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# Volume-Weighted Z-Score (V-Score) Projected Bands Pro (v3.10)
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Quantitative Rolling Gaussian Volatility Envelopes & Dynamic Fair-Value Bands Suite
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---
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## 1. Summary (Introduction)
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**V-Score Bands Pro** is an institutional-grade on-chart volatility envelope that projects the statistical deviation thresholds of the **V-Score (VWAP Z-Score)** directly onto the candlestick chart around the Volume-Weighted Average Price.
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While standard Bollinger Bands project moving standard deviations around an unweighted, lagging Moving Average (SMA), **V-Score Bands Pro anchors its centerline to the true Volume-Weighted Average Price (VWAP)**. It projects three dynamic, rolling standard deviation bands above and below VWAP:
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1. **Flow Bands ($\pm 1.50\sigma$):** The institutional momentum flow channel (Point of No Return).
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2. **Extreme Bands ($\pm 2.00\sigma$):** Statistical overbought/oversold boundaries.
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3. **Wall Bands ($\pm 2.50\sigma$):** Extreme climax exhaustion caps (Reversal Walls).
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```text
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┌────────────────────────────────────────────────────────────────────────┐
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│ V-SCORE BANDS ON-CHART ENVELOPE │
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├────────────────────────────────────────────────────────────────────────┤
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│ Upper Wall: VWAP(t) + [2.50 × σ_rolling(t)] (clrMidnightBlue) │
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│ Upper Extreme: VWAP(t) + [2.00 × σ_rolling(t)] (clrDeepSkyBlue) │
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│ Upper Flow: VWAP(t) + [1.50 × σ_rolling(t)] (clrLightSkyBlue) │
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│ Centerline: Volume-Weighted Average Price (clrOrange) │
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│ Lower Flow: VWAP(t) - [1.50 × σ_rolling(t)] (clrCoral) │
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│ Lower Extreme: VWAP(t) - [2.00 × σ_rolling(t)] (clrOrangeRed) │
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│ Lower Wall: VWAP(t) - [2.50 × σ_rolling(t)] (clrDarkRed) │
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└────────────────────────────────────────────────────────────────────────┘
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```
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### Core Architectural Distinctions
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* **`VWAP_Bands_Pro` vs `VScore_Bands_Pro`:** `VWAP_Bands_Pro` calculates *cumulative* standard deviation anchored from the session open (bands start at $\sigma=0$ and widen over time). `VScore_Bands_Pro` calculates *rolling* standard deviation over the last $N = \text{InpPeriod}$ bars, providing an **open-ended, continuous volatility channel** across all session opens.
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* **14-Buffer Synchronized Architecture:** Employs dual Odd/Even buffers for the VWAP centerline and all 6 band levels, guaranteeing zero diagonal connecting lines across session resets.
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* **Open-Ended Session Sampling:** Intelligently samples across overnight non-session gaps to preserve authentic rolling market volatility at custom session opens (e.g. LSE 08:00).
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* **Unified 2026 MTF Framework:** Synchronized with `DataSync_Tools.mqh` to project higher-timeframe V-Score envelopes (e.g. H1 or Daily) onto lower-timeframe execution charts (M1, M5, M15) with flat, non-warping steps.
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---
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## 2. Mathematical Foundations & Rolling Dispersion
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```text
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Upper Wall: VWAP + (2.50 · σ)
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═══════════════════════════════════════════════════════════ clrMidnightBlue
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Upper Extreme: VWAP + (2.00 · σ)
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─────────────────────────────────────────────────────────── clrDeepSkyBlue
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Upper Flow: VWAP + (1.50 · σ)
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- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - clrLightSkyBlue
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Centerline: VWAP Equilibrium
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─────────────────────────────────────────────────────────── clrOrange
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Lower Flow: VWAP - (1.50 · σ)
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- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - clrCoral
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Lower Extreme: VWAP - (2.00 · σ)
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─────────────────────────────────────────────────────────── clrOrangeRed
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Lower Wall: VWAP - (2.50 · σ)
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═══════════════════════════════════════════════════════════ clrDarkRed
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```
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### 2.1. Volume-Weighted Centerline ($\mu_{\text{VWAP}, t}$)
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$$\mu_{\text{VWAP}, t} = \frac{\sum_{k=\text{anchor}}^{t} \text{TP}_k \cdot V_k}{\sum_{k=\text{anchor}}^{t} V_k}$$
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### 2.2. Rolling Standard Deviation Around VWAP ($\sigma_t$)
