EwKyleLambda#

Description#

Kyle's lambda (Kyle 1985) is the slope of price change on signed order flow, the price-impact or illiquidity coefficient: a high value signals an illiquid market with large price impact per unit of net flow, a low value signals a liquid one. EwKyleLambda estimates it using exponential weighting rather than a fixed rolling window, so recent observations receive higher weight and the estimate adapts faster to changing liquidity conditions than RollingKyleLambda.

EwKyleLambda(span)(signed_flow, return_) returns the EW regression slope of return_ on signed_flow. It is a documented specialization of EwBeta: internally it calls EwBeta(span=span)(return_, signed_flow).

Parameters:

  • span (float, default 20.0): EW span, where the decay factor is alpha = 2 / (span + 1). Larger spans place more weight on older data and produce smoother, slower-adapting estimates.

Return value: the price-impact coefficient lambda at each time step. The first output is NaN (EwBeta warmup). Subsequent NaN values occur when signed_flow has zero variance over the effective EW window.

Because the implementation delegates entirely to EwBeta, causality and the nan_policy: ignore contract are inherited from the C++ engine.

Reference: Kyle, A. S. (1985). "Continuous Auctions and Insider Trading." Econometrica, 53(6), 1315-1335.

Examples#

Usage plot#

import numpy as np
import plotly.graph_objects as go
from plotly.subplots import make_subplots
from screamer import EwKyleLambda, RollingKyleLambda

rng = np.random.default_rng(7)
n = 400
flow = rng.standard_normal(n)
# the true impact slope steps up halfway through
true_lambda = np.where(np.arange(n) < n // 2, 0.3, 0.7)
ret = true_lambda * flow + rng.standard_normal(n) * 0.5
ew = EwKyleLambda(60.0)(flow, ret)
roll = RollingKyleLambda(60)(flow, ret)

fig = go.Figure()
fig.add_trace(go.Scatter(y=true_lambda, mode='lines', name='true lambda',
                         line=dict(color='gray', dash='dot')))
fig.add_trace(go.Scatter(y=roll, mode='lines', name='rolling',
                         line=dict(color='lightslategray')))
fig.add_trace(go.Scatter(y=ew, mode='lines', name='exponentially weighted',
                         line=dict(color='steelblue')))
fig.update_layout(title='EwKyleLambda: adapts faster to a change in liquidity',
                  xaxis_title='observation', yaxis_title="Kyle's lambda",
                  margin=dict(l=20, r=20, t=60, b=20), legend=dict(orientation='h', yanchor='bottom', y=1.02, xanchor='right', x=1))
fig.show()