Discrete Stochastic Volatility Optimal Stopping## Technical Documentation: Discrete Approximation of Bivariate Optimal Stopping Boundaries
### Overview
This document outlines the mathematical methodology for discretizing a continuous-time stochastic volatility model to identify optimal execution boundaries. The algorithm maps an asset's price and variance processes into standardized state spaces to detect joint extrema, triggering execution when predefined statistical thresholds are breached.
---
### 1. Price Process Normalization
To evaluate structural price dislocation, the raw asset price $P_t$ is transformed into a standardized normal state space (Z-score).
**Mathematical Formulation:**
$$Z^{(S)}_t = \frac{P_t - \mu_S}{\sigma_S}$$
Where the sample mean ($\mu_S$) and sample standard deviation ($\sigma_S$) are calculated over an $N$-period lookback window:
* **Sample Mean:** $\mu_S = \frac{1}{N} \sum_{i=0}^{N-1} P_{t-i}$
* **Sample Standard Deviation:** $\sigma_S = \sqrt{\frac{1}{N} \sum_{i=0}^{N-1} (P_{t-i} - \mu_S)^2}$
**Purpose:** This isolates the magnitude of the price deviation relative to its recent equilibrium, providing the orthogonal $x$-axis for the state space.
---
### 2. Instantaneous Variance Estimation
Continuous-time models rely on instantaneous variance, which is unobservable in discrete time. The algorithm approximates this using the annualized rolling realized variance of geometric returns.
**Mathematical Formulation:**
$$v_t = \frac{252}{N} \sum_{i=0}^{N-1} r_{t-i}^2$$
Where the continuously compounded return $r_t$ is defined as:
$$r_t = \ln\left(\frac{P_t}{P_{t-1}}\right)$$
**Purpose:** Assuming the mean daily return is zero ($\mu \approx 0$), the squared log return $r_t^2$ serves as an unbiased estimator of daily variance. The factor $\frac{252}{N}$ standardizes the sum of these squared returns into an annualized volatility metric ($v_t$).
---
### 3. Variance Process Normalization
Because variance $v_t$ is heteroskedastic and mean-reverting, the empirical variance series must also be standardized to evaluate expansion or compression relative to its own baseline.
**Mathematical Formulation:**
$$Z^{(v)}_t = \frac{v_t - \mu_v}{\sigma_v}$$
Where $\mu_v$ and $\sigma_v$ are the $N$-period sample mean and standard deviation of the variance series $v_t$.
**Purpose:** This yields a unitless metric representing the statistical extremity of the current volatility regime, forming the orthogonal $y$-axis of the state space.
---
### 4. Boundary Evaluation Logic
The discrete optimal stopping conditions approximate the analytical Hamilton-Jacobi-Bellman (HJB) boundaries by evaluating the intersection of the two state variables ($Z^{(S)}_t$ and $Z^{(v)}_t$) against arbitrary static thresholds ($\alpha$ for maxima, $\beta$ for minima).
**Entry Condition (Buy):**
Execution is triggered exclusively at the joint minimum of price and variance, defined by the logical intersection:
$$\tau_B = \inf \{ t \ge 0 \mid (Z^{(S)}_t \le \beta_S) \land (Z^{(v)}_t \le \beta_v) \}$$
*Requires price to be heavily discounted while the market regime is highly compressed.*
**Exit Condition (Sell):**
Liquidation is triggered exclusively at the joint maximum, defined by the logical intersection:
$$\tau_S = \inf \{ t \ge \tau_B \mid (Z^{(S)}_t \ge \alpha_S) \land (Z^{(v)}_t \ge \alpha_v) \}$$
*Requires price to be statistically overextended during a regime of extreme variance expansion.* Indicator
Price*Volume Z-Score OscillatorUseful for finding statistically significant order blocks for OTM options on stocks. Used to find "informed traders".
To understand the math behind this indicator, we have to break it down into three distinct layers: the **Variable Construction**, the **Central Limit Theorem application**, and the **Z-Transformation**.
---
### 1. The Variable: Dollar Volume ( BMV:PV $)
Instead of looking at Price or Volume in isolation, we create a composite variable:
$$PV_t = P_t \times V_t$$
* **$P_t$**: The closing price at time $t$.
* **$V_t$**: The number of shares/contracts traded at time $t$.
This represents the total **nominal value** flowing through the asset. It is a more rigorous measure of market conviction than volume alone because it accounts for the capital required to move the price at that specific level.
---
### 2. The Moving Window (Rolling Statistics)
We don't compare the current BMV:PV $ to the beginning of time; we compare it to a **lookback window** ($n=20$).
#### The Arithmetic Mean ($\mu$)
We calculate the Simple Moving Average of the BMV:PV $ product:
$$\mu_{PV} = \frac{1}{n} \sum_{i=0}^{n-1} PV_{t-i}$$
This establishes the "expected" liquidity environment for the current regime.
#### The Standard Deviation ($\sigma$)
We measure the dispersion (volatility) of the BMV:PV $ product over that same window:
$$\sigma_{PV} = \sqrt{\frac{1}{n} \sum_{i=0}^{n-1} (PV_{t-i} - \mu_{PV})^2}$$
This tells us how much the "Dollar Volume" typically fluctuates. If $\sigma$ is high, the market is erratic; if $\sigma$ is low, the market is consistent.
---
### 3. The Z-Score Transformation
The Z-score is a "dimensionless" number. It strips away the dollar signs and the share counts, leaving only a pure measure of **distance in units of volatility**.
$$Z = \frac{PV_{current} - \mu_{PV}}{\sigma_{PV}}$$
* **If $Z = 0$**: The current Dollar Volume is exactly average.
* **If $Z = 1$**: The current Dollar Volume is 1 Standard Deviation above average.
* **If $Z = 4$**: The current Dollar Volume is an extreme outlier.
