Building a VIX-Filtered Mean Reversion Strategy: Part 2 - Technical Indicator Construction and Statistical Foundations

 Introduction to Indicator-Based Market Analysis

The transition from raw market data to actionable trading signals requires the construction of technical indicators that quantify market structure and identify statistical extremes. In mean reversion frameworks, the primary challenge involves defining a dynamic equilibrium price level from which deviations can be measured objectively. This second installment develops a comprehensive technical indicator library centered on Volume Weighted Average Price (VWAP) as the equilibrium reference, complemented by volatility-adjusted bands, risk measurement tools, and volume distribution analysis. Each indicator serves a specific role in the strategy's decision hierarchy: VWAP establishes the fair value anchor, standard deviation bands define entry and exit thresholds, Average True Range (ATR) calibrates position risk, and volume profile metrics provide additional market structure context. The indicator implementations prioritize mathematical precision and computational efficiency, ensuring that calculations remain consistent with institutional trading platforms while maintaining compatibility with the backtesting.py framework's vectorized architecture.

Volume Weighted Average Price: The Equilibrium Anchor

VWAP represents the average price at which a security has traded throughout the session, weighted by volume at each price level. Unlike simple moving averages that treat all price observations equally regardless of transaction volume, VWAP gives greater weight to prices where significant volume occurred, providing a more accurate representation of the session's true average execution price. Institutional traders utilize VWAP as a benchmark for trade execution quality, making it a natural reference point for mean reversion strategies since price deviations from VWAP often trigger institutional rebalancing activity. The calculation requires three components: typical price for each bar (the average of high, low, and close), cumulative volume-weighted typical price, and cumulative volume, with the quotient representing VWAP at each timestamp:

python
def calculate_vwap(close, volume, high, low, index):
    """
    Calculate VWAP (Volume Weighted Average Price) - resets daily

    Formula: VWAP = Σ(Typical Price × Volume) / Σ(Volume)
    Where Typical Price = (High + Low + Close) / 3

    The calculation resets at the start of each trading day.
    """
    typical_price = (high + low + close) / 3

    df = pd.DataFrame({
        'tp': typical_price,
        'vol': volume,
        'date': index.date
    })

    df['cum_tp_vol'] = df.groupby('date')['tp'].transform(
        lambda x: (x * df.loc[x.index, 'vol']).cumsum()
    )
    df['cum_vol'] = df.groupby('date')['vol'].transform('cumsum')

    vwap = df['cum_tp_vol'] / df['cum_vol']

    return vwap.values

The critical architectural decision in this implementation involves the daily reset mechanism, which anchors VWAP to each trading session rather than calculating a rolling VWAP across multiple days. This session-anchored approach aligns with institutional practice where VWAP benchmarks reset at the beginning of each trading day, and ensures that the indicator remains responsive to intraday price action without carrying forward stale information from previous sessions. The groupby operation on the date field creates separate cumulative calculations for each trading day, preventing volume and price data from one session from contaminating the next session's VWAP calculation. This temporal segmentation is particularly important for futures contracts that trade nearly continuously across global sessions, as it maintains distinct equilibrium references for each calendar day rather than blending overnight activity into a single continuous calculation.

VWAP Standard Deviation Bands: Defining Statistical Extremes

While VWAP establishes the equilibrium price level, standard deviation bands quantify the magnitude of deviations from that equilibrium, providing objective thresholds for identifying mean reversion opportunities. The statistical foundation rests on the assumption that price deviations from VWAP follow a roughly normal distribution, such that movements beyond one or two standard deviations represent increasingly rare events that warrant trading consideration. The implementation calculates unweighted standard deviation of typical price around VWAP, matching the methodology employed by professional charting platforms such as ThinkorSwim. Each bar contributes equally to the variance calculation regardless of its volume, distinguishing this approach from volume-weighted variance measures that would further emphasize high-volume price levels:

python
def calculate_vwap_bands(close, volume, high, low, index, std_mult=1.0):
    """
    Calculate VWAP Standard Deviation Bands using UNWEIGHTED standard deviation

    Formula:
    1. Calculate VWAP first
    2. For each bar: deviation = (Typical Price - VWAP)
    3. Variance = Σ(deviation²) / N  (where N = number of bars)
    4. Std Dev = sqrt(Variance)
    5. Upper Band = VWAP + (std_mult × Std Dev)
    6. Lower Band = VWAP - (std_mult × Std Dev)

    This matches ThinkorSwim and standard statistical definition.
    Each bar contributes equally to the standard deviation regardless of volume.
    """
    vwap = calculate_vwap(close, volume, high, low, index)
    typical_price = (high + low + close) / 3

    df = pd.DataFrame({
        'tp': typical_price,
        'vwap': vwap,
        'date': index.date
    })

    df['sq_diff'] = (df['tp'] - df['vwap']) ** 2

    df['cum_sq_diff'] = df.groupby('date')['sq_diff'].transform('cumsum')
    df['count'] = df.groupby('date').cumcount() + 1

    variance = df['cum_sq_diff'] / df['count']
    std_dev = np.sqrt(variance)

    upper = vwap + (std_mult * std_dev)
    lower = vwap - (std_mult * std_dev)

    return upper, lower

The function accepts a standard deviation multiplier parameter that allows for multiple band levels simultaneously, enabling the strategy to distinguish between first standard deviation touches (one sigma events) and second standard deviation touches (two sigma events) which represent increasingly extreme price dislocations. The strategy employs this dual-band structure to adjust position sizing or entry aggressiveness based on the magnitude of deviation from equilibrium. The cumulative squared difference calculation updates incrementally throughout the trading day, ensuring that the standard deviation measure adapts to evolving intraday volatility patterns. This running calculation approach provides more responsive bands compared to a fixed lookback window, as the bands naturally expand during volatile sessions and contract during range-bound periods, automatically adjusting the strategy's sensitivity to prevailing market conditions.

Average True Range: Volatility-Adjusted Risk Measurement

Position risk management requires an objective measure of recent price volatility to calibrate stop loss distances and position sizing appropriately. Average True Range (ATR) serves this purpose by quantifying the average movement range over a specified lookback period, accounting for both intrabar volatility and overnight gaps. The True Range calculation takes the maximum of three values: the current bar's high-to-low range, the absolute distance from the current high to the previous close, and the absolute distance from the current low to the previous close. This comprehensive approach captures price movement that might be missed by examining only the current bar's range, particularly in markets that gap significantly between sessions:

python
def calculate_atr(high, low, close, period=14):
    """
    Calculate ATR (Average True Range)

    True Range is the maximum of:
    1. Current High - Current Low
    2. |Current High - Previous Close|
    3. |Current Low - Previous Close|

    ATR is the Exponential Moving Average of True Range over the period.
    """
    h = pd.Series(high)
    l = pd.Series(low)
    c = pd.Series(close)

    tr1 = h - l
    tr2 = abs(h - c.shift())
    tr3 = abs(l - c.shift())

    tr = pd.concat([tr1, tr2, tr3], axis=1).max(axis=1)

    atr = tr.ewm(span=period, adjust=False).mean()

    return atr.values

The exponential moving average smoothing applied to the True Range series creates a responsive yet stable volatility measure that adapts gradually to changing market conditions without reacting excessively to single outlier bars. The fourteen-period default represents an industry standard that balances responsiveness with stability, though this parameter can be optimized for specific market regimes or trading timeframes. In the strategy implementation, ATR serves as the foundation for stop loss placement, with stop distances specified as multiples of ATR rather than fixed point values. This volatility-adjusted approach ensures that stop losses remain appropriately scaled to recent market movement, tightening automatically during low-volatility periods to protect profits and widening during high-volatility periods to avoid premature stopouts from normal price noise.

VWAP Slope Analysis: Trend Context for Mean Reversion

While mean reversion strategies profit from price oscillations around an equilibrium level, the direction and magnitude of that equilibrium's movement provides important contextual information for trade selection. A rapidly rising or falling VWAP suggests directional pressure that may override mean reversion tendencies, while a stable VWAP confirms range-bound conditions where reversion mechanics remain dominant. The VWAP slope calculation measures the percentage change in VWAP over a specified lookback period, providing a normalized trend strength indicator that accounts for the absolute price level of the instrument:

python
def calculate_vwap_slope(close, volume, high, low, index, lookback=6):
    """
    Calculate VWAP slope as percentage change

    Formula: Slope = ((VWAP_current - VWAP_lookback) / VWAP_lookback) × 100

    Args:
        lookback: Number of periods to look back for slope calculation

    Returns:
        Slope as percentage
    """
    vwap = calculate_vwap(close, volume, high, low, index)
    slope = pd.Series(vwap).pct_change(periods=lookback) * 100

    return slope.values

The percentage-based formulation allows for consistent interpretation across different instruments and price levels, with typical threshold values around 0.15 percent representing a neutral boundary between trending and range-bound conditions. While the current strategy implementation does not actively filter trades based on VWAP slope, this indicator remains available for future enhancements that might restrict entries to periods where the slope confirms range-bound behavior, or alternatively, could be inverted to create a trend-following variant that enters in the direction of VWAP momentum rather than against it.

Volume Profile: Market Structure and Value Area Analysis

Volume profile analysis extends beyond simple volume measurement to examine the price distribution of trading activity, identifying price levels where the market has established acceptance through sustained volume concentration. The calculation divides each day's price range into discrete bins and distributes volume across these bins based on where price traded, creating a histogram of volume by price rather than volume by time. From this distribution, three key metrics emerge: the Point of Control (POC) representing the price level with maximum volume, and the Value Area High (VAH) and Value Area Low (VAL) representing the boundaries that contain seventy percent of the day's volume centered around the POC:

python
def calculate_volume_profile(high, low, close, volume, index, num_bins=24):
    """
    Calculate Volume Profile metrics: VAH (Value Area High), VAL (Value Area Low), POC (Point of Control)

    Process:
    1. Divide the day's price range into bins (default 24)
    2. Distribute volume across bins based on where price traded
    3. POC = price level with highest volume
    4. Value Area = 70% of total volume centered around POC
    5. VAH = upper boundary of value area
    6. VAL = lower boundary of value area

    The calculation resets daily.
    """
    df = pd.DataFrame({
        'high': high,
        'low': low,
        'close': close,
        'volume': volume,
        'date': index.date
    })

    vah_list, val_list, poc_list = [], [], []

    for date in df['date'].unique():
        day_data = df[df['date'] == date]

        if len(day_data) < 3:
            vah_list.extend([np.nan] * len(day_data))
            val_list.extend([np.nan] * len(day_data))
            poc_list.extend([np.nan] * len(day_data))
            continue

        price_min = day_data['low'].min()
        price_max = day_data['high'].max()

        if price_max == price_min:
            vah_list.extend([day_data['close'].iloc[0]] * len(day_data))
            val_list.extend([day_data['close'].iloc[0]] * len(day_data))
            poc_list.extend([day_data['close'].iloc[0]] * len(day_data))
            continue

        bins = np.linspace(price_min, price_max, num_bins)
        vol_profile = np.zeros(len(bins) - 1)

        for _, row in day_data.iterrows():
            for i in range(len(bins) - 1):
                if row['low'] <= bins[i+1] and row['high'] >= bins[i]:
                    overlap = min(row['high'], bins[i+1]) - max(row['low'], bins[i])
                    bar_range = row['high'] - row['low']

                    if bar_range > 0:
                        vol_profile[i] += row['volume'] * (overlap / bar_range)
                    else:
                        vol_profile[i] += row['volume'] / (len(bins) - 1)

        poc_idx = np.argmax(vol_profile)
        poc_price = (bins[poc_idx] + bins[poc_idx + 1]) / 2

        total_vol = vol_profile.sum()
        if total_vol == 0:
            vah_list.extend([day_data['close'].mean()] * len(day_data))
            val_list.extend([day_data['close'].mean()] * len(day_data))
            poc_list.extend([day_data['close'].mean()] * len(day_data))
            continue

        va_vol = total_vol * 0.70
        va_indices = [poc_idx]
        current_vol = vol_profile[poc_idx]

        lower_idx = poc_idx - 1
        upper_idx = poc_idx + 1

        while current_vol < va_vol:
            lower_vol = vol_profile[lower_idx] if lower_idx >= 0 else 0
            upper_vol = vol_profile[upper_idx] if upper_idx < len(vol_profile) else 0

            if lower_vol >= upper_vol and lower_idx >= 0:
                va_indices.append(lower_idx)
                current_vol += lower_vol
                lower_idx -= 1
            elif upper_idx < len(vol_profile):
                va_indices.append(upper_idx)
                current_vol += upper_vol
                upper_idx += 1
            else:
                break

        vah = bins[max(va_indices) + 1] if max(va_indices) + 1 < len(bins) else bins[-1]
        val = bins[min(va_indices)]

        vah_list.extend([vah] * len(day_data))
        val_list.extend([val] * len(day_data))
        poc_list.extend([poc_price] * len(day_data))

    return np.array(vah_list), np.array(val_list), np.array(poc_list)

The volume distribution algorithm proportionally allocates each bar's volume across the price bins it overlaps, ensuring that a bar trading from 4500 to 4520 contributes its volume across all bins within that range rather than assigning it arbitrarily to a single bin. The value area calculation expands iteratively from the POC by comparing volume in adjacent bins and incorporating whichever direction contains more volume until seventy percent of total daily volume is captured. This bidirectional expansion ensures that the value area remains centered on the POC while accounting for asymmetric volume distributions. While the current strategy implementation does not actively utilize volume profile metrics for trade filtering, these indicators provide valuable context for understanding market structure and could be incorporated in future refinements to preference trades that enter near value area extremes or avoid trades during periods where price remains well outside the established value area.

Indicator Integration and Validation

With the complete indicator library defined, the next phase involves integrating these calculations into the backtesting.py framework through the strategy's initialization method. The framework's indicator interface wraps each calculation function, ensuring that results are properly cached and accessible throughout strategy execution. This completes the technical foundation required for strategy logic implementation. Part 3 will construct the strategy class itself, implementing VIX-based regime filtering, VWAP band entry logic, profit target and stop loss management, and the complete backtesting and optimization pipeline that validates the strategy's statistical edge across varying market conditions and parameter configurations.