Volatility is a crucial concept in trading and investing, as it measures the degree of variation in an asset’s price over time. There are several methods to measure volatility, each with its own advantages and applications. Below is a comprehensive list of volatility measurement methods used in trading:
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### **1. Historical Volatility (HV)**
– Measures past price fluctuations over a specific period.
– Calculated as the standard deviation of logarithmic returns.
– Formula:
\[
\sigma = \sqrt{\frac{1}{N-1} \sum_{i=1}^{N} (r_i – \bar{r})^2}
\]
where \( r_i = \ln\left(\frac{P_i}{P_{i-1}}\right) \) and \( \bar{r} \) is the mean return.
– Used for assessing past risk and forecasting future volatility.
—
### **2. Implied Volatility (IV)**
– Derived from option prices using models like Black-Scholes.
– Reflects market expectations of future volatility.
– Higher IV → Higher expected price swings.
– Used in options pricing (e.g., VIX measures S&P 500 IV).
—
### **3. Parkinson Volatility**
– Uses high-low price ranges instead of closing prices.
– Captures intraday volatility better than HV.
– Formula:
\[
\sigma = \sqrt{\frac{1}{4N \ln 2} \sum_{i=1}^{N} \left(\ln \frac{H_i}{L_i}\right)^2}
\]
where \( H_i \) and \( L_i \) are daily high/low prices.
—
### **4. Garman-Klass Volatility**
– Extends Parkinson by incorporating opening/closing prices.
– More efficient estimator than standard HV.
– Formula:
\[
\sigma = \sqrt{\frac{1}{N} \sum_{i=1}^{N} \left[\frac{1}{2}\left(\ln \frac{H_i}{L_i}\right)^2 – (2 \ln 2 – 1)\left(\ln \frac{C_i}{O_i}\right)^2\right]}
\]
—
### **5. Rogers-Satchell Volatility**
– Accounts for intraday price movements and drift (trend).
– Works well for assets with trends.
– Formula:
\[
\sigma = \sqrt{\frac{1}{N} \sum_{i=1}^{N} \left(\ln \frac{H_i}{C_i} \ln \frac{H_i}{O_i} + \ln \frac{L_i}{C_i} \ln \frac{L_i}{O_i}\right)}
\]
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### **6. Yang-Zhang Volatility**
– Combines overnight (close-to-open) and intraday (open-to-close) volatility.
– Minimizes estimation error.
– Formula:
\[
\sigma^2 = \sigma_{\text{overnight}}^2 + k \sigma_{\text{intraday}}^2 + (1 – k) \sigma_{\text{RS}}^2
\]
where \( \sigma_{\text{RS}} \) is Rogers-Satchell volatility.
—
### **7. Realized Volatility (RV)**
– Calculated from high-frequency intraday data.
– Sum of squared returns over tiny intervals (e.g., 5-minute returns).
– Formula:
\[
RV = \sum_{i=1}^{N} r_i^2
\]
– Used in algo/HFT trading.
—
### **8. Conditional Volatility Models (GARCH, EGARCH)**
– Models volatility clustering (e.g., high volatility follows high volatility).
– **GARCH (Generalized Autoregressive Conditional Heteroskedasticity)**:
\[
\sigma_t^2 = \alpha_0 + \alpha_1 r_{t-1}^2 + \beta_1 \sigma_{t-1}^2
\]
– **EGARCH**: Captures asymmetric effects (e.g., negative shocks increase volatility more).
—
### **9. Average True Range (ATR)**
– Measures market volatility using true range (accounts for gaps).
– True Range = Max of:
\[
(H – L), |H – C_{\text{prev}}|, |L – C_{\text{prev}}|
\]
– ATR = Smoothed average of true ranges (typically 14-day).
—
### **10. Chaikin Volatility**
– Combines price range and volume.
– Formula:
\[
\text{Chaikin Volatility} = \frac{\text{EMA}(H – L, n) – \text{EMA}(H – L, m)}{\text{EMA}(H – L, m)}
\]
where \( n < m \) (e.g., 10-day and 20-day EMAs).
—
### **11. VIX (CBOE Volatility Index)**
– Measures 30-day implied volatility of S&P 500 options.
– Known as the “fear gauge.”
– Calculated using weighted IV of SPX options.
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### **12. Moving Standard Deviation**
– Rolling window standard deviation of returns.
– Simple but effective for trend-following strategies.
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### **Key Takeaways:**
– **Historical/Realized Volatility**: Backward-looking.
– **Implied Volatility**: Forward-looking (options market).
– **Intraday Methods (Parkinson, GK, RS, YZ)**: Better for capturing daily ranges.
– **GARCH/ATR**: Adaptive to changing market conditions.
Different methods suit different trading styles (e.g., options traders rely on IV, while swing traders may prefer ATR or HV). Combining multiple measures can provide a fuller picture of market volatility.