: #dnProb#%", lblX, ly, sansserif, bold, 14) COLOURED(lr, lg, lb, 230)
ELSIF lfs = 18 THEN
DRAWTEXT("↓ #thrTxt#% 50%: #dMed#m Prob: #dnProb#%", lblX, ly, sansserif, bold, 18) COLOURED(lr, lg, lb, 230)
ELSE
DRAWTEXT("↓ #thrTxt#% 50%: #dMed#m Prob: #dnProb#%", lblX, ly, sansserif, bold, 12) COLOURED(lr, lg, lb, 230)
ENDIF
ELSIF lu = 1 THEN
IF lfs = 8 THEN
DRAWTEXT("↓ #thrTxt#% 50%: #dMed#h Prob: #dnProb#%", lblX, ly, sansserif, bold, 8) COLOURED(lr, lg, lb, 230)
ELSIF lfs = 10 THEN
DRAWTEXT("↓ #thrTxt#% 50%: #dMed#h Prob: #dnProb#%", lblX, ly, sansserif, bold, 10) COLOURED(lr, lg, lb, 230)
ELSIF lfs = 14 THEN
DRAWTEXT("↓ #thrTxt#% 50%: #dMed#h Prob: #dnProb#%", lblX, ly, sansserif, bold, 14) COLOURED(lr, lg, lb, 230)
ELSIF lfs = 18 THEN
DRAWTEXT("↓ #thrTxt#% 50%: #dMed#h Prob: #dnProb#%", lblX, ly, sansserif, bold, 18) COLOURED(lr, lg, lb, 230)
ELSE
DRAWTEXT("↓ #thrTxt#% 50%: #dMed#h Prob: #dnProb#%", lblX, ly, sansserif, bold, 12) COLOURED(lr, lg, lb, 230)
ENDIF
ELSIF lu = 2 THEN
IF lfs = 8 THEN
DRAWTEXT("↓ #thrTxt#% 50%: #dMed#d Prob: #dnProb#%", lblX, ly, sansserif, bold, 8) COLOURED(lr, lg, lb, 230)
ELSIF lfs = 10 THEN
DRAWTEXT("↓ #thrTxt#% 50%: #dMed#d Prob: #dnProb#%", lblX, ly, sansserif, bold, 10) COLOURED(lr, lg, lb, 230)
ELSIF lfs = 14 THEN
DRAWTEXT("↓ #thrTxt#% 50%: #dMed#d Prob: #dnProb#%", lblX, ly, sansserif, bold, 14) COLOURED(lr, lg, lb, 230)
ELSIF lfs = 18 THEN
DRAWTEXT("↓ #thrTxt#% 50%: #dMed#d Prob: #dnProb#%", lblX, ly, sansserif, bold, 18) COLOURED(lr, lg, lb, 230)
ELSE
DRAWTEXT("↓ #thrTxt#% 50%: #dMed#d Prob: #dnProb#%", lblX, ly, sansserif, bold, 12) COLOURED(lr, lg, lb, 230)
ENDIF
ELSE
IF lfs = 8 THEN
DRAWTEXT("↓ #thrTxt#% 50%: N/A Prob: #dnProb#%", lblX, ly, sansserif, bold, 8) COLOURED(lr, lg, lb, 230)
ELSIF lfs = 10 THEN
DRAWTEXT("↓ #thrTxt#% 50%: N/A Prob: #dnProb#%", lblX, ly, sansserif, bold, 10) COLOURED(lr, lg, lb, 230)
ELSIF lfs = 14 THEN
DRAWTEXT("↓ #thrTxt#% 50%: N/A Prob: #dnProb#%", lblX, ly, sansserif, bold, 14) COLOURED(lr, lg, lb, 230)
ELSIF lfs = 18 THEN
DRAWTEXT("↓ #thrTxt#% 50%: N/A Prob: #dnProb#%", lblX, ly, sansserif, bold, 18) COLOURED(lr, lg, lb, 230)
ELSE
DRAWTEXT("↓ #thrTxt#% 50%: N/A Prob: #dnProb#%", lblX, ly, sansserif, bold, 12) COLOURED(lr, lg, lb, 230)
ENDIF
ENDIF
ENDIF
NEXT
ENDIF
//----------------------------------------------
// === RESULTS TABLE (anchored to the window, top-right) ===
// Columns: level | upside | downside. Row height 20 px.
