Simplified (derived) formula for faking the parallax of an object given a camera position, in the form of a Unity component. This may not work for VR??

ParallaxFaker2D.cs

using UnityEngine;

public class ParallaxFaker2D : MonoBehaviour {
	// The Transform of the camera to fake the parallax for.
	public Transform cameraTransform;

	// The world position to mimick the parallax of.
	public Vector3 fakePosition;

	// The Transform's target (actual) distance from the camera.
	// This will be scaled according to the parallax factor so moving the camera along the Z will also result in a proportionate Z movement according to the fake position.
	public float targetCameraDistance;

	// An arbitrary value. Set this according to what you think your typical camera.transform.position.z will be.
	const float BaseCameraZ = -10f; // Setting this to 0 will collapse the transformation.

	void LateUpdate () {
		Vector3 cameraPosition = cameraTransform.position;

		float fakePositionBaseDistance = (fakePosition.z - BaseCameraZ);
		float parallaxFactor = fakePositionBaseDistance == 0 ? 0 : (targetCameraDistance / fakePositionBaseDistance);
		Vector3 parallaxedCameraOffset = (fakePosition - cameraPosition) * parallaxFactor;

		transform.localPosition = cameraPosition + parallaxedCameraOffset; // Apply worldPosition as localPosition if you know it doesn't inherit any Transform.
	}
}