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Miha Kralj
245 lines
8.5 KiB
Markdown
245 lines
8.5 KiB
Markdown
# CVI: Chaikin's Volatility
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> *Volatility expansion precedes major moves—when the trading range starts widening, pay attention.*
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| Property | Value |
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| ---------------- | -------------------------------- |
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| **Category** | Volatility |
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| **Inputs** | OHLCV bar (TBar) |
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| **Parameters** | `rocLength` (default 10), `smoothLength` (default 10) |
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| **Outputs** | Single series (Cvi) |
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| **Output range** | $\geq 0$ |
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| **Warmup** | 1 bar |
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| **PineScript** | [cvi.pine](cvi.pine) |
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- Chaikin's Volatility (CVI) measures the rate of change of the EMA-smoothed high-low trading range.
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- **Similar:** [ATR](../atr/atr.md) | **Complementary:** BandWidth | **Trading note:** Chaikin Volatility; ROC of high-low EMA range.
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- Validated against TA-Lib, Skender, and Tulip reference implementations where available.
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Chaikin's Volatility (CVI) measures the rate of change of the EMA-smoothed high-low trading range. Unlike traditional volatility measures that focus on returns, CVI directly tracks the expansion and contraction of price ranges over time. A positive CVI indicates expanding volatility (wider trading ranges), while a negative CVI signals contracting volatility (narrower ranges). This makes CVI particularly useful for identifying breakout conditions and market transitions.
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## Historical Context
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Marc Chaikin developed this indicator as part of his suite of technical analysis tools focused on price and volume dynamics. The indicator emerged from a practical observation: before significant price moves, the trading range often expands as buyers and sellers contest prices more aggressively.
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Traditional volatility measures like standard deviation or ATR tell you the *level* of volatility, but CVI answers a different question: is volatility *increasing* or *decreasing*? This directional information can be more actionable for traders timing entries and exits.
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The indicator combines two smoothing mechanisms: EMA smoothing on the raw high-low range to reduce noise, followed by a Rate of Change (ROC) calculation to measure the trend in volatility. This two-stage approach filters out day-to-day noise while capturing meaningful shifts in market character.
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## Architecture & Physics
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### 1. Range Calculation
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The daily trading range is the difference between high and low prices:
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$$
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R_t = H_t - L_t
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$$
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where:
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- $H_t$ = high price at time $t$
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- $L_t$ = low price at time $t$
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- $R_t$ = range at time $t$
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This captures the full extent of intraday price movement.
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### 2. EMA Smoothing
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The range is smoothed using an Exponential Moving Average:
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$$
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EMA_t = \alpha \cdot R_t + (1 - \alpha) \cdot EMA_{t-1}
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$$
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where:
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- $\alpha = \frac{2}{smoothLength + 1}$ (smoothing factor)
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- Default $smoothLength = 10$ gives $\alpha \approx 0.182$
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Equivalently, using FMA optimization:
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$$
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EMA_t = (R_t - EMA_{t-1}) \cdot \alpha + EMA_{t-1}
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$$
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### 3. Rate of Change Calculation
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CVI is the percentage change of the smoothed range over the ROC period:
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$$
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CVI_t = \frac{EMA_t - EMA_{t-rocLength}}{EMA_{t-rocLength}} \times 100
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$$
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where:
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- $rocLength$ = lookback period for ROC (default 10)
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- Output is expressed as a percentage
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### 4. Interpretation
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$$
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CVI_t = \begin{cases}
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> 0 & \text{Expanding volatility (range increasing)} \\
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= 0 & \text{Stable volatility (range unchanged)} \\
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< 0 & \text{Contracting volatility (range decreasing)}
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\end{cases}
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$$
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## Mathematical Foundation
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### EMA Properties
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**Smoothing Factor:**
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$$
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\alpha = \frac{2}{n + 1}
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$$
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| smoothLength | α | Half-life (bars) |
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| :---: | :---: | :---: |
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| 5 | 0.333 | 1.7 |
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| 10 | 0.182 | 3.4 |
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| 14 | 0.133 | 4.8 |
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| 20 | 0.095 | 6.9 |
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**Exponential Decay:**
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The weight of a value $k$ bars ago is:
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$$
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w_k = \alpha (1 - \alpha)^k
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$$
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### ROC Properties
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**Percentage Change Formula:**
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$$
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ROC = \frac{V_{current} - V_{prior}}{V_{prior}} \times 100
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$$
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**Symmetry Note:**
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A +50% increase followed by -33% decrease returns to the original value. CVI preserves this percentage-based interpretation.
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### Combined Effect
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The warmup period is the sum of both smoothing requirements:
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$$
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WarmupPeriod = smoothLength + rocLength
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$$
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This ensures both the EMA has stabilized and enough history exists for the ROC calculation.
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## Performance Profile
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### Operation Count (Streaming Mode, Scalar)
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Per-bar operations after warmup:
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| Operation | Count | Cost (cycles) | Subtotal |
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| :--- | :---: | :---: | :---: |
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| SUB (range) | 1 | 1 | 1 |
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| FMA (EMA) | 1 | 4 | 4 |
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| Buffer lookup | 1 | 3 | 3 |
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| SUB | 1 | 1 | 1 |
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| DIV | 1 | 15 | 15 |
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| MUL (×100) | 1 | 3 | 3 |
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| **Total** | — | — | **~27 cycles** |
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The primary cost is the division for the ROC calculation.
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### Batch Mode (512 values, SIMD/FMA)
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| Operation | Scalar Ops | SIMD Ops (AVX2) | Speedup |
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| :--- | :---: | :---: | :---: |
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| Range calculation | 512 | 64 | 8× |
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| EMA (sequential) | 512 | 512 | 1× |
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| ROC calculation | 512 | 64 | 8× |
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**Note:** EMA is inherently sequential due to the $EMA_{t-1}$ dependency. Total batch improvement is limited by this constraint.
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### Memory Profile
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- **Per instance:** ~80 bytes (state struct + RingBuffer header)
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- **RingBuffer:** $(rocLength + 1) \times 8$ bytes for EMA history
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- **Default (10,10):** ~80 + 88 = ~168 bytes per instance
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### Quality Metrics
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| Metric | Score | Notes |
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| :--- | :---: | :--- |
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| **Accuracy** | 8/10 | Direct measure of range dynamics |
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| **Timeliness** | 7/10 | EMA introduces lag |
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| **Smoothness** | 8/10 | Two-stage smoothing reduces noise |
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| **Interpretability** | 9/10 | Clear meaning: + expanding, - contracting |
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| **Robustness** | 8/10 | Handles gaps and spikes well |
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## Validation
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CVI is a classic indicator with multiple implementations:
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| Library | Status | Notes |
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| :--- | :---: | :--- |
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| **TA-Lib** | N/A | Not implemented |
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| **Skender** | N/A | Not implemented |
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| **Tulip** | N/A | Not implemented |
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| **OoplesFinance** | N/A | Not implemented |
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| **PineScript** | ✅ | Matches cvi.pine reference |
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| **Manual** | ✅ | Validated against formula |
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Note: While many libraries include ATR or standard deviation-based volatility, Chaikin's specific ROC-of-EMA-range formulation is less common.
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## Common Pitfalls
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1. **Warmup period**: CVI requires $smoothLength + rocLength$ bars before producing meaningful results. With defaults (10,10), this means 20 bars. The `IsHot` property indicates when warmup is complete.
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2. **Zero/near-zero old EMA**: If the historical EMA value is very small (near zero), the division can produce extreme or infinite values. The implementation guards against this with an epsilon threshold.
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3. **Interpretation of magnitude**: CVI values are percentages, not absolute ranges. A CVI of +50 means volatility increased 50% compared to $rocLength$ bars ago, regardless of the actual range values.
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4. **Not a directional indicator**: CVI measures volatility direction, not price direction. High CVI can precede moves in either direction.
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5. **Parameter sensitivity**:
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- Shorter $smoothLength$ = more responsive to range changes but noisier
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- Shorter $rocLength$ = more volatile CVI readings
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- Common combinations: (10,10), (14,10), (10,14)
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6. **Requires OHLC data**: Unlike many indicators that work with closing prices only, CVI requires high and low prices. When using TValue input, the value is interpreted as a pre-calculated range.
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7. **Negative ranges**: If TValue input has negative values (invalid for a range), the implementation substitutes the last valid value.
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## Trading Applications
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### Breakout Detection
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High positive CVI values suggest expanding volatility, often preceding breakouts:
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```
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Entry signal: CVI crosses above +20 (volatility expanding)
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Confirmation: Price breaks key support/resistance
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```
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### Consolidation Identification
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Sustained negative CVI indicates contracting ranges, typical of consolidation:
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```
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Consolidation: CVI < -10 for several bars
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Watch for: CVI reversal signaling potential breakout
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```
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### Volatility Regime Filter
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CVI can filter other signals based on volatility conditions:
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```
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Trade breakouts when: CVI > 0 (expanding volatility)
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Avoid range trades when: CVI rising sharply
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```
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## References
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- Chaikin, M. (1966). "Stock Market Trading Systems." Various publications and interviews.
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- Achelis, S. B. (2000). "Technical Analysis from A to Z." McGraw-Hill. Chapter on Chaikin Volatility.
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- Murphy, J. J. (1999). "Technical Analysis of the Financial Markets." New York Institute of Finance. |