VueJs: Textarea input binding

I'm trying to figure out how to detect change of the value on the textarea from within the component.

For input we can simply use

<input
  :value="value"
  @input="update($event.target.value)"
>

However on textarea this won't work.

What I'm working with is the CKEditor component, which should update wysiwyg's content when model value of the parent component (attached to this child component) is updated.

My Editor component currently looks like this:

<template>
    <div class="editor" :class="groupCss">
        <textarea :id="id" v-model="input"></textarea>
    </div>
</template>

<script>
    export default {
        props: {
            value: {
                type: String,
                default: ''
            },
            id: {
                type: String,
                required: false,
                default: 'editor'
            }
        },
        data() {
            return {
                input: this.$slots.default ? this.$slots.default[0].text : '',
                config: {
                    ...
                }
            }
        },
        watch: {
            input(value) {
                this.update(value);
            }
        },
        methods: {
            update(value) {
                CKEDITOR.instances[this.id].setData(value);
            },
            fire(value) {
                this.$emit('input', value);
            }
        },
        mounted () {
            CKEDITOR.replace(this.id, this.config);
            CKEDITOR.instances[this.id].setData(this.input);
            this.fire(this.input);
            CKEDITOR.instances[this.id].on('change', () => {
                this.fire(CKEDITOR.instances[this.id].getData());
            });
        },
        destroyed () {
            if (CKEDITOR.instances[this.id]) {
                CKEDITOR.instances[this.id].destroy()
            }
        }
    }
</script>

and I include it within the parent component

<html-editor
    v-model="fields.body"
    id="body"
></html-editor>

however, whenever parent component's model value changes - it does not trigger the watcher - effectively not updating the editor's window.

I only need update() method to be called when parent component's model fields.body is updated.

Any pointer as to how could I approach it?