---
### 4. The "4 StDev" Threshold (Statistical Significance)
Why is $Z \ge 4$ significant? We use the **Empirical Rule** and **Chebyshev’s Inequality** to understand the probability:
| Z-Score | Probability (Normal Dist.) | Frequency of Occurrence |
| --- | --- | --- |
| **1.0** | 68.2% | Common |
| **2.0** | 95.4% | Significant (95th percentile) |
| **3.0** | 99.7% | Rare (The "Three-Sigma" event) |
| **4.0** | **99.993%** | **Extreme Outlier** |
In a perfectly normal distribution, a Z-score of 4 should only happen roughly **once every 15,000 bars**.
> **The Reality of "Fat Tails":** Financial data is not perfectly normal; it has "leptokurtosis" (fat tails). This means 4 StDev events happen more often than 0.01% in trading. When you see $Z > 4$, you aren't seeing random noise; you are seeing a **non-random liquidity shock**—likely institutional block trades or massive delta-hedging rebalancing.
### Why this matters for your 0DTE research:
In 0DTE options, Gamma is at its peak. A $Z > 4$ event in the underlying BMV:PV $ product suggests a sudden burst of activity that can force market makers to hedge aggressively. Since $Z$ is rolling, the "average" adapts to the day's volatility, ensuring that a "spike" in the morning is measured differently than a "spike" during the slow lunch hour.
Indicator
Twiggs Go Money Flow Enhanced [KingThies]█ OVERVIEW
The Twiggs Money Flow (TMF) is a volume-weighted momentum oscillator that
measures buying and sellistng pressure by analyzing where price closes within
each bar's true range. It's an enhanced version of Chaikin Money Flow that
uses Wilder's smoothing method, providing better trend persistence and
smoother signals.
The indicator oscillates around a zero listne:
Values above zero indicate accumulation (buying pressure)
Values below zero indicate distribution (sellistng pressure)
TMF was developed by Colistn Twiggs as an improvement over traditional money
flow indicators by incorporating true range calculations and Wilder's
exponential moving average.
█ CONCEPTS
True Range Boundaries
TMF calculates a modified true range for each bar by comparing the current
bar's high and low with the previous close:
True Range High = maximum of (previous close, current high)
True Range Low = minimum of (previous close, current low)
This accounts for overnight gaps and ensures price continuity between bars.
Average Daily Value (ADV)
The ADV represents the portion of volume attributable to buying versus sellistng:
ADV = Volume × ((Close - TR Low) - (TR High - Close)) / True Range
When price closes near the high of the true range, ADV is positive and large.
When price closes near the low, ADV is negative and large.
A close in the middle produces values near zero.
Wilder's Moving Average
Unlistke simple moving averages, Wilder's smoothing method gives more weight
to recent values while maintaining memory of historical data:
WMA = (Previous WMA × (Period - 1) + Current Value) / Period
This creates smoother trends that are less prone to whipsaws than standard
moving averages.
Final Calculation
TMF = Wilder's MA(ADV, Period) / Wilder's MA(Volume, Period)
By dividing smoothed ADV by smoothed volume, TMF normalistzes the reading and
makes it comparable across different securities and timeframes.
█ HOW TO USE
Zero listne Crossovers
The most straightforward trading signals:
A cross above zero suggests buyers are gaining control.
Consider this a bullistsh signal, especially when confirmed by price action.
A cross below zero suggests sellers are gaining control.
Consider this a bearish signal.
The longer TMF remains above or below zero, the stronger the trend.
Extreme Values
Strong positive or negative readings indicate intense buying or sellistng pressure:
Sustained high positive values (above +0.4) suggest strong accumulation
but may also indicate overbought conditions.
Sustained low negative values (below -0.4) suggest strong distribution
but may also indicate oversold conditions.
These extremes work best when used in conjunction with price levels and
support/resistance zones.
Divergences
Divergences between price and TMF often signal potential reversals:
Bearish divergence: Price makes a higher high but TMF makes a
lower high — suggests buying pressure is weakening despite rising prices.
Bullistsh divergence: Price makes a lower low but TMF makes a
higher low — suggests sellistng pressure is weakening despite fallistng prices.
Trend Confirmation
Use TMF to confirm the strength of existing trends:
In an uptrend, TMF should remain mostly positive with occasional dips below zero.
In a downtrend, TMF should remain mostly negative with occasional rises above zero.
If TMF contradicts the price trend, consider the trend weak or potentially ending.
█ FEATURES
Period (default: 21)
The lookback length for Wilder's moving average calculation:
Shorter periods (10–15) make TMF more responsive to recent changes but
increase noise and false signals.
Longer periods (30–50) create smoother readings but lag price action more
significantly.
The default 21-period setting balances responsiveness with relistabilistty.
Consider adjusting the period based on your trading timeframe and the
volatilistty of the security you're analyzing.
█ LIMITATIONS
TMF is a lagging indicator due to its smoothing method. Signals may occur
after optimal entry or exit points.
In low-volume or illistquid markets, TMF can produce erratic readings that
may not reflect true buying or sellistng pressure.
Ranging or choppy markets often generate frequent zero-listne crosses that
can lead to whipsaws.
listke all volume-based indicators, TMF's relistabilistty depends on accurate
volume data.
For securities with unrelistable volume reporting, consider using
price-based momentum indicators instead.
█ NOTES
This indicator uses area-style plotting in the original version to visualistze
the magnitude of buying and sellistng pressure. The filled area makes it easy
to see at a glance whether the market is in accumulation or distribution mode.
TMF works on any timeframe but tends to be most relistable on daily charts
where volume data is most accurate and meaningful.
█ CREDITS
Original indicator developed by
LazyBear .
Based on the Twiggs Money Flow concept from Incredible Charts:
Incredible Charts – Twiggs Money Flow .
Indicator
Fibonacci-Based Volume Flow (VFI)Fibonacci-based Volume Flow is an advanced next-generation evolution of LazyBear’s original VFI script that calculates and averages up to 21 Fibonacci-based VFI pairings to create a smoothed composite volume flow signal. This unique and powerful approach reduces noise, adapts to volatility, and provides a clearer view of trend strength and market structure across all timeframes. It also includes dynamic fibonacci guide levels, adaptive lookbacks, EMA crossovers, and structure-aware pivot labeling to help traders identify high-quality reversals, confirm directional bias, and detect divergences with greater precision. It's ideal for traders looking to enhance momentum analysis through volume-based confirmation.