// Rows are contiguous, as in the original (its unused row numbers take no space).
//----------------------------------------------
c2R = dashX
c2L = dashX - 100
c1R = c2L
c1L = c1R - 100
c0R = c1L
c0L = c0R - 130
c0X = (c0L + c0R) / 2
c1X = (c1L + c1R) / 2
c2X = (c2L + c2R) / 2
// header
hy = dashY
DRAWRECTANGLE(c0L, hy + 10, c0R, hy - 10) ANCHOR(TOPRIGHT, XSHIFT, YSHIFT) COLOURED(255, 255, 255, 255) FILLCOLOR(33, 150, 243, 255)
DRAWRECTANGLE(c1L, hy + 10, c1R, hy - 10) ANCHOR(TOPRIGHT, XSHIFT, YSHIFT) COLOURED(255, 255, 255, 255) FILLCOLOR(76, 175, 80, 255)
DRAWRECTANGLE(c2L, hy + 10, c2R, hy - 10) ANCHOR(TOPRIGHT, XSHIFT, YSHIFT) COLOURED(255, 255, 255, 255) FILLCOLOR(242, 54, 69, 255)
IF distType = 0 THEN
DRAWTEXT("Percentile", c0X, hy, sansserif, bold, 10) COLOURED(255, 255, 255, 255) ANCHOR(TOPRIGHT, XSHIFT, YSHIFT)
ELSE
DRAWTEXT("Std Dev", c0X, hy, sansserif, bold, 10) COLOURED(255, 255, 255, 255) ANCHOR(TOPRIGHT, XSHIFT, YSHIFT)
ENDIF
thrHd = round(thresholdPct * 10) / 10
DRAWTEXT("Upside +#thrHd#%", c1X, hy, sansserif, bold, 10) COLOURED(255, 255, 255, 255) ANCHOR(TOPRIGHT, XSHIFT, YSHIFT)
DRAWTEXT("Downside -#thrHd#%", c2X, hy, sansserif, bold, 10) COLOURED(255, 255, 255, 255) ANCHOR(TOPRIGHT, XSHIFT, YSHIFT)
// percentile / sigma rows
FOR k = 0 TO nRows - 1 DO
ry = dashY - 20 * (k + 1)
IF (k MOD 2) = 0 THEN
ga = 102
ELSE
ga = 64
ENDIF
DRAWRECTANGLE(c0L, ry + 10, c0R, ry - 10) ANCHOR(TOPRIGHT, XSHIFT, YSHIFT) COLOURED(255, 255, 255, 255) FILLCOLOR(120, 123, 134, ga)
DRAWRECTANGLE(c1L, ry + 10, c1R, ry - 10) ANCHOR(TOPRIGHT, XSHIFT, YSHIFT) COLOURED(255, 255, 255, 255) FILLCOLOR(76, 175, 80, 102)
DRAWRECTANGLE(c2L, ry + 10, c2R, ry - 10) ANCHOR(TOPRIGHT, XSHIFT, YSHIFT) COLOURED(255, 255, 255, 255) FILLCOLOR(242, 54, 69, 102)
rowPct = $pctL[k]
IF distType = 0 THEN
DRAWTEXT("#rowPct#%", c0X, ry, sansserif, standard, 10) COLOURED(0, 0, 0, 255) ANCHOR(TOPRIGHT, XSHIFT, YSHIFT)
ELSIF k = 0 THEN
DRAWTEXT("2σ (2.28%)", c0X, ry, sansserif, standard, 10) COLOURED(0, 0, 0, 255) ANCHOR(TOPRIGHT, XSHIFT, YSHIFT)
ELSE
DRAWTEXT("1σ (15.87%)", c0X, ry, sansserif, standard, 10) COLOURED(0, 0, 0, 255) ANCHOR(TOPRIGHT, XSHIFT, YSHIFT)
ENDIF
NEXT
// sigma mode: theoretical minimum row
IF distType = 1 THEN
