What is a good way to keep an object in front of the player?

I want to simulate loading and shooting an arrow. I would like to make it so that while the player is holding down the fire button, an arrow appears and stays in the center of the camera. I've done all this except I can't get the arrow to stay with the player, it spawns and stays there instead of move with the player. Here is my code:

public class BowScript : MonoBehaviour {

 private float charge;
 public float chargeMax;
 public float chargeRate;
 public KeyCode fireButton;
 public Transform spawn;
 public Rigidbody arrowObject;
 private bool arrowReady = false;
 private Rigidbody arrow;

 void loadArrow() {
     charge += Time.deltaTime * chargeRate;
     if (!arrowReady) {//if there is no arrow ready
         arrowReady = true;//now there's an arrow
         arrow = Instantiate (arrowObject, spawn.position, Quaternion.identity) as Rigidbody;//puts an arrow in the bow spot
         this.arrow.position = spawn.position;
         this.arrow.isKinematic = true;
     }
 }

 void fireArrow() {
     arrowReady = false;
     if (arrow != null) {
         arrow.isKinematic = false;
         arrow.AddForce (spawn.forward * charge, ForceMode.Impulse);//adds force to the arrow all at once
     }
     charge = 0;
 }

 void Update