🧠 Key Features🧠
🔹 Multi-VFI Fibonacci Fusion🔹
Blends up to 21 VFI signals (5, 13, 21, 34… up to 610) into smartly paired averages (e.g., 13/34, 55/144) — forming a smoothed composite VFI that’s more adaptive, less noisy, and highly responsive across market conditions.
🔸🔸 Dynamic Lookbacks🔸 🔸
Automatically adjusts histogram high/low tracking based on your chart’s timeframe — no more static tuning. Perfect for scalping fast charts or confirming long-term trends.
🟥🟩 Color-Coded Histogram🟥🟩
Visualizes VFI momentum with gradient coloring.
🧩🧩 Signal Crossovers 🧩🧩
Color-coded crossover lines persistently show bullish or bearish dominance.
Includes three powerful crossover systems:
➖5/13 VFI: Fast, early reversal detection
➖8/21 VFI: Swing-trading sweet spot
➖55/144 VFI: Trend confirmation across long cycles
🏷️ 🏷️Pivot Structure Labels🏷️🏷️
Labels oscillator swings with full structural logic:
➖HH, HL, LH, LL, EQ
➖Displays percent change, price at pivot, oscillator reading
➖Smart coloring detects divergence & trend continuation
📈 📈Dynamic Histogram Guides📈📈
Optional zero and ±50% bands anchor histogram levels based on real histogram extremes, not static thresholds — visually frame momentum shifts with context.
📍 📍Persistent High/Low Pivot Lines📍📍
Track the most significant histogram pivots (not price) across time, with smart labels:
➖Volume flow structure zones
➖Label shows price at pivot, oscillator level, and bars since event
➖Ideal for spotting divergence zones, momentum failures, and trend exhaustion.
🔍 🔍Volatility Table (ATR%)🔍🔍
💡Shows real-time volatility compression or expansion
💡Uses multiple ATR periods (e.g., 14 & 55) for short- and medium-term comparison
💡Helps traders understand whether momentum is likely to continue or stall
🔩🔩Volume-weighted VFI baselines🔩🔩
🟢A daily session-based VWAP of the VFI, which resets each day and highlights intraday volume flow context.
🟠A rolling VWA of VFI, which acts like a VWMA over a fixed window (e.g., 55 bars), smoothing short-term fluctuations and supporting trend/momentum confirmation.
These VWAP-style overlays help traders identify strength vs. weakness relative to volume-weighted baselines — useful for divergence spotting, mean reversion setups, or breakout confirmation.
🧰 🧰Under the Hood: How It Works🧰🧰
🔧 Core VFI Logic
Based on LazyBear’s foundational VFI:
➖Uses log returns of price (HLC3)
➖Filters insignificant moves using volatility-weighted thresholds
➖Normalizes volume via adaptive capping (e.g., 2.5× average)
🌀 Composite Blend System
Each VFI instance is smoothed and then fused via user-selectable pairs. This creates a customizable average VFI representing short, mid, and long-term pressure — one value, many time horizons.
📊 EMA Signal Layer
Crosses trigger persistent color shifts in signal lines, making trend strength clear at a glance.
VFI blend feeds into EMA crossovers. You can toggle visibility for:
➖Fast (5/13)
➖Medium (8/21)
➖Slow (55/144)
🧭 Pivot Framework
Structure logic only compares pivots on same-side polarity:
➖Highs compare to highs above zero
➖Lows compare to lows below zero
This avoids nonsensical comparisons and preserves logical sequences (HH → LH → HL).
🧱 Dynamic Labels
All pivots and persistent levels display:
➖Oscillator value
➖Price value
➖Structure tag (e.g., LH, HL)
➖% change from prior pivot
➖Lookback info
➖Bar age
Unlike traditional VFI:
✅ It blends timeframes with Fibonacci precision
✅ Uses dynamic, volatility-aware logic
✅ Embeds visual structure & divergence intelligence
✅ Enhances entry confidence and exit timing
🔧 This isn’t just an indicator — it’s a volume-informed decision engine.
Ideal For:
🔶Trend-followers wanting cleaner volume-based confirmation
🔶Reversal traders spotting structure + divergence
🔶Scalpers or investors needing adaptable signals
🔶Those who loved LazyBear's VFI
📌 Final Note:
As powerful as Fibonacci Blended Volume Flow is, no single indicator should be used in isolation. For best results, combine it with price action analysis, higher-timeframe context, and complementary tools like trendlines, moving averages, or support/resistance levels. Use it as part of a well-rounded trading approach to confirm setups — not to define them alone. Indicator
Adaptive Squeeze Momentum +Adaptive Squeeze Momentum+ (Auto-Timeframe Version)
Overview
Adaptive Squeeze Momentum+ is an enhanced volatility and momentum indicator designed to identify compression and expansion phases in price action. It is inspired by the classic Squeeze Momentum Indicator by LazyBear but introduces automatic parameter adaptation to any timeframe, making it simpler to use across different markets without manual configuration.
Concepts and Methodology
The script combines Bollinger Bands (BB) and Keltner Channels (KC) to detect periods when volatility contracts (squeeze) or expands (release).
A squeeze occurs when BB are inside KC, suggesting low volatility and potential breakout scenarios.
A squeeze release is detected when BB expand outside KC.
Momentum is derived using a linear regression applied to the difference between price and a midrange reference level.
Original Improvements
Compared to the original Squeeze Momentum Indicator, this version offers several enhancements:
Automatic Adaptation: BB and KC lengths and multipliers are dynamically adjusted based on the chart’s timeframe (from 1 minute up to 1 month), removing the need for manual tuning.
Simplified Visualization: A clean, minimalist histogram and clear squeeze state cross markers allow for faster interpretation.
Flexible Application: Designed to work consistently on intraday, daily, and higher timeframes across crypto, forex, stocks, and indices.
