diff --git a/pandas/io/formats/format.py b/pandas/io/formats/format.py
index 61af935bd8227..8ff4b9bda0430 100644
--- a/pandas/io/formats/format.py
+++ b/pandas/io/formats/format.py
@@ -549,7 +549,8 @@ def __init__(
         decimal: str = ".",
         table_id: Optional[str] = None,
         render_links: bool = False,
-        **kwds
+        bold_rows: bool = False,
+        escape: bool = True,
     ):
         self.frame = frame
         self.show_index_names = index_names
@@ -580,7 +581,8 @@ def __init__(
         else:
             self.justify = justify
 
-        self.kwds = kwds
+        self.bold_rows = bold_rows
+        self.escape = escape
 
         if columns is not None:
             self.columns = ensure_index(columns)
diff --git a/pandas/io/formats/html.py b/pandas/io/formats/html.py
index 4b44893df70ed..8c4a7f4a1213d 100644
--- a/pandas/io/formats/html.py
+++ b/pandas/io/formats/html.py
@@ -37,7 +37,7 @@ class HTMLFormatter(TableFormatter):
     def __init__(
         self,
         formatter: DataFrameFormatter,
-        classes: Optional[Union[str, List, Tuple]] = None,
+        classes: Optional[Union[str, List[str], Tuple[str, ...]]] = None,
         border: Optional[int] = None,
     ) -> None:
         self.fmt = formatter
@@ -46,11 +46,11 @@ def __init__(
         self.frame = self.fmt.frame
         self.columns = self.fmt.tr_frame.columns
         self.elements = []  # type: List[str]
-        self.bold_rows = self.fmt.kwds.get("bold_rows", False)
-        self.escape = self.fmt.kwds.get("escape", True)
+        self.bold_rows = self.fmt.bold_rows
+        self.escape = self.fmt.escape
         self.show_dimensions = self.fmt.show_dimensions
         if border is None:
-            border = get_option("display.html.border")
+            border = cast(int, get_option("display.html.border"))
         self.border = border
         self.table_id = self.fmt.table_id
         self.render_links = self.fmt.render_links
diff --git a/pandas/io/formats/latex.py b/pandas/io/formats/latex.py
index c60e15b733f0a..4c4d5ec73269a 100644
--- a/pandas/io/formats/latex.py
+++ b/pandas/io/formats/latex.py
@@ -39,12 +39,13 @@ def __init__(
     ):
         self.fmt = formatter
         self.frame = self.fmt.frame
-        self.bold_rows = self.fmt.kwds.get("bold_rows", False)
+        self.bold_rows = self.fmt.bold_rows
         self.column_format = column_format
         self.longtable = longtable
         self.multicolumn = multicolumn
         self.multicolumn_format = multicolumn_format
         self.multirow = multirow
+        self.escape = self.fmt.escape
 
     def write_result(self, buf: IO[str]) -> None:
         """
@@ -142,7 +143,7 @@ def pad_empties(x):
                     buf.write("\\endfoot\n\n")
                     buf.write("\\bottomrule\n")
                     buf.write("\\endlastfoot\n")
-            if self.fmt.kwds.get("escape", True):
+            if self.escape:
                 # escape backslashes first
                 crow = [
                     (