nTime = 2 * nRows + 2
ELSE
nTime = 2 * nRows
ENDIF
IF distType = 1 THEN
ry = dashY - 20 * (nRows + 1)
DRAWRECTANGLE(c0L, ry + 10, c0R, ry - 10) ANCHOR(TOPRIGHT, XSHIFT, YSHIFT) COLOURED(255, 255, 255, 255) FILLCOLOR(156, 39, 176, 255)
DRAWRECTANGLE(c1L, ry + 10, c1R, ry - 10) ANCHOR(TOPRIGHT, XSHIFT, YSHIFT) COLOURED(255, 255, 255, 255) FILLCOLOR(156, 39, 176, 102)
DRAWRECTANGLE(c2L, ry + 10, c2R, ry - 10) ANCHOR(TOPRIGHT, XSHIFT, YSHIFT) COLOURED(255, 255, 255, 255) FILLCOLOR(156, 39, 176, 102)
DRAWTEXT("Theoretical Min", c0X, ry, sansserif, standard, 9) COLOURED(255, 255, 255, 255) ANCHOR(TOPRIGHT, XSHIFT, YSHIFT)
ENDIF
// time cells: slot, column centre, row centre, "~" prefix
FOR j = 0 TO nTime - 1 DO
IF j < nRows THEN
slot = j
cx = c1X
cy = dashY - 20 * (j + 1)
pre = 0
ELSIF j < 2 * nRows THEN
slot = 5 + j - nRows
cx = c2X
cy = dashY - 20 * (j - nRows + 1)
pre = 0
ELSIF j = 2 * nRows THEN
slot = 12
cx = c1X
cy = dashY - 20 * (nRows + 1)
pre = 1
ELSE
slot = 13
cx = c2X
cy = dashY - 20 * (nRows + 1)
pre = 1
ENDIF
tv = $fN[slot]
tu = $fU[slot]
IF pre = 0 THEN
IF tu = 0 THEN
DRAWTEXT("#tv#m", cx, cy, sansserif, standard, 10) COLOURED(0, 0, 0, 255) ANCHOR(TOPRIGHT, XSHIFT, YSHIFT)
ELSIF tu = 1 THEN
DRAWTEXT("#tv#h", cx, cy, sansserif, standard, 10) COLOURED(0, 0, 0, 255) ANCHOR(TOPRIGHT, XSHIFT, YSHIFT)
ELSIF tu = 2 THEN
DRAWTEXT("#tv#d", cx, cy, sansserif, standard, 10) COLOURED(0, 0, 0, 255) ANCHOR(TOPRIGHT, XSHIFT, YSHIFT)
ELSE
DRAWTEXT("N/A", cx, cy, sansserif, standard, 10) COLOURED(0, 0, 0, 255) ANCHOR(TOPRIGHT, XSHIFT, YSHIFT)
ENDIF
ELSE
IF tu = 0 THEN
DRAWTEXT("~#tv#m", cx, cy, sansserif, standard, 9) COLOURED(0, 0, 0, 255) ANCHOR(TOPRIGHT, XSHIFT, YSHIFT)
ELSIF tu = 1 THEN
DRAWTEXT("~#tv#h", cx, cy, sansserif, standard, 9) COLOURED(0, 0, 0, 255) ANCHOR(TOPRIGHT, XSHIFT, YSHIFT)
ELSE
DRAWTEXT("~#tv#d", cx, cy, sansserif, standard, 9) COLOURED(0, 0, 0, 255) ANCHOR(TOPRIGHT, XSHIFT, YSHIFT)
ENDIF
ENDIF
NEXT
// first hit rate
IF distType = 1 THEN
rowN = nRows + 2
ELSE
rowN = nRows + 1
ENDIF
ry = dashY - 20 * rowN
upRt = round(upRate * 10) / 10
dnRt = round(dnRate * 10) / 10
DRAWRECTANGLE(c0L, ry + 10, c0R, ry - 10) ANCHOR(TOPRIGHT, XSHIFT, YSHIFT) COLOURED(255, 255, 255, 255) FILLCOLOR(255, 152, 0, 255)
