Make WordPress embeds of local content responsive

functions.php

<?php
/**
 * Filter function, converts fixed width to '100%' width
 */
function responsive_wp_video_shortcode( $html, $atts, $video, $post_id, $library ) {
	$replace_value = array(
		'width: ' . $atts['width'] . 'px'
	);
	$replace_with  = array(
		'width: 100%'
	);

	return str_ireplace( $replace_value, $replace_with, $html );
}

add_filter( 'wp_video_shortcode', 'responsive_wp_video_shortcode', 10, 5 );