QuanTAlib/lib/dynamics/super/Super.md

SUPER: SuperTrend

Property	Value
Category	Dynamic
Inputs	OHLCV bar (TBar)
Parameters	period (default 10), multiplier (default 3.0)
Outputs	Multiple series (UpperBand, LowerBand)
Output range	Varies (see docs)
Warmup	> period + 1 bars

TL;DR

• SuperTrend is a trend-following overlay that uses ATR-scaled bands around the HL2 midpoint, switching between upper and lower bands based on close ...
• Parameterized by period (default 10), multiplier (default 3.0).
• Output range: Varies (see docs).
• Requires > period + 1 bars of warmup before first valid output (IsHot = true).
• Validated against TA-Lib, Skender, and Tulip reference implementations where available.

"It's not an indicator; it's a trailing stop with a marketing budget."

SuperTrend is a trend-following overlay that uses ATR-scaled bands around the HL2 midpoint, switching between upper and lower bands based on close price breakouts. A ratchet mechanism prevents the active band from moving against the trend, creating a step-like trailing stop that adapts to volatility. The indicator is a two-state machine (bullish/bearish) with O(1) per-bar updates and zero allocations in the hot path.

Historical Context

Olivier Seban created SuperTrend, which gained massive popularity in the retail trading community for its visual simplicity: a single line that is green during uptrends and red during downtrends. The construction combines Wilder's ATR volatility measurement (1978) with a breakout/ratchet mechanism. Unlike moving-average crossover systems that produce continuous values, SuperTrend outputs a binary trend state with a concrete stop level, making it directly actionable as a trailing stop-loss. The indicator does not repaint historical values, though the current bar's value can oscillate until the close is finalized.

Architecture & Physics

1. Basic Bands

The raw bands center on the HL2 midpoint, offset by ATR times a multiplier:

\text{Upper}_{\text{basic}} = \frac{H_t + L_t}{2} + m \cdot \text{ATR}(N) \text{Lower}_{\text{basic}} = \frac{H_t + L_t}{2} - m \cdot \text{ATR}(N)

where m is the multiplier (default 3.0) and N is the ATR period (default 10).

2. Ratchet Logic

The bands act as a one-way ratchet that prevents regression against the trend:

Upper band (bearish stop) can only move down:

\text{Upper}_{\text{final}} = \begin{cases} \min(\text{Upper}_{\text{basic}},\ \text{Upper}_{\text{prev}}) & \text{if } C_{t-1} \leq \text{Upper}_{\text{prev}} \\ \text{Upper}_{\text{basic}} & \text{otherwise} \end{cases}

Lower band (bullish stop) can only move up:

\text{Lower}_{\text{final}} = \begin{cases} \max(\text{Lower}_{\text{basic}},\ \text{Lower}_{\text{prev}}) & \text{if } C_{t-1} \geq \text{Lower}_{\text{prev}} \\ \text{Lower}_{\text{basic}} & \text{otherwise} \end{cases}

3. Trend State Machine

\text{Trend}_t = \begin{cases} \text{Bullish} & \text{if } C_t > \text{Upper}_{\text{final}} \\ \text{Bearish} & \text{if } C_t < \text{Lower}_{\text{final}} \\ \text{Trend}_{t-1} & \text{otherwise (hysteresis)} \end{cases} \text{SuperTrend} = \begin{cases} \text{Lower}_{\text{final}} & \text{if Bullish} \\ \text{Upper}_{\text{final}} & \text{if Bearish} \end{cases}

The output is the active stop level. Crossing the active band flips the state.

4. Complexity

Metric	Value
Time	O(1) per bar
Space	O(1) (ATR state + 2 band values + 1 trend boolean)
Allocations	Zero in hot path
Warmup	N bars (ATR stabilization)

Mathematical Foundation

Parameters

Parameter	Type	Default	Constraint	Description
atrPeriod	int	10	> 0	ATR lookback period
multiplier	double	3.0	> 0	ATR multiplier for band width

Pseudo-code

SUPERTREND(bar, atrPeriod=10, multiplier=3.0):

  // ATR update (Wilder's smoothing or SMA)
  atr = ATR.Update(bar, atrPeriod)

  // Basic bands
  hl2 = (bar.High + bar.Low) / 2
  upper_basic = hl2 + multiplier * atr
  lower_basic = hl2 - multiplier * atr

  // Ratchet: upper can only decrease, lower can only increase
  if prev_close <= prev_upper_final:
    upper_final = min(upper_basic, prev_upper_final)
  else:
    upper_final = upper_basic

  if prev_close >= prev_lower_final:
    lower_final = max(lower_basic, prev_lower_final)
  else:
    lower_final = lower_basic

  // State machine transition
  if bar.Close > upper_final:
    is_bullish = true
  else if bar.Close < lower_final:
    is_bullish = false
  // else: retain previous state (hysteresis)

  // Output active stop level
  if is_bullish:
    supertrend = lower_final
  else:
    supertrend = upper_final

  return supertrend

Band Behavior by State

State	Active Band	Ratchet Direction	Flip Condition
Bullish	Lower (support)	Can only rise	Close < Lower
Bearish	Upper (resistance)	Can only fall	Close > Upper

The step-like output results from the ratchet constraint: the band remains flat until a new extremum pushes it in the trend direction. Whipsaws occur in ranging markets where close repeatedly crosses both bands.

Performance Profile

Operation Count (Streaming Mode)

Supertrend uses ATR-based bands with a state-machine ratchet: upper/lower bands only move in their respective directions, and the trend flips when price crosses the active band.

Post-warmup steady state (per bar):

Operation	Count	Cost (cycles)	Subtotal
TR computation (SUB×3, ABS×2, MAX×2)	7	1	7
FMA (RMA ATR update)	1	4	4
MUL (ATR × multiplier)	1	3	3
ADD + SUB (upper/lower basic bands)	2	1	2
MAX/MIN (ratchet: clamp to prev band)	2	1	2
CMP × 2 (trend flip conditions)	2	1	2
CMP × 2 (final band selection)	2	1	2
Total	19	—	~22 cycles

The ratchet logic adds branch overhead (~3 cycles average from the CMPs), but overall ~22 cycles per bar.

Batch Mode (SIMD Analysis)

Operation	Vectorizable?	Notes
TR + ATR (RMA)	No	Recursive RMA — sequential
Band arithmetic	Yes	VADDPD + VSUBPD + VMULPD after ATR pass
Ratchet clamp	No	State-dependent MAX/MIN — depends on prior band value
Trend flip state machine	No	Branch-heavy flip logic depends on prior trend state

The ratchet and trend-flip logic create strong sequential dependencies. The ATR and band arithmetic sub-steps are vectorizable as intermediate passes.

Quality Metrics

Metric	Score	Notes
Accuracy	9/10	FMA ATR; ratchet logic exact
Timeliness	7/10	ATR period warmup; ratchet responds immediately to band crosses
Smoothness	9/10	One-way ratchet eliminates oscillation; clean directional band
Noise Rejection	8/10	ATR-scaled bands self-adjust to volatility regime

Resources

• Seban, O. SuperTrend indicator documentation.
• Wilder, J. W. (1978). New Concepts in Technical Trading Systems. Trend Research.