Features
Dynamic Squeeze Detection:
Gray Cross: Neutral (no squeeze detected)
Blue Cross: Active squeeze
Yellow Cross: Squeeze released
Momentum Histogram:
Positive/negative momentum shown with slope-based coloring.
Timeframe-Aware Parameters:
Automatically sets optimal BB/KC configurations.
Usage
Watch for blue crosses indicating an active squeeze phase that may precede a directional move.
Use the histogram color and slope to gauge momentum strength and direction.
Combine squeeze release signals with momentum confirmation for potential entries or exits.
Credits and Licensing
This script was inspired by LazyBear’s OLD “Squeeze Momentum Indicator” (). The implementation here significantly expands upon the original by introducing auto-adaptive parameters, restructured logic, and a new visualization approach. Published under the Mozilla Public License 2.0.
Disclaimer
This indicator is for educational purposes only and does not constitute financial advice. Use at your own risk.
Indicator
RSI-Adaptive T3 + Squeeze Momentum Strategy✅ Strategy Guide: RSI-Adaptive T3 + Squeeze Momentum Strategy
📌 Overview
The RSI-Adaptive T3 + Squeeze Momentum Strategy is a dynamic trend-following strategy based on an RSI-responsive T3 moving average and Squeeze Momentum detection .
It adapts in real-time to market volatility to enhance entry precision and optimize risk.
⚠️ This strategy is provided for educational and research purposes only.
Past performance does not guarantee future results.
🎯 Strategy Objectives
The main objective of this strategy is to catch the early phase of a trend and generate consistent entry signals.
Designed to be intuitive and accessible for traders from beginner to advanced levels.
✨ Key Features
RSI-Responsive T3: T3 length dynamically adjusts according to RSI values for adaptive trend detection
Squeeze Momentum: Combines Bollinger Bands and Keltner Channels to identify trend buildup phases
Visual Triggers: Entry signals are generated from T3 crossovers and momentum strength after squeeze release
📊 Trading Rules
Long Entry:
When T3 crosses upward, momentum is positive, and the squeeze has just been released.
Short Entry:
When T3 crosses downward, momentum is negative, and the squeeze has just been released.
Exit (Reversal):
When the opposite condition to the entry is triggered, the position is reversed.
💰 Risk Management Parameters
Pair & Timeframe: BTC/USD (30-minute chart)
Capital (simulated): $30,00
Order size: `$100` per trade (realistic, low-risk sizing)
Commission: 0.02%
Slippage: 2 pips
Risk per Trade: 5%
Number of Trades (backtest period): 181
📊 Performance Overview
Symbol: BTC/USD
Timeframe: 30-minute chart
Date Range: January 1, 2024 – July 3, 2025
Win Rate: 47.8%
Profit Factor: 2.01
Net Profit: 173.16 (units not specified)
Max Drawdown: 5.77% or 24.91 (0.79%)
⚙️ Indicator Parameters
Indicator Name: RSI-Adaptive T3 + Squeeze Momentum
RSI Length: 14
T3 Min Length: 5
T3 Max Length: 50
T3 Volume Factor: 0.7
BB Length: 27 (Multiplier: 2.0)
KC Length: 20 (Multiplier: 1.5, TrueRange enabled)
🖼 Visual Support
T3 slope direction, squeeze status, and momentum bars are visually plotted on the chart,
providing high clarity for quick trend analysis and execution.
🔧 Strategy Improvements & Uniqueness
Inspired by the RSI Adaptive T3 by ChartPrime and Squeeze Momentum Indicator by LazyBear ,
this strategy fuses both into a hybrid trend-reversal and momentum breakout detection system .
Compared to traditional trend-following methods, it excels at capturing early trend signals with greater sensitivity .
✅ Summary
The RSI-Adaptive T3 + Squeeze Momentum Strategy combines momentum detection with volatility-responsive risk management.
With a strong balance between visual clarity and practicality, it serves as a powerful tool for traders seeking high repeatability.
⚠️ This strategy is based on historical data and does not guarantee future profits.
Always use appropriate risk management when applying it. Strategy
TTM Squeeze Momentum MTF [Cometreon]TTM Squeeze Momentum MTF combines the core logic of both the Squeeze Momentum by LazyBear and the TTM Squeeze by John Carter into a single, unified indicator. It offers a complete system to analyze the phase, direction, and strength of market movements.
Unlike the original versions, this indicator allows you to choose how to calculate the trend, select from 15 different types of moving averages, customize every parameter, and adapt the visual style to your trading preferences.
If you are looking for a powerful, flexible and highly configurable tool, this is the perfect choice for you.
🔷 New Features and Improvements
🟩 Unified System: Trend Detection + Visual Style
You can decide which logic to use for the trend via the "Show TTM Squeeze Trend" input:
✅ Enabled → Trend calculated using TTM Squeeze
❌ Disabled → Trend based on Squeeze Momentum
You can also customize the visual style of the indicator:
✅ Enable "Show Histogram" for a visual mode using Histogram, Area, or Column
❌ Disable it to display the classic LazyBear-style line
Everything updates automatically and dynamically based on your selection.
🟩 Full Customization
Every base parameter of the original indicator is now fully configurable: lengths, sources, moving average types, and more.
You can finally adapt the squeeze logic to your strategy — not the other way around.
🟩 Multi-MA Engine
Choose from 15 different Moving Averages for each part of the calculation:
SMA (Simple Moving Average)
EMA (Exponential Moving Average)
WMA (Weighted Moving Average)
RMA (Smoothed Moving Average)
HMA (Hull Moving Average)
JMA (Jurik Moving Average)
DEMA (Double Exponential Moving Average)
TEMA (Triple Exponential Moving Average)
LSMA (Least Squares Moving Average)
VWMA (Volume-Weighted Moving Average)
SMMA (Smoothed Moving Average)
KAMA (Kaufman’s Adaptive Moving Average)
ALMA (Arnaud Legoux Moving Average)
FRAMA (Fractal Adaptive Moving Average)
VIDYA (Variable Index Dynamic Average)
🟩 Dynamic Signal Line
Apply a moving average to the momentum for real-time cross signals, with full control over its length and type.
