Edit in JSFiddle

var renderMarkdown = Vue.extend({
	template: '#renderMarkdownTemplate',
	props: ['markdown'],
  computed: {
  	convertedMessage: function() {
    	var text = markdown.toHTML(this.markdown);
      return text;
    }
  }
});
new Vue({
    el: '#container',
    data: {
        message: '#This is a title'
    },
    components: {
    	'render-markdown': renderMarkdown
    }
});
<div id="container">
    <render-markdown :markdown="message"></render-markdown>
    <textarea rows="30" cols="50" v-model="message"></textarea>
</div>

<template id="renderMarkdownTemplate">
  <div>{{{ convertedMessage }}}</div>
</template>