krishvishal · February 20, 2022 02:48 · Dec 23, 2021 · Dec 23, 2021 · Dec 13, 2021
diff --git a/high_low_spread_estimator.py b/high_low_spread_estimator.py
@@ -1,34 +1,36 @@
-# high-low spread estimator (hlse) provides an estimate of bid-offer spreads, a measure of liquidity risk
-# described in Corwin and Schultz (2011): https://papers.ssrn.com/sol3/papers.cfm?abstract_id=1106193
-
-def hlse(df, frequency='daily'):
-
+# high-low spread estimator (hlse)
+def hlse(ohlc_df, frequency='daily'):
     """
-    Computes the high-low spread estimator, an estimate of bid-offer spreads, described by Corwin & Schultz (2011)
+    Computes the high-low spread estimator, an estimate of bid-offer spreads, a measure of liquidity risk.
+    See Corwin & Schultz (2011) for details: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=1106193
 
     Parameters
     ----------
-    df: DataFrame
-        dataframe with date, open, high, low and close (OHLC) time series
-    frequency: str
-        'daily' for daily bid-offer spread estimate, or 'monthly' for monthly bid-offer spread estimate, defaults to daily
+    ohlc_df: DataFrame
+        DataFrame with DatetimeIndex and Open, High, Low and Close (OHLC) prices from which to compute the high-low spread estimates.
+    frequency: str, {'daily', 'weekly', 'monthly'}, default 'daily'
+        daily: daily bid-offer spread estimate.
+        weekly: weekly bid-offer spread estimate, resampled over a weekly frequency as the mean of daily estimates.
+        monthly: monthly bid-offer spread estimate, resampled over a monthly frequency as the mean of daily estimates.
 
     Returns
     -------
-    S: series
-        time series of high-low spread estimate
+    S: Series
+        Datetimeindex and time series of high-low spread estimates.
     """
 
-    # define mid, 2 day high and 2 day low vars
-    mid, high_2d, low_2d = (df.high + df.low)/2, df.high.rolling(2).max(), df.low.rolling(2).min()
+    # define vars: mid, 2 day high and 2 day low vars
+    mid, high_2d, low_2d = (ohlc_df.high + ohlc_df.low)/2, ohlc_df.high.rolling(2).max(), ohlc_df.low.rolling(2).min()
 
-    # adjustment for overnight price moves
-    df['gap_up'], df['gap_down'] = df.low - df.close.shift(1), df.high - df.close.shift(1)
-    df['high_adj'], df['low_adj'] = np.where(df.gap_up > 0, df.high - df.gap_up, df.high), np.where(df.gap_up > 0, df.low - df.gap_up, df.low)
-    df['high_adj'], df['low_adj'] = np.where(df.gap_down < 0, df.high - df.gap_down, df.high), np.where(df.gap_down < 0, df.low - df.gap_down, df.low)
+    # compute adjustment for overnight price moves
+    ohlc_df['gap_up'], ohlc_df['gap_down'] = ohlc_df.low - ohlc_df.close.shift(1), ohlc_df.high - ohlc_df.close.shift(1)
+    # adjustment for gap up
+    ohlc_df['high_adj'], ohlc_df['low_adj'] = np.where(ohlc_df.gap_up > 0, ohlc_df.high - ohlc_df.gap_up, ohlc_df.high), np.where(ohlc_df.gap_up > 0, ohlc_df.low - ohlc_df.gap_up, ohlc_df.low)
+    # adjustment for gap down
+    ohlc_df['high_adj'], ohlc_df['low_adj'] = np.where(ohlc_df.gap_down < 0, ohlc_df.high - ohlc_df.gap_down, ohlc_df.high), np.where(ohlc_df.gap_down < 0, ohlc_df.low - ohlc_df.gap_down, ohlc_df.low)
 
     # B beta
-    B = (np.log(df.high_adj/df.low_adj))**2 + (np.log(df.high_adj.shift(1)/df.low_adj.shift(1)))**2
+    B = (np.log(ohlc_df.high_adj/ohlc_df.low_adj))**2 + (np.log(ohlc_df.high_adj.shift(1)/ohlc_df.low_adj.shift(1)))**2
     # G gamma
     G = (np.log(high_2d/low_2d))**2
     # alpha
@@ -38,9 +40,11 @@ def hlse(df, frequency='daily'):
     # substitute alpha into equation 14 to get high-low spread estimate S
     S = (2 * (np.exp(alpha) - 1)) / (1 + np.exp(alpha))
     # resample using daily mean
+    if frequency == 'weekly':
+        S = S.resample('W').mean()
     if frequency == 'monthly':
         S = S.resample('M').mean()
     # drop NaNs
     S.dropna(inplace=True)
 
-    return S
+    return S
diff --git a/high_low_spread_estimator.py b/high_low_spread_estimator.py
@@ -0,0 +1,46 @@
+# high-low spread estimator (hlse) provides an estimate of bid-offer spreads, a measure of liquidity risk
+# described in Corwin and Schultz (2011): https://papers.ssrn.com/sol3/papers.cfm?abstract_id=1106193
+
+def hlse(df, frequency='daily'):
+
+    """
+    Computes the high-low spread estimator, an estimate of bid-offer spreads, described by Corwin & Schultz (2011)
+
+    Parameters
+    ----------
+    df: DataFrame
+        dataframe with date, open, high, low and close (OHLC) time series
+    frequency: str
+        'daily' for daily bid-offer spread estimate, or 'monthly' for monthly bid-offer spread estimate, defaults to daily
+
+    Returns
+    -------
+    S: series
+        time series of high-low spread estimate
+    """
+
+    # define mid, 2 day high and 2 day low vars
+    mid, high_2d, low_2d = (df.high + df.low)/2, df.high.rolling(2).max(), df.low.rolling(2).min()
+
+    # adjustment for overnight price moves
+    df['gap_up'], df['gap_down'] = df.low - df.close.shift(1), df.high - df.close.shift(1)
+    df['high_adj'], df['low_adj'] = np.where(df.gap_up > 0, df.high - df.gap_up, df.high), np.where(df.gap_up > 0, df.low - df.gap_up, df.low)
+    df['high_adj'], df['low_adj'] = np.where(df.gap_down < 0, df.high - df.gap_down, df.high), np.where(df.gap_down < 0, df.low - df.gap_down, df.low)
+
+    # B beta
+    B = (np.log(df.high_adj/df.low_adj))**2 + (np.log(df.high_adj.shift(1)/df.low_adj.shift(1)))**2
+    # G gamma
+    G = (np.log(high_2d/low_2d))**2
+    # alpha
+    alpha = ((np.sqrt(2 * B) - np.sqrt(B)) / (3 - 2 * np.sqrt(2))) - (np.sqrt(G/(3 - 2 * np.sqrt(2))))
+    # replace negative values by 0
+    alpha = pd.Series(np.where(alpha < 0, 0, alpha), index=alpha.index)
+    # substitute alpha into equation 14 to get high-low spread estimate S
+    S = (2 * (np.exp(alpha) - 1)) / (1 + np.exp(alpha))
+    # resample using daily mean
+    if frequency == 'monthly':
+        S = S.resample('M').mean()
+    # drop NaNs
+    S.dropna(inplace=True)
+
+    return S