Efficient Estimation of Bid-Ask Spreads from Open, High, Low, and Close Prices

Implements the efficient estimator of bid-ask spreads from open, high, low, and close prices described in Ardia, Guidotti, & Kroencke (JFE, 2024): https://doi.org/10.1016/j.jfineco.2024.103916

Installation

pip install bidask

Usage

There are three functions in this package. The function edge computes a single bid-ask spread estimate from vectors of open, high, low, and close prices. The functions edge_rolling and edge_expanding are optimized for fast calculations over rolling and expanding windows, respectively.

from bidask import edge, edge_rolling, edge_expanding

Function: edge

The input prices must be sorted in ascending order of the timestamp. The output value is the spread estimate. A value of 0.01 corresponds to a spread of 1%.

edge(open, high, low, close, sign=False)

Function: edge_rolling

Implements a rolling window calculation of edge. The input is a pandas data frame. The output is a pandas series of rolling spread estimates. A value of 0.01 corresponds to a spread of 1%.

edge_rolling(df, window, sign=False, **kwargs)

Function: edge_expanding

Implements an expanding window calculation of edge. The input is a pandas data frame. The output is a pandas series of expanding spread estimates. A value of 0.01 corresponds to a spread of 1%.

edge_expanding(df, min_periods=1, sign=False)

Examples

Load the test data.

import pandas as pd
df = pd.read_csv("https://raw.githubusercontent.com/eguidotti/bidask/main/pseudocode/ohlc.csv")

Compute the spread estimate using all the observations.

from bidask import edge
edge(df.Open, df.High, df.Low, df.Close)

Compute rolling estimates using a window of 21 observations.

from bidask import edge_rolling
edge_rolling(df=df, window=21)

Compute expanding estimates starting with a minimum of 21 observations.

from bidask import edge_expanding
edge_expanding(df=df, min_periods=21)

Notes

The rolling estimates:

rolling_estimates = edge_rolling(df=df, window=window, step=step, sign=sign)

are equivalent to, but much faster than:

expected_estimates = []
for t in range(0, len(df), step):
    t1 = t + 1
    t0 = t1 - window
    expected_estimates.append(edge(
        df.Open.values[t0:t1],
        df.High.values[t0:t1],
        df.Low.values[t0:t1],
        df.Close.values[t0:t1],
        sign=sign
    ) if t0 >= 0 else np.nan)

The expanding estimates:

expanding_estimates = edge_expanding(df=df, min_periods=min_periods, sign=sign)

are equivalent to, but much faster than:

expected_estimates = []
for t in range(0, len(df)):
    t1 = t + 1
    expected_estimates.append(edge(
        df.Open.values[0:t1],
        df.High.values[0:t1],
        df.Low.values[0:t1],
        df.Close.values[0:t1],
        sign=sign
    ) if t1 >= min_periods else np.nan)

Cite as

Ardia, D., Guidotti, E., Kroencke, T.A. (2024). Efficient Estimation of Bid-Ask Spreads from Open, High, Low, and Close Prices. Journal of Financial Economics, 161, 103916. doi: 10.1016/j.jfineco.2024.103916

A BibTex entry for LaTeX users is:

@article{edge,
  title = {Efficient estimation of bid–ask spreads from open, high, low, and close prices},
  journal = {Journal of Financial Economics},
  volume = {161},
  pages = {103916},
  year = {2024},
  doi = {https://doi.org/10.1016/j.jfineco.2024.103916},
  author = {David Ardia and Emanuele Guidotti and Tim A. Kroencke},
}