RollingYangZhangVol#

Description#

The Yang-Zhang (2000) estimator combines three variance components:

\[\begin{split} \begin{aligned} \sigma^2_o &= \text{sample variance of overnight log returns } \ln(O_t / C_{t-1}) \\ \sigma^2_c &= \text{sample variance of open-to-close log returns } \ln(C_t / O_t) \\ \sigma^2_{RS} &= \text{mean of per-bar Rogers-Satchell estimates} \\ k &= \dfrac{0.34}{1.34 + (n+1)/(n-1)} \\ \sigma^2_{YZ} &= \sigma^2_o + k\ \cdot\ \sigma^2_c + (1-k)\ \cdot\ \sigma^2_{RS} \end{aligned} \end{split}\]

The only classical estimator that handles both drift and overnight gaps. ~14x efficient vs close-to-close.

4-input, 1-output on (open, high, low, close). First valid output at sample index window_size (we need n+1 price bars to form n overnight returns). The Vol variant returns sqrt(Var) (bit-exact via the same internal state).

No EW form is exposed because the k factor depends on a discrete window size; any "EW analogue" would require an arbitrary mapping from span to n that varies by convention.

NaN handling#

Policy: ignore. A NaN in any input at index t causes the function to skip that step: output at t is NaN and internal state is unchanged. Subsequent finite samples are processed as if step t had not occurred.

Examples#

Usage example#

import numpy as np
import plotly.graph_objects as go
from plotly.subplots import make_subplots
from screamer import RollingYangZhangVol

np.random.seed(0)
close = 100*np.exp(np.cumsum(np.random.normal(0, 0.01, size=300)))
open_ = np.concatenate([[close[0]], close[:-1]])
wick = np.abs(np.random.normal(0, 0.4, size=300))
high = np.maximum(open_, close) + wick
low  = np.minimum(open_, close) - wick
out = RollingYangZhangVol(window_size=20)(open_, high, low, close)

fig = make_subplots(rows=2, cols=1, shared_xaxes=True,
                    row_heights=[0.55, 0.45], vertical_spacing=0.08)
fig.add_trace(go.Scatter(y=close, name="close"), row=1, col=1)
fig.add_trace(go.Scatter(y=out, name="RollingYangZhangVol", line=dict(color="red")), row=2, col=1)
fig.update_layout(title="Rolling Yang-Zhang volatility (RollingYangZhangVol)",
                  margin=dict(l=20, r=20, t=60, b=20),
                  legend=dict(orientation="h", yanchor="bottom", y=1.02, xanchor="right", x=1))
fig.update_yaxes(title_text="price", row=1, col=1)
fig.update_yaxes(title_text="volatility", row=2, col=1)
fig.show()