🟩 Multi-Timeframe & Multi-Ticker Support
You're no longer limited to the chart's current timeframe or ticker. Apply the squeeze to any symbol or timeframe without repainting.
🔷 Technical Details and Customizable Inputs
This indicator offers a fully modular structure with configurable parameters for every component:
1️⃣ Squeeze Momentum Settings – Choose the source, length, and type of moving average used to calculate the base momentum.
2️⃣ Trend Mode Selector – Toggle "Show TTM Squeeze Trend" to select the trend logic displayed on the chart:
✅ Enabled – Shows the trend based on TTM Squeeze (Bollinger Bands inside/outside Keltner Channel)
❌ Disabled – Displays the trend based on Squeeze Momentum logic
🔁 The moving average type for the Keltner Channel is handled automatically, so you don't need to select it manually, even if the custom input is disabled.
3️⃣ Signal Line – Toggle the Signal Line on the Squeeze Momentum. Select its length and MA type to generate visual cross signals.
4️⃣ Bollinger Bands – Configure the length, multiplier, source, and MA type used in the bands.
5️⃣ Keltner Channel – Adjust the length, multiplier, source, and MA type. You can also enable or disable the True Range option.
6️⃣ Advanced MA Parameters – Customize the parameters for advanced MAs (JMA, ALMA, FRAMA, VIDYA), including Phase, Power, Offset, Sigma, and Shift values.
7️⃣ Ticker & Input Source – Select the ticker and manage inputs for alternative chart types like Renko, Kagi, Line Break, and Point & Figure.
8️⃣ Style Settings – Choose how the squeeze is displayed:
Enable "Show Histogram" for Histogram, Area, or Column style
Disable it to show the classic LazyBear-style line
Use Reverse Color to invert line colors
Toggle Show Label to highlight Signal Line cross signals
Customize trend colors to suit your preferences
9️⃣ Multi-Timeframe Options - Timeframe – Use the squeeze on higher timeframes for stronger confirmation
🔟 Wait for Timeframe Closes -
✅ Enabled – Prevents multiple signals within the same candle
❌ Disabled – Displays the indicator smoothly without delay
🔧 Default Settings Reference
To replicate the default settings of the original indicators as they appear when first applied to the chart, use the following configurations:
🟩 TTM Squeeze (John Carter Style)
Squeeze
Length: 20
MA Type: SMA
Show TTM Squeeze Trend: Enabled
Bollinger Bands
Length: 20
Multiplier: 2.0
MA Type: SMA
Keltner Channel
Length: 20
Multiplier: 1.0
Use True Range: ON
MA Type: EMA
Style
Show Histogram: Enabled
Reverse Color: Enabled
🟩 Squeeze Momentum (LazyBear Style)
Squeeze
Length: 10
MA Type: SMA
Show TTM Squeeze Trend: Disabled
Bollinger Bands
Length: 20
Multiplier: 1.5
MA Type: SMA
Keltner Channel
Length: 10
Multiplier: 1.5
Use True Range: ON
MA Type: SMA
Style
Show Histogram: Disabled
Reverse Color: Disabled
⚠️ These values are intended as a starting point. The Cometreon indicator lets you fully customize every input to fit your trading style.
🔷 How to Use Squeeze Momentum Pro
🔍 Identifying Trends
Squeeze Momentum Pro supports two different methods for identifying the trend visually, each based on a distinct logic:
Squeeze Momentum Trend (LazyBear-style):
Displays 3 states based on the position of the Bollinger Bands relative to the Keltner Channel:
🔵 Blue = No Squeeze (BB outside KC and KC outside BB)
⚪️ White = Squeeze Active (BB fully inside KC)
⚫️ Gray = Neutral state (none of the above)
TTM Squeeze Trend (John Carter-style):
Calculates the difference in width between the Bollinger Bands and the Keltner Channel:
🟩 Green = BB width is greater than KC → potential expansion phase
🟥 Red = BB are tighter than KC → possible compression or pre-breakout
📈 Interpreting Signals
Depending on the active configuration, the indicator can provide various signals, including:
Trend color → Reflects the current compression/expansion state (based on selected mode)
Momentum value (above or below 0) → May indicate directional pressure
Signal Line cross → Can highlight momentum shifts
Color change in the momentum → May suggest a potential trend reversal
🛠 Integration with Other Tools
Squeeze Momentum Pro works well alongside other indicators to strengthen market context:
✅ Volume Profile / OBV – Helps confirm accumulation or distribution during squeezes
✅ RSI – Useful to detect divergence between momentum and price
✅ Moving Averages – Ideal for defining primary trend direction and filtering signals
☄️ If you find this indicator useful, leave a Boost to support its development!
Every piece of feedback helps improve the tool and deliver an even better trading experience.
🔥 Share your ideas or feature requests in the comments! Indicator
Squeeze Momentum Indicator Strategy [LazyBear + PineIndicators]The Squeeze Momentum Indicator Strategy (SQZMOM_LB Strategy) is an automated trading strategy based on the Squeeze Momentum Indicator developed by LazyBear, which itself is a modification of John Carter's "TTM Squeeze" concept from his book Mastering the Trade (Chapter 11). This strategy is designed to identify low-volatility phases in the market, which often precede explosive price movements, and to enter trades in the direction of the prevailing momentum.
Concept & Indicator Breakdown
The strategy employs a combination of Bollinger Bands (BB) and Keltner Channels (KC) to detect market squeezes:
Squeeze Condition:
When Bollinger Bands are inside the Keltner Channels (Black Crosses), volatility is low, signaling a potential upcoming price breakout.
When Bollinger Bands move outside Keltner Channels (Gray Crosses), the squeeze is released, indicating an expansion in volatility.
Momentum Calculation:
A linear regression-based momentum value is used instead of traditional momentum indicators.
The momentum histogram is color-coded to show strength and direction:
Lime/Green: Increasing bullish momentum
Red/Maroon: Increasing bearish momentum
Signal Colors:
Black: Market is in a squeeze (low volatility).
Gray: Squeeze is released, and volatility is expanding.