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To maintain natural open ends across custom session boundaries, standard deviation samples the last $P = \text{InpPeriod}$ valid in-session bars:
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$$\text{Diff}_k = C_k - \mu_{\text{VWAP}, k}$$
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$$\sigma_t = \sqrt{\frac{1}{P} \sum_{k \in \text{valid session bars}}^{P} \left( \text{Diff}_k \right)^2}$$
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### 2.3. Dynamic Envelope Band Projections
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$$\text{Upper Flow}_t = \mu_{\text{VWAP}, t} + (L_{\text{Flow}} \cdot \sigma_t), \quad\quad \text{Lower Flow}_t = \mu_{\text{VWAP}, t} - (L_{\text{Flow}} \cdot \sigma_t)$$
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$$\text{Upper Extr}_t = \mu_{\text{VWAP}, t} + (L_{\text{Extr}} \cdot \sigma_t), \quad\quad \text{Lower Extr}_t = \mu_{\text{VWAP}, t} - (L_{\text{Extr}} \cdot \sigma_t)$$
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$$\text{Upper Wall}_t = \mu_{\text{VWAP}, t} + (L_{\text{Wall}} \cdot \sigma_t), \quad\quad \text{Lower Wall}_t = \mu_{\text{VWAP}, t} - (L_{\text{Wall}} \cdot \sigma_t)$$
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*where $L_{\text{Flow}} = 1.50$, $L_{\text{Extr}} = 2.00$, and $L_{\text{Wall}} = 2.50$.*
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---
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## 3. MQL5 Architecture & Engineering Standards
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```text
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┌────────────────────────────────────────────────────────┐
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│ VWAP_Calculator.mqh │
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│ (Core Engine: Deterministic Stateless VWAP Evaluator)│
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└──────────────────────────┬─────────────────────────────┘
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│ Outputs Base VWAP Odd/Even Buffers in O(1)
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▼
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┌────────────────────────────────────────────────────────┐
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│ VScore_Bands_Pro.mq5 │
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│ (Unified Wrapper: Native Timeframe & MTF Engine) │
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├──────────────────────────┬─────────────────────────────┤
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│ Buffer Layer (14) │ Centralized Framework │
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│ • 2 Centerline Plots │ • DataSync_Tools.mqh │
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│ • 12 Volatility Bands │ • Staircase Flat-Force │
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│ • Gapped Odd/Even Lines│ • Open-Ended Sampling │
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└──────────────────────────┴─────────────────────────────┘
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```
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1. **14-Buffer Odd/Even Gapped Engine:** Prevents diagonal line artifacts across session resets by toggling odd session bars to `Buf..._Odd` and even session bars to `Buf..._Even`.
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2. **Open-Ended In-Session Sampling:** Scans backward to collect genuine in-session variance across off-session gaps, ensuring the envelope begins with wide, natural boundaries on the opening bar of custom trading windows.
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3. **2026 MTF Framework with Staircase Solution:** Maps higher-timeframe rolling envelopes onto lower-timeframe charts using `first_bar_of_forming_htf` dynamic anchoring and `DataSync_Tools.mqh`.
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---
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## 4. Parameters Reference
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### Timeframe Settings
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* `InpTimeframe` (*default: `PERIOD_CURRENT`*): Calculation timeframe. When set to `PERIOD_CURRENT`, it operates in native zero-lag mode. When set to a higher timeframe (e.g., `PERIOD_M15`, `PERIOD_H1`), it activates the synchronized MTF engine.
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### V-Score Core Settings
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* `InpPeriod` (*default: `20`*): Rolling lookback period ($P$) for computing standard deviation around VWAP.
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* `InpVWAPReset` (*default: `PERIOD_SESSION`*): VWAP anchor reset mode (`PERIOD_SESSION`, `PERIOD_WEEK`, `PERIOD_MONTH`, `PERIOD_CUSTOM_SESSION`).
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* `InpTzShift` (*default: `0`*): Timezone offset in hours vs broker server time.
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* `InpCustomSessionStart` (*default: `"09:30"`*): Session start time (`HH:MM`).
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* `InpCustomSessionEnd` (*default: `"16:00"`*): Session end time (`HH:MM`).
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### Calculation Settings
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* `InpVolumeType` (*default: `VOLUME_TICK`*): Volume data source (`VOLUME_TICK` or `VOLUME_REAL`).
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* `InpCandleSource` (*default: `CANDLE_STANDARD`*): Price source (`CANDLE_STANDARD` or `CANDLE_HEIKIN_ASHI`).
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### V-Score Z-Levels (Standard Deviations)
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* `InpLevelFlow` (*default: `1.5`*): Flow boundary multiplier ($\pm 1.50\sigma$).
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* `InpLevelExtreme` (*default: `2.0`*): Extreme boundary multiplier ($\pm 2.00\sigma$).
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* `InpLevelWall` (*default: `2.5`*): Climax Exhaustion Wall multiplier ($\pm 2.50\sigma$).