DRAWRECTANGLE(c1L, ry + 10, c1R, ry - 10) ANCHOR(TOPRIGHT, XSHIFT, YSHIFT) COLOURED(255, 255, 255, 255) FILLCOLOR(76, 175, 80, 102)
DRAWRECTANGLE(c2L, ry + 10, c2R, ry - 10) ANCHOR(TOPRIGHT, XSHIFT, YSHIFT) COLOURED(255, 255, 255, 255) FILLCOLOR(242, 54, 69, 102)
DRAWTEXT("First Hit (#upFirst# ↑ #dnFirst# ↓)", c0X, ry, sansserif, standard, 9) COLOURED(255, 255, 255, 255) ANCHOR(TOPRIGHT, XSHIFT, YSHIFT)
DRAWTEXT("#upRt#%", c1X, ry, sansserif, standard, 10) COLOURED(0, 0, 0, 255) ANCHOR(TOPRIGHT, XSHIFT, YSHIFT)
DRAWTEXT("#dnRt#%", c2X, ry, sansserif, standard, 10) COLOURED(0, 0, 0, 255) ANCHOR(TOPRIGHT, XSHIFT, YSHIFT)
// warning when many paths never reach a barrier
IF totalFirst < numSims * 0.9 THEN
rowN = rowN + 1
ry = dashY - 20 * rowN
DRAWRECTANGLE(c0L, ry + 10, c0R, ry - 10) ANCHOR(TOPRIGHT, XSHIFT, YSHIFT) COLOURED(255, 255, 255, 255) FILLCOLOR(255, 152, 0, 255)
DRAWRECTANGLE(c1L, ry + 10, c1R, ry - 10) ANCHOR(TOPRIGHT, XSHIFT, YSHIFT) COLOURED(255, 255, 255, 255) FILLCOLOR(255, 152, 0, 102)
DRAWRECTANGLE(c2L, ry + 10, c2R, ry - 10) ANCHOR(TOPRIGHT, XSHIFT, YSHIFT) COLOURED(255, 255, 255, 255) FILLCOLOR(255, 152, 0, 102)
DRAWTEXT("⚠ Low Hit Rate", c0X, ry, sansserif, standard, 9) COLOURED(255, 255, 255, 255) ANCHOR(TOPRIGHT, XSHIFT, YSHIFT)
DRAWTEXT("Increase Max", c1X, ry, sansserif, standard, 9) COLOURED(0, 0, 0, 255) ANCHOR(TOPRIGHT, XSHIFT, YSHIFT)
DRAWTEXT("Periods!", c2X, ry, sansserif, standard, 9) COLOURED(0, 0, 0, 255) ANCHOR(TOPRIGHT, XSHIFT, YSHIFT)
ENDIF
// average time when hit
rowN = rowN + 1
ry = dashY - 20 * rowN
DRAWRECTANGLE(c0L, ry + 10, c0R, ry - 10) ANCHOR(TOPRIGHT, XSHIFT, YSHIFT) COLOURED(255, 255, 255, 255) FILLCOLOR(255, 152, 0, 255)
DRAWRECTANGLE(c1L, ry + 10, c1R, ry - 10) ANCHOR(TOPRIGHT, XSHIFT, YSHIFT) COLOURED(255, 255, 255, 255) FILLCOLOR(76, 175, 80, 102)
DRAWRECTANGLE(c2L, ry + 10, c2R, ry - 10) ANCHOR(TOPRIGHT, XSHIFT, YSHIFT) COLOURED(255, 255, 255, 255) FILLCOLOR(242, 54, 69, 102)
DRAWTEXT("Avg Time (if hit)", c0X, ry, sansserif, standard, 9) COLOURED(255, 255, 255, 255) ANCHOR(TOPRIGHT, XSHIFT, YSHIFT)
FOR j = 0 TO 1 DO
IF j = 0 THEN
tv = $fN[14]
tu = $fU[14]
cx = c1X
ELSE
tv = $fN[15]
tu = $fU[15]
cx = c2X
ENDIF
IF tu = 0 THEN