Blue: No squeeze condition is present.
Strategy Logic
The script uses historical volatility conditions and momentum trends to generate buy/sell signals and manage positions.
1. Entry Conditions
Long Position (Buy)
The squeeze just released (Gray Cross after Black Cross).
The momentum value is increasing and positive.
The momentum is at a local low compared to the past 100 bars.
The price is above the 100-period EMA.
The closing price is higher than the previous close.
Short Position (Sell)
The squeeze just released (Gray Cross after Black Cross).
The momentum value is decreasing and negative.
The momentum is at a local high compared to the past 100 bars.
The price is below the 100-period EMA.
The closing price is lower than the previous close.
2. Exit Conditions
Long Exit:
The momentum value starts decreasing (momentum lower than previous bar).
Short Exit:
The momentum value starts increasing (momentum higher than previous bar).
Position Sizing
Position size is dynamically adjusted based on 8% of strategy equity, divided by the current closing price, ensuring risk-adjusted trade sizes.
How to Use This Strategy
Apply on Suitable Markets:
Best for stocks, indices, and forex pairs with momentum-driven price action.
Works on multiple timeframes but is most effective on higher timeframes (1H, 4H, Daily).
Confirm Entries with Additional Indicators:
The author recommends ADX or WaveTrend to refine entries and avoid false signals.
Risk Management:
Since the strategy dynamically sizes positions, it's advised to use stop-losses or risk-based exits to avoid excessive drawdowns.
Final Thoughts
The Squeeze Momentum Indicator Strategy provides a systematic approach to trading volatility expansions, leveraging the classic TTM Squeeze principles with a unique linear regression-based momentum calculation. Originally inspired by John Carter’s method, LazyBear's version and this strategy offer a refined, adaptable tool for traders looking to capitalize on market momentum shifts. Strategy
Squeeze Momentum DeluxeThe Squeeze Momentum Deluxe is a comprehensive trading toolkit built with features of momentum, volatility, and price action. This script offers a suite for both mean reversion and trend-following analysis. Developed based on the original TTM Squeeze implementation by @LazyBear, this indicator introduces several innovative components to enhance your trading insights.
🔲 Components and Features
Momentum Oscillator - as rooted in the TTM Squeeze, quantifies the relationship between price and its extremes over a defined period. By normalizing the calculation, the values become comparable throughout time and across securities, allowing for a nuanced assessment of Bullish and Bearish momentum. Furthermore, by presenting it as a ribbon with a signal line we gain additional information about the direction of price swings.
Squeeze Bars - The original squeeze concept is based on the relationship between the Bollinger Bands and Keltner Channel , once the BB resides inside the KC a squeeze occurs. By understanding their fundamentals a new form of calculation can be inferred.
method bb(float src, simple int len, simple float mult) => method kc(float src, simple int len, simple float mult) =>
float basis = ta.sma (src, len) float basis = ta.sma (src, len)
float dev = ta.stdev(src, len) float rng = ta.atr ( len)
float upper = basis + dev * mult float upper = basis + rng * mult
float lower = basis - dev * mult float lower = basis - rng * mult
Both BB and KC are constructed upon a moving average with the addition of Standard Deviation and Average True Range respectively. Therefore, the calculation can be transformed to when the Stdev is lower than the ATR a squeeze occurs.
method sqz(float src, simple int len) =>
float dev = ta.stdev(src, len)
float atr = ta.atr ( len)
dev < atr ? true : false
This indicator uses three different thresholds for the ATR to gain three levels of price "Squeeze" for further analysis.
Directional Flux- This component measures the overall direction of price volatility, offering insights into trend sentiment. Presented as waves in the background, it includes an OverFlux feature to signal extreme market bias in a particular direction which can signal either exhaustion or vital continuation. Additionally, the user can choose if to base the calculation on Heikin-Ashi Candles to bias the tool toward trend assessment.
Confluence Gauges - Placed at the top and bottom of the indicator, these gauges measure confluence in the relationship between the Momentum Oscillator and Directional Flux. They provide traders with an easily interpretable visual aid for detecting market sentiment. Reversal doritos displayed alongside them contribute to mean reversion analysis.
Divergences (Real-Time) - Equipped with a custom algorithm, the indicator detects real-time divergences between price and the oscillator. This dynamic feature enhances your ability to spot potential trend reversals as they occur.
🔲 Settings
Directional Flux Length - Adjusts the period of which the background volatility waves operate on.
Trend Bias - Bases the calculation of the Flux to HA candles to bias its behavior toward the trend of price action.
Squeeze Momentum Length - Calibrates the length of the main oscillator ribbon as well as the period for the squeeze algorithm.
Signal - Controls the width of the ribbon. Lower values result in faster responsiveness at the cost of premature positives.
Divergence Sensitivity - Adjusts a threshold to limit the amount of divergences detected based on strength. Higher values result in less detections, stronger structure.
🔲 Alerts
Sell Signal
Buy Signal
Bullish Momentum
Bearish Momentum
Bullish Flux
Bearish Flux
Bullish Swing
Bearish Swing
Strong Bull Gauge
Strong Bear Gauge
Weak Bull Gauge
Weak Bear Gauge
High Squeeze
Normal Squeeze
Low Squeeze
Bullish Divergence
Bearish Divergence
As well as the option to trigger 'any alert' call.
The Squeeze Momentum Deluxe is a comprehensive tool that goes beyond traditional momentum indicators, offering a rich set of features to elevate your trading strategy. I recommend using toolkit alongside other indicators to have a wide variety of confluence to therefore gain higher probabilistic and better informed decisions. Indicator
Enhanced WaveTrend OscillatorThe Enhanced WaveTrend Oscillator is a modified version of the original WaveTrend. The WaveTrend indicator is a popular technical analysis tool used to identify overbought and oversold conditions in the market and generate trading signals. The enhanced version addresses certain limitations of the original indicator and introduces additional features for improved analysis and comparison across assets.
