QuanTAlib/lib/volume/iii/Iii.md

III: Intraday Intensity Index

Property	Value
Category	Volume
Inputs	OHLCV bar (TBar)
Parameters	period (default 14), cumulative (default false)
Outputs	Single series (III)
Output range	Unbounded
Warmup	period bars

TL;DR

• The Intraday Intensity Index (III) measures buying and selling pressure by analyzing where the close price falls within the high-low range, weighte...
• Parameterized by period (default 14), cumulative (default false).
• Output range: Unbounded.
• Requires period bars of warmup before first valid output (IsHot = true).
• Validated against TA-Lib, Skender, and Tulip reference implementations where available.

"Where the close lands within the day's range tells you who won the battle—bulls or bears. Volume tells you how hard they fought."

The Intraday Intensity Index (III) measures buying and selling pressure by analyzing where the close price falls within the high-low range, weighted by volume. Originally developed by David Bostian, this indicator quantifies whether money is flowing into or out of a security on an intraday basis. Values range from -1 (close at low, maximum selling pressure) to +1 (close at high, maximum buying pressure), multiplied by volume for magnitude.

Historical Context

David Bostian developed the Intraday Intensity Index in the 1980s as a way to measure money flow within the trading day. The concept builds on the intuition that the closing price's position within the day's range reveals whether buyers or sellers controlled the session.

Unlike indicators that only look at price direction or volume alone, III combines both: a close near the high with heavy volume suggests strong accumulation, while a close near the low with heavy volume indicates distribution. This makes III particularly useful for confirming price trends and identifying potential reversals through divergences.

Architecture & Physics

The indicator operates in two modes: smoothed (default) and cumulative.

1. Position Multiplier

The core calculation determines where the close falls within the high-low range:

PM_t = \begin{cases}
\frac{2 \times C_t - H_t - L_t}{H_t - L_t} & \text{if } H_t \neq L_t \\
0 & \text{if } H_t = L_t
\end{cases}

The position multiplier ranges from:

• +1: Close equals High (maximum bullish)
• 0: Close at midpoint (neutral)
• -1: Close equals Low (maximum bearish)

2. Raw Intensity

The raw III value multiplies position by volume:

III_{raw,t} = PM_t \times V_t

This weights the directional signal by the conviction behind it (volume).

3. Smoothing / Accumulation

In smoothed mode (default), a Simple Moving Average is applied:

III_t = \frac{1}{n} \sum_{i=0}^{n-1} III_{raw,t-i}

In cumulative mode, values are accumulated over time:

III_{cum,t} = \sum_{i=0}^{t} III_{raw,i}

Mathematical Foundation

Position Multiplier Derivation

The formula (2C - H - L) / (H - L) can be rewritten as:

PM = \frac{(C - L) - (H - C)}{H - L} = \frac{2(C - M)}{H - L}

where M = (H + L) / 2 is the midpoint. This shows that PM measures how far the close deviates from the midpoint, normalized by the range.

Interpretation

• PM > 0: Close above midpoint → buyers dominated
• PM < 0: Close below midpoint → sellers dominated
• PM × V: Large volume amplifies the signal

Smoothed vs Cumulative

• Smoothed: Shows recent average buying/selling pressure; oscillates around zero
• Cumulative: Shows cumulative money flow over time; trends with price

Performance Profile

Operation Count (Streaming Mode, Scalar)

Operation	Count	Cost (cycles)	Subtotal
SUB	3	1	3
MUL	1	3	3
DIV	1	15	15
CMP	1	1	1
Ring buffer update	1	~5	5
Total	7	—	~27 cycles

The algorithm is simple and efficient with O(1) streaming complexity.

Quality Metrics

Metric	Score	Notes
Accuracy	9/10	Mathematically exact
Timeliness	7/10	SMA smoothing adds lag
Simplicity	9/10	Intuitive formula
Usefulness	8/10	Good for divergence analysis

Validation

III is a relatively uncommon indicator in mainstream libraries, but the algorithm is straightforward.

Library	Status	Notes
TA-Lib	N/A	Not implemented
Skender	N/A	Not implemented
Tulip	N/A	Not implemented
Ooples	N/A	Not implemented
PineScript	✅	Reference implementation

Validation focuses on internal consistency (streaming vs batch vs span modes).

Common Pitfalls

1. Warmup Period: The indicator requires period bars before the SMA is fully primed. Before warmup, values are averaged over available data.

2. Zero Range: When High equals Low (flat bars), the position multiplier is undefined. The implementation returns 0 in this case.

3. Volume Importance: III is volume-weighted, so low-volume bars contribute less. Zero volume is treated as minimum value of 1 to avoid division issues.

4. Cumulative vs Smoothed: Cumulative mode creates a trending line that can grow unbounded; smoothed mode oscillates. Choose based on use case.

5. Scale Dependency: Raw III values scale with volume, making cross-security comparison difficult without normalization.

6. Bar Corrections: The isNew=false parameter allows updating the current bar. State rollback restores the previous state before recalculating.

References

• Bostian, D. "Intraday Intensity Index." Technical Analysis of Stocks & Commodities.
• Arms, R. W. (1989). "The Arms Index (TRIN)." Dow Jones-Irwin.