QuanTAlib/lib/dynamics/ttm_squeeze/TtmSqueeze.md

# TTM_SQUEEZE: TTM Squeeze

> "Volatility compression is the market holding its breath before screaming."

John Carter's TTM Squeeze detects low-volatility compression by comparing Bollinger Band width against Keltner Channel width: when BB fits inside KC, a "squeeze" is on, signaling imminent breakout. The momentum component uses linear regression of price deviation from the Donchian midline to indicate direction. The indicator outputs a boolean squeeze state plus a continuous momentum histogram, requiring BB(20,2.0) and KC(20,1.5) as default parameters with a combined warmup of 20 bars.

## Historical Context

John Carter developed TTM Squeeze as his signature volatility breakout indicator, popularized through *Mastering the Trade* (2005) and the thinkorswim platform. The core insight combines two independent volatility measures: Bollinger's standard-deviation bands and Keltner's ATR-based channels. When the faster-reacting BB contracts inside the slower KC, it signals unusually low volatility, a condition that reliably precedes explosive directional moves. Carter added a momentum oscillator based on linear regression to provide directional bias during squeeze releases. The indicator became one of the most widely used proprietary tools in retail trading.

## Architecture & Physics

### 1. Bollinger Band Width

$$\text{BB}_{\text{upper}} = \text{SMA}(C, N_{\text{BB}}) + k_{\text{BB}} \cdot \sigma(C, N_{\text{BB}})$$

$$\text{BB}_{\text{lower}} = \text{SMA}(C, N_{\text{BB}}) - k_{\text{BB}} \cdot \sigma(C, N_{\text{BB}})$$

where $N_{\text{BB}} = 20$, $k_{\text{BB}} = 2.0$, and $\sigma$ is population standard deviation.

### 2. Keltner Channel Width

$$\text{KC}_{\text{upper}} = \text{EMA}(C, N_{\text{KC}}) + k_{\text{KC}} \cdot \text{ATR}(N_{\text{KC}})$$

$$\text{KC}_{\text{lower}} = \text{EMA}(C, N_{\text{KC}}) - k_{\text{KC}} \cdot \text{ATR}(N_{\text{KC}})$$

where $N_{\text{KC}} = 20$, $k_{\text{KC}} = 1.5$.

### 3. Squeeze Detection

$$\text{SqueezeOn} = (\text{BB}_{\text{lower}} > \text{KC}_{\text{lower}}) \text{ and } (\text{BB}_{\text{upper}} < \text{KC}_{\text{upper}})$$

When BB fits entirely inside KC, the squeeze is active. The first bar where squeeze transitions from on to off ("squeeze fires") signals the breakout.

### 4. Momentum Histogram

$$\text{midline} = \frac{\text{Highest}(H, N) + \text{Lowest}(L, N)}{2}$$

$$\delta_t = C_t - \frac{\text{midline}_t + \text{SMA}(C, N)}{2}$$

$$\text{Momentum} = \text{LinReg}(\delta, N)$$

The linear regression extracts the trend component of the deviation, filtering noise. Momentum sign indicates direction; slope indicates acceleration.

### 5. Momentum Color States

| Color | Condition |
|:------|:----------|
| Cyan | Momentum > 0 and rising |
| Blue | Momentum > 0 and falling |
| Red | Momentum < 0 and falling |
| Yellow | Momentum < 0 and rising |

### 6. Complexity

| Metric | Value |
|:-------|:------|
| Time | O(1) per bar (incremental BB, KC, LinReg updates) |
| Space | O(N) for sliding window buffers (SMA, StdDev, ATR, high/low, LinReg) |
| Warmup | N bars (default 20) |

## Mathematical Foundation

### Parameters

| Parameter | Type | Default | Constraint | Description |
|:----------|:-----|:--------|:-----------|:------------|
| bbLength | int | 20 | > 1 | Bollinger Band period |
| bbMult | double | 2.0 | > 0 | BB standard deviation multiplier |
| kcLength | int | 20 | > 1 | Keltner Channel period |
| kcMult | double | 1.5 | > 0 | KC ATR multiplier |

### Pseudo-code

```
TTM_SQUEEZE(bar, bbLen=20, bbMult=2.0, kcLen=20, kcMult=1.5):

  // Bollinger Bands
  sma_val  = SMA(close, bbLen)
  stddev   = StdDev(close, bbLen)
  bb_upper = sma_val + bbMult * stddev
  bb_lower = sma_val - bbMult * stddev

  // Keltner Channel
  ema_val  = EMA(close, kcLen)
  atr_val  = ATR(bar, kcLen)
  kc_upper = ema_val + kcMult * atr_val
  kc_lower = ema_val - kcMult * atr_val

  // Squeeze state
  squeeze_on = (bb_lower > kc_lower) AND (bb_upper < kc_upper)

  // Momentum via linear regression of deviation
  highest_high = Highest(high, bbLen)
  lowest_low   = Lowest(low, bbLen)
  midline      = (highest_high + lowest_low) / 2
  delta        = close - (midline + sma_val) / 2
  momentum     = LinReg(delta, bbLen)

  // Momentum direction
  momentum_rising  = momentum > prev_momentum
  momentum_positive = momentum > 0

  return (momentum, squeeze_on, momentum_rising, momentum_positive)
```

### Squeeze-Fire Signal

The critical trading signal occurs on the transition bar:

$$\text{SqueezeFired}_t = \text{SqueezeOn}_{t-1} \text{ and } \neg\text{SqueezeOn}_t$$

Combined with momentum direction, this yields entry signals: long when squeeze fires with positive rising momentum, short when squeeze fires with negative falling momentum.

## Resources

- Carter, J. (2005). *Mastering the Trade*. McGraw-Hill.
- Bollinger, J. (2001). *Bollinger on Bollinger Bands*. McGraw-Hill.
- Keltner, C. (1960). *How to Make Money in Commodities*. The Keltner Statistical Service.