WaveTrend:
The original WaveTrend indicator calculates two lines based on exponential moving averages and their relationship to the asset's price. The first line measures the distance between the asset's price and its EMA, while the second line smooths the first line over a specific period. The result is divided by 0.015 multiplied by the smoothed difference ('d' for reference). The indicator aims to identify overbought and oversold conditions by analyzing the relationship between the two lines.
In the original formula, the rudimentary estimation factor 0.015 times 'd' fails to accomodate for approximately a quarter of the data, preventing the indicator from reaching the traditional stationary levels of +-100. This limitation renders the indicator quantitatively biased, as it relies on the user's subjective adjustment of the levels. The enhanced version replaces this factor with the standard deviation of the asset's price, resulting in improved estimation accuracy and provides a more dynamic and robust outcome, we thereafter multiply the result by 100 to achieve a more traditional oscillation.
Enhancements and Features:
The enhanced version of the WaveTrend indicator addresses several limitations of the original indicator and introduces additional features-
Dynamic Estimation: The original indicator uses an arbitrary estimation factor, while the enhanced version replaces it with the standard deviation of the asset's price. This modification provides a more dynamic and accurate estimation, adapting to the specific price characteristics of each asset.
Stationary Support and Resistance Levels: The enhanced version provides stationary key support and resistance levels that range from -150 to 150. These levels are determined based on the analysis of the indicator's data and encompass more than 95% of the indicator's values. These levels offer important reference points for traders to identify potential price reversals or significant price movements.
Comparison Across Assets: The enhanced version allows for better comparison and analysis across different assets. By incorporating the standard deviation of the asset's price, the indicator provides a more consistent and comparable interpretation of the market conditions across multiple assets.
Upon closer inspection of the modification in the enhanced version, we can observe that the resulting indicator is a smoothed variation of the Z-Score!
f_ewave(src, chlen, avglen) =>
basis = ta.ema(src, chlen)
dev = ta.stdev(src, chlen)
wave = (src - basis) / dev * 100
ta.ema(wave, avglen)
Z-Score Analysis:
The Z-Score is a statistical measurement that quantifies how far a particular data point deviates from the mean in terms of standard deviations. In the enhanced version, the calculation involves determining the basis (mean) and deviation (standard deviation) of the asset's price to calculate its Z-Score, thereafter applying a smoothing technique to generate the final WaveTrend value.
Utility:
The 𝗘𝗻𝗵𝗮𝗻𝗰𝗲𝗱 𝗪𝗧 indicator offers traders and investors valuable insights into overbought and oversold conditions in the market. By analyzing the indicator's values and referencing the stationary support and resistance levels, traders can identify potential trend reversals, evaluate market strength, and make better informed analysis.
It is important to note that this indicator should be used in conjunction with other technical analysis tools and indicators to confirm trading signals and validate market dynamics.
Credit:
The 𝗘𝗻𝗵𝗮𝗻𝗰𝗲𝗱 𝗪𝗧 indicator is a modification of the original WaveTrend Oscillator developed by @LazyBear on PulseWire.
Example Charts:
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1st Gray Cross Signals ━ Histogram SQZMOM [whvntr][LazyBear]This is the Histogram Version of one of my other indicators named: SQZ Momentum + 1st Gray Cross Signals (with arrows) Which is a modification of "Squeeze Momentum Indicator" by user: "LazyBear". In that indicator of his he described, and suggested, the use of his gray cross signals to find points of interest for trading based on the direction of momentum when the first gray cross appears... I have programmed these points, and highlighted them, for ease of use. The 1st gray cross strategy, he said , is from John F. Carter's book, Chapter 11, "Mastering the Trade".
Here we have the Histogram version, with background highlights only, and nothing on the chart, in true SQZ Momentum style.
Disclaimer: using this indicator, or any indicator anywhere, involves risk when trading and isn't a guarantee of 100% accurate results. Indicator
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Squeeze Momentum MTF [LPWN]//ENGLISH
Squeeze momentum of lazy bear, multiple time frames, It gives you information if the cycles with high temporality momentums are in harmony, by default two more momentums are shown, I prefer to use only one extra, in the options you can change the time frame of the momentums, in addition to the momentums you can add the RSI and ADX, if the momentum look small, you can change the value of general scale to make them bigger, the table gives us information on how the momentums and the adx are, in the options you can set the candles to color according to the harmony of the momentums
// SPANISH
Squeeze momentum de lazy bear, multiple time frames, te da informacion si los ciclos con momentums de temporalidad alta estan en armonia,por defecto se muestran dos momentums mas, yo prefiero usar solo uno extra, en las opcoines puedes cambiar la temporalidad de los momentums, ademas de los momentums puedes agregar el RSI y el ADX, si el momentum se ve pequeño, puedes cambiar el valor de general scale para hacerlos mas grandes, la tabla nos da infomracion de como estan los momentums y el adx, en las opciones puedes poner que las velas se pongan del color de acuerdo a la armonia de los momentums Indicator
WaveTrend 3D█ OVERVIEW
WaveTrend 3D (WT3D) is a novel implementation of the famous WaveTrend (WT) indicator and has been completely redesigned from the ground up to address some of the inherent shortcomings associated with the traditional WT algorithm.
█ BACKGROUND
The WaveTrend (WT) indicator has become a widely popular tool for traders in recent years. WT was first ported to PineScript in 2014 by the user @LazyBear, and since then, it has ascended to become one of the Top 5 most popular scripts on PulseWire.
The WT algorithm appears to have origins in a lesser-known proprietary algorithm called Trading Channel Index (TCI), created by AIQ Systems in 1986 as an integral part of their commercial software suite, TradingExpert Pro. The software’s reference manual states that “TCI identifies changes in price direction” and is “an adaptation of Donald R. Lambert’s Commodity Channel Index (CCI)”, which was introduced to the world six years earlier in 1980. Interestingly, a vestige of this early beginning can still be seen in the source code of LazyBear’s script, where the final EMA calculation is stored in an intermediate variable called “tci” in the code.
█ IMPLEMENTATION DETAILS
WaveTrend 3D is an alternative implementation of WaveTrend that directly addresses some of the known shortcomings of the indicator, including its unbounded extremes, susceptibility to whipsaw, and lack of insight into other timeframes.
In the canonical WT approach, an exponential moving average (EMA) for a given lookback window is used to assess the variability between price and two other EMAs relative to a second lookback window. Since the difference between the average price and its associated EMA is essentially unbounded, an arbitrary scaling factor of 0.015 is typically applied as a crude form of rescaling but still fails to capture 20-30% of values between the range of -100 to 100. Additionally, the trigger signal for the final EMA (i.e., TCI) crossover-based oscillator is a four-bar simple moving average (SMA), which further contributes to the net lag accumulated by the consecutive EMA calculations in the previous steps.
The core idea behind WT3D is to replace the EMA-based crossover system with modern Digital Signal Processing techniques. By assuming that price action adheres approximately to a Gaussian distribution, it is possible to sidestep the scaling nightmare associated with unbounded price differentials of the original WaveTrend method by focusing instead on the alteration of the underlying Probability Distribution Function (PDF) of the input series. Furthermore, using a signal processing filter such as a Butterworth Filter, we can eliminate the need for consecutive exponential moving averages along with the associated lag they bring.
Ideally, it is convenient to have the resulting probability distribution oscillate between the values of -1 and 1, with the zero line serving as a median. With this objective in mind, it is possible to borrow a common technique from the field of Machine Learning that uses a sigmoid-like activation function to transform our data set of interest. One such function is the hyperbolic tangent function (tanh), which is often used as an activation function in the hidden layers of neural networks due to its unique property of ensuring the values stay between -1 and 1. By taking the first-order derivative of our input series and normalizing it using the quadratic mean, the tanh function performs a high-quality redistribution of the input signal into the desired range of -1 to 1. Finally, using a dual-pole filter such as the Butterworth Filter popularized by John Ehlers, excessive market noise can be filtered out, leaving behind a crisp moving average with minimal lag.
Furthermore, WT3D expands upon the original functionality of WT by providing:
First-class support for multi-timeframe (MTF) analysis
Kernel-based regression for trend reversal confirmation
Various options for signal smoothing and transformation
A unique mode for visualizing an input series as a symmetrical, three-dimensional waveform useful for pattern identification and cycle-related analysis
█ SETTINGS
This is a summary of the settings used in the script listed in roughly the order in which they appear. By default, all default colors are from Google's TensorFlow framework and are considered to be colorblind safe.
Source: The input series. Usually, it is the close or average price, but it can be any series.
Use Mirror: Whether to display a mirror image of the source series; for visualizing the series as a 3D waveform similar to a soundwave.
Use EMA: Whether to use an exponential moving average of the input series.
EMA Length: The length of the exponential moving average.
Use COG: Whether to use the center of gravity of the input series.
COG Length: The length of the center of gravity.
Speed to Emphasize: The target speed to emphasize.
Width: The width of the emphasized line.
Display Kernel Moving Average: Whether to display the kernel moving average of the signal. Like PCA, an unsupervised Machine Learning technique whereby neighboring vectors are projected onto the Principal Component.
Display Kernel Signal: Whether to display the kernel estimator for the emphasized line. Like the Kernel MA, it can show underlying shifts in bias within a more significant trend by the colors reflected on the ribbon itself.
Show Oscillator Lines: Whether to show the oscillator lines.
Offset: The offset of the emphasized oscillator plots.
Fast Length: The length scale factor for the fast oscillator.
Fast Smoothing: The smoothing scale factor for the fast oscillator.
Normal Length: The length scale factor for the normal oscillator.
Normal Smoothing: The smoothing scale factor for the normal frequency.
Slow Length: The length scale factor for the slow oscillator.
Slow Smoothing: The smoothing scale factor for the slow frequency.
Divergence Threshold: The number of bars for the divergence to be considered significant.
Trigger Wave Percent Size: How big the current wave should be relative to the previous wave.
Background Area Transparency Factor: Transparency factor for the background area.
Foreground Area Transparency Factor: Transparency factor for the foreground area.
Background Line Transparency Factor: Transparency factor for the background line.
Foreground Line Transparency Factor: Transparency factor for the foreground line.
Custom Transparency: Transparency of the custom colors.
Total Gradient Steps: The maximum amount of steps supported for a gradient calculation is 256.
Fast Bullish Color: The color of the fast bullish line.
Normal Bullish Color: The color of the normal bullish line.
Slow Bullish Color: The color of the slow bullish line.
Fast Bearish Color: The color of the fast bearish line.
Normal Bearish Color: The color of the normal bearish line.
Slow Bearish Color: The color of the slow bearish line.
Bullish Divergence Signals: The color of the bullish divergence signals.
Bearish Divergence Signals: The color of the bearish divergence signals.
█ ACKNOWLEDGEMENTS
@LazyBear - For authoring the original WaveTrend port on PulseWire
@PineCoders - For the beautiful color gradient framework used in this indicator
@veryfid - For the inspiration of using mirrored signals for cycle analysis and using multiple lookback windows as proxies for other timeframes
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Squeeze Momentum Indicator [LazyBear] vHMAThis is a remake of the famous LazyBear Indicator, the Squeeze Momentum Indicator.
All i did was take out the SMA's and replace them with HMA's. HMA is a more responsive moving average.
Hull Moving Average.
This is a derivative of John Carter's "TTM Squeeze" volatility indicator, as discussed in his book "Mastering the Trade" (chapter 11).
Black crosses on the midline show that the market just entered a squeeze ( Bollinger Bands are with in Keltner Channel). This signifies low volatility , market preparing itself for an explosive move (up or down). Gray crosses signify "Squeeze release".
Mr.Carter suggests waiting till the first gray after a black cross, and taking a position in the direction of the momentum (for ex., if momentum value is above zero, go long). Exit the position when the momentum changes (increase or decrease --- signified by a color change). My (limited) experience with this shows, an additional indicator like ADX / WaveTrend, is needed to not miss good entry points. Also, Mr.Carter uses simple momentum indicator , while I have used a different method (linreg based) to plot the histogram.
More info:
- Book: Mastering The Trade by John F Carter
Here is the original version:
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