DRAWTEXT("#tv#m", cx, ry, sansserif, standard, 10) COLOURED(0, 0, 0, 255) ANCHOR(TOPRIGHT, XSHIFT, YSHIFT)
ELSIF tu = 1 THEN
DRAWTEXT("#tv#h", cx, ry, sansserif, standard, 10) COLOURED(0, 0, 0, 255) ANCHOR(TOPRIGHT, XSHIFT, YSHIFT)
ELSIF tu = 2 THEN
DRAWTEXT("#tv#d", cx, ry, sansserif, standard, 10) COLOURED(0, 0, 0, 255) ANCHOR(TOPRIGHT, XSHIFT, YSHIFT)
ELSE
DRAWTEXT("N/A", cx, ry, sansserif, standard, 10) COLOURED(0, 0, 0, 255) ANCHOR(TOPRIGHT, XSHIFT, YSHIFT)
ENDIF
NEXT
// directional bias
rowN = rowN + 1
ry = dashY - 20 * rowN
biasStr = round(abs(upRate - dnRate) * 10) / 10
IF upRate > dnRate THEN
bR = 76
bG = 175
bB = 80
ELSIF dnRate > upRate THEN
bR = 242
bG = 54
bB = 69
ELSE
bR = 120
bG = 123
bB = 134
ENDIF
DRAWRECTANGLE(c0L, ry + 10, c0R, ry - 10) ANCHOR(TOPRIGHT, XSHIFT, YSHIFT) COLOURED(255, 255, 255, 255) FILLCOLOR(255, 152, 0, 255)
DRAWRECTANGLE(c1L, ry + 10, c1R, ry - 10) ANCHOR(TOPRIGHT, XSHIFT, YSHIFT) COLOURED(255, 255, 255, 255) FILLCOLOR(bR, bG, bB, 102)
DRAWRECTANGLE(c2L, ry + 10, c2R, ry - 10) ANCHOR(TOPRIGHT, XSHIFT, YSHIFT) COLOURED(255, 255, 255, 255) FILLCOLOR(120, 123, 134, 102)
DRAWTEXT("Directional Bias", c0X, ry, sansserif, standard, 10) COLOURED(255, 255, 255, 255) ANCHOR(TOPRIGHT, XSHIFT, YSHIFT)
IF upRate > dnRate THEN
DRAWTEXT("Bullish ↑", c1X, ry, sansserif, bold, 10) COLOURED(0, 0, 0, 255) ANCHOR(TOPRIGHT, XSHIFT, YSHIFT)
ELSIF dnRate > upRate THEN
DRAWTEXT("Bearish ↓", c1X, ry, sansserif, bold, 10) COLOURED(0, 0, 0, 255) ANCHOR(TOPRIGHT, XSHIFT, YSHIFT)
ELSE
DRAWTEXT("Neutral ↔", c1X, ry, sansserif, bold, 10) COLOURED(0, 0, 0, 255) ANCHOR(TOPRIGHT, XSHIFT, YSHIFT)
ENDIF
DRAWTEXT("#biasStr#%", c2X, ry, sansserif, standard, 10) COLOURED(0, 0, 0, 255) ANCHOR(TOPRIGHT, XSHIFT, YSHIFT)
// diagnostics: annualised drift (scaled by the square root of the periods per year) and drift mode
periodsYear = 525600 / tfMin
IF showDiag = 1 THEN
rowN = rowN + 1
ry = dashY - 20 * rowN
annDrift = round(driftRaw * sqrt(periodsYear) * 100 * 100) / 100
DRAWRECTANGLE(c0L, ry + 10, c0R, ry - 10) ANCHOR(TOPRIGHT, XSHIFT, YSHIFT) COLOURED(255, 255, 255, 255) FILLCOLOR(156, 39, 176, 255)
DRAWRECTANGLE(c1L, ry + 10, c2R, ry - 10) ANCHOR(TOPRIGHT, XSHIFT, YSHIFT) COLOURED(255, 255, 255, 255) FILLCOLOR(156, 39, 176, 102)
DRAWTEXT("Ann. Drift", c0X, ry, sansserif, standard, 9) COLOURED(255, 255, 255, 255) ANCHOR(TOPRIGHT, XSHIFT, YSHIFT)
DRAWTEXT("#annDrift#%", c1X, ry, sansserif, standard, 9) COLOURED(0, 0, 0, 255) ANCHOR(TOPRIGHT, XSHIFT, YSHIFT)
rowN = rowN + 1
ry = dashY - 20 * rowN
DRAWRECTANGLE(c0L, ry + 10, c0R, ry - 10) ANCHOR(TOPRIGHT, XSHIFT, YSHIFT) COLOURED(255, 255, 255, 255) FILLCOLOR(156, 39, 176, 255)
DRAWRECTANGLE(c1L, ry + 10, c2R, ry - 10) ANCHOR(TOPRIGHT, XSHIFT, YSHIFT) COLOURED(255, 255, 255, 255) FILLCOLOR(156, 39, 176, 102)
DRAWTEXT("Drift Mode", c0X, ry, sansserif, standard, 9) COLOURED(255, 255, 255, 255) ANCHOR(TOPRIGHT, XSHIFT, YSHIFT)
IF driftMode = 1 THEN
DRAWTEXT("Zero (Neutral)", c1X, ry, sansserif, standard, 9) COLOURED(0, 0, 0, 255) ANCHOR(TOPRIGHT, XSHIFT, YSHIFT)
ELSIF driftMode = 2 THEN
DRAWTEXT("50% Reduced", c1X, ry, sansserif, standard, 9) COLOURED(0, 0, 0, 255) ANCHOR(TOPRIGHT, XSHIFT, YSHIFT)
ELSE
DRAWTEXT("Historical", c1X, ry, sansserif, standard, 9) COLOURED(0, 0, 0, 255) ANCHOR(TOPRIGHT, XSHIFT, YSHIFT)
ENDIF
ENDIF
// annualised volatility
rowN = rowN + 1
ry = dashY - 20 * rowN
annVol = round(volat * sqrt(periodsYear) * 100 * 100) / 100
DRAWRECTANGLE(c0L, ry + 10, c0R, ry - 10) ANCHOR(TOPRIGHT, XSHIFT, YSHIFT) COLOURED(255, 255, 255, 255) FILLCOLOR(255, 152, 0, 255)
DRAWRECTANGLE(c1L, ry + 10, c2R, ry - 10) ANCHOR(TOPRIGHT, XSHIFT, YSHIFT) COLOURED(255, 255, 255, 255) FILLCOLOR(120, 123, 134, 102)
DRAWTEXT("Ann. Volatility", c0X, ry, sansserif, standard, 10) COLOURED(255, 255, 255, 255) ANCHOR(TOPRIGHT, XSHIFT, YSHIFT)
DRAWTEXT("#annVol#%", c1X, ry, sansserif, standard, 10) COLOURED(0, 0, 0, 255) ANCHOR(TOPRIGHT, XSHIFT, YSHIFT)
ENDIF
RETURN
Conclusion
First Passage Time turns volatility into something a trader can plan with: a waiting time and a probability. It does not predict direction, but it makes the cost of time visible, which is often the missing piece when choosing between a tight and a wide target. Use it as a sanity check before setting targets, stops or expiries, and remember that its numbers inherit the assumptions of the random walk behind them.
Download
Filename:
PRC_First-Passage-Time.itf
Downloads:
5
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