diff --git a/marshmallow_jsonschema/__init__.py b/marshmallow_jsonschema/__init__.py
index 8f3b233..9995cd8 100644
--- a/marshmallow_jsonschema/__init__.py
+++ b/marshmallow_jsonschema/__init__.py
@@ -6,5 +6,5 @@
 from .base import JSONSchema
 
 __all__ = (
-        'JSONSchema'
+    'JSONSchema',
 )
diff --git a/marshmallow_jsonschema/base.py b/marshmallow_jsonschema/base.py
index 9314088..8c74aaa 100644
--- a/marshmallow_jsonschema/base.py
+++ b/marshmallow_jsonschema/base.py
@@ -10,7 +10,9 @@
 from .validation import handle_length, handle_one_of, handle_range
 
 
-__all__ = ['JSONSchema']
+__all__ = (
+    'JSONSchema',
+)
 
 
 TYPE_MAP = {
@@ -105,7 +107,6 @@ def _get_default_mapping(self, obj):
 
     def get_properties(self, obj):
         """Fill out properties field."""
-        mapping = self._get_default_mapping(obj)
         properties = {}
 
         for field_name, field in sorted(obj.fields.items()):
@@ -122,7 +123,7 @@ def get_required(self, obj):
             if field.required:
                 required.append(field.name)
 
-        return required
+        return required or missing
 
     def _from_python_type(self, obj, field, pytype):
         """Get schema definition from python type."""
@@ -242,6 +243,6 @@ def wrap(self, data):
         self._nested_schema_classes[name] = data
         root = {
             'definitions': self._nested_schema_classes,
-            '$ref': '#/definitions/{}'.format(name)
+            '$ref': '#/definitions/{name}'.format(name=name)
         }
         return root
diff --git a/tests/test_dump.py b/tests/test_dump.py
index b099516..740224c 100644
--- a/tests/test_dump.py
+++ b/tests/test_dump.py
@@ -440,3 +440,13 @@ class TestSchema(Schema):
         'type': 'string',
         'description': 'Directly on the field!',
     }
+
+
+def test_required_excluded_when_empty():
+
+    class TestSchema(Schema):
+        optional_value = fields.String()
+    schema = TestSchema()
+    json_schema = JSONSchema()
+    dumped = json_schema.dump(schema).data
+    assert 'required' not in dumped['definitions']['TestSchema']