There is no option for this, but you can extend the ‘walker’ object that WordPress uses to create the menu HTML. Only one method needs to be overridden:
class My_Walker_Nav_Menu extends Walker_Nav_Menu {
function start_lvl(&$output, $depth) {
$indent = str_repeat("\t", $depth);
$output .= "\n$indent<ul class=\"my-sub-menu\">\n";
}
}
Then you just pass an instance of your walker as an argument to wp_nav_menu
like so:
'walker' => new My_Walker_Nav_Menu()