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### Visual Settings
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* Independent color, style, and width controls for the VWAP centerline and all three level-pairs (`Flow`, `Extreme`, `Wall`).
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---
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## 5. Institutional Trading Playbooks
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```text
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┌────────────────────────────────────────────────────────────────────────┐
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│ V-SCORE BANDS TRADING PLAYBOOKS │
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├────────────────────────────────────────────────────────────────────────┤
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│ 1. Flow Channel Breakout: Ride momentum when candles close beyond │
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│ Upper/Lower Flow Band (±1.5σ). │
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│ 2. Extreme Reversal Fade: Look for pin-bar rejection at Extreme (±2.0σ)│
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│ targeting mean reversion back to VWAP. │
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│ 3. Wall Climax Bounce: Touch of the ±2.5σ Wall represents an │
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│ exhaustion ceiling; initiate counter-trades. │
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└────────────────────────────────────────────────────────────────────────┘
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```
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### 5.1. The Flow Channel Trend Expansion ($\pm 1.50\sigma$)
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* **Bullish Expansion:** Price breaks above the `Bull Flow Band (+1.50σ)` and holds $\rightarrow$ Institutional momentum markup is confirmed. Ride long positions with trailing stop anchored to the VWAP centerline.
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* **Bearish Expansion:** Price breaks below the `Bear Flow Band (-1.50σ)` and holds $\rightarrow$ Institutional markdown is active.
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### 5.2. The 2.0σ Extreme Mean Reversion Fade
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* **Context:** Market is in a rotational or ranging regime.
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* **Short Entry:** Price thrusts into the `Bull Extreme Band (+2.00σ)` and forms a rejection wick $\rightarrow$ Target: VWAP Centerline ($0.0\sigma$).
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* **Long Entry:** Price drops into the `Bear Extreme Band (-2.00σ)` and rejects $\rightarrow$ Target: VWAP Centerline ($0.0\sigma$).
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### 5.3. The 2.5σ Exhaustion Wall Reversal
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* A sharp spike into the **`Bull Wall (+2.50σ)`** (`clrMidnightBlue`) or **`Bear Wall (-2.50σ)`** (`clrDarkRed`) represents a $99\%$ statistical tail event.
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* When this coincides with volume exhaustion or divergence on `VScore_Pro`, it signals an institutional blow-off climax, offering prime asymmetrical risk-to-reward reversal opportunities.
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---
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## 6. Indicator Buffer Map (For Developers & EA Integration)
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| Buffer Index | Name | Type | Description |
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| :---: | :---: | :--- | :--- |
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| **0** | `BufVWAP_Odd` | `INDICATOR_DATA` | VWAP Centerline (Odd Periods) |
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| **1** | `BufVWAP_Even` | `INDICATOR_DATA` | VWAP Centerline (Even Periods - Gapped) |
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| **2** | `BufUpFlow_Odd` | `INDICATOR_DATA` | Upper Flow Band ($+1.50\sigma$, Odd Periods) |
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| **3** | `BufUpFlow_Even` | `INDICATOR_DATA` | Upper Flow Band ($+1.50\sigma$, Even Periods) |
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| **4** | `BufDnFlow_Odd` | `INDICATOR_DATA` | Lower Flow Band ($-1.50\sigma$, Odd Periods) |
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| **5** | `BufDnFlow_Even` | `INDICATOR_DATA` | Lower Flow Band ($-1.50\sigma$, Even Periods) |
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| **6** | `BufUpExtr_Odd` | `INDICATOR_DATA` | Upper Extreme Band ($+2.00\sigma$, Odd Periods) |
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| **7** | `BufUpExtr_Even` | `INDICATOR_DATA` | Upper Extreme Band ($+2.00\sigma$, Even Periods) |
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| **8** | `BufDnExtr_Odd` | `INDICATOR_DATA` | Lower Extreme Band ($-2.00\sigma$, Odd Periods) |
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| **9** | `BufDnExtr_Even` | `INDICATOR_DATA` | Lower Extreme Band ($-2.00\sigma$, Even Periods) |
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| **10** | `BufUpWall_Odd` | `INDICATOR_DATA` | Upper Wall Band ($+2.50\sigma$, Odd Periods) |
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| **11** | `BufUpWall_Even` | `INDICATOR_DATA` | Upper Wall Band ($+2.50\sigma$, Even Periods) |
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| **12** | `BufDnWall_Odd` | `INDICATOR_DATA` | Lower Wall Band ($-2.50\sigma$, Odd Periods) |
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| **13** | `BufDnWall_Even` | `INDICATOR_DATA` | Lower Wall Band ($-2.50\sigma$, Even Periods) |
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*All buffers strictly maintain non-series chronological order (`ArraySetAsSeries = false`), ensuring seamless integration with Expert Advisors via `iCustom()`.*
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