Volatility Signature

Two-scale realized vol, noise variance estimation, and optimal sampling frequency

Realized volatility from high-frequency data is biased upward by microstructure noise (bid-ask bounce, discrete ticks, stale quotes). The volatility signature plot reveals this bias, and the two-scale realized volatility estimator (Zhang-Mykland-Ait-Sahalia) corrects for it.

API

Volatility signature plot

Compute realized vol at multiple sampling frequencies. At high frequencies the estimate is inflated by noise; it stabilizes as frequency decreases.

python

result = hz.volatility_signature(prices, freqs=[1, 2, 5, 10, 30, 60, 300])
# prices: list of (timestamp, price) tuples
# freqs: sampling intervals in seconds
# Returns: list of (frequency, realized_vol) tuples

for freq, vol in result:
    print(f"{freq:>4}s: {vol:.4f}")

# Output (typical):
#    1s: 0.2834    <-- inflated by noise
#    2s: 0.2401
#    5s: 0.2012
#   10s: 0.1856
#   30s: 0.1791
#   60s: 0.1782    <-- stabilizes here
#  300s: 0.1775

Two-scale realized volatility

The TSRV estimator combines a fast-scale and slow-scale estimator to cancel out the noise bias. Returns an unbiased vol estimate directly.

python

vol = hz.two_scale_realized_vol(prices)
# prices: list of (timestamp, price) tuples
# Returns: float -- noise-corrected annualized volatility

Optimal sampling frequency

python

freq = hz.optimal_sampling(prices)
# Returns: float -- optimal sampling interval in seconds

Practical usage

Corrected vol for position sizing

python

# Naive RV from 1-second bars is biased upward
naive_vol = hz.volatility_signature(tick_data, freqs=[1])[0][1]

# TSRV gives the corrected estimate
true_vol = hz.two_scale_realized_vol(tick_data)

print(f"Naive: {naive_vol:.4f}, Corrected: {true_vol:.4f}")
# Using naive vol would make you size positions too small (overestimating risk)

Noise-aware signal filtering

python

noise = hz.noise_variance(tick_data)
signal_move = current_price - fair_value

# Only trade if the move exceeds the noise level
if abs(signal_move) > 3 * noise ** 0.5:
    # This is a real move, not microstructure noise
    pass

When to use

High-frequency strategies: any strategy sampling prices faster than every 5 minutes needs noise correction.
Position sizing: using uncorrected vol overestimates risk and undersizes positions.
Signal filtering: distinguish real price moves from bid-ask bounce before acting on them.
Sampling rate selection: when designing a data pipeline, optimal_sampling() tells you the right frequency to avoid both noise contamination and information loss.

For daily or hourly data, microstructure noise is negligible and standard realized vol works fine.

ACD Duration Models Model the timing of trade arrivals. Microstructure Invariance Universal scaling laws for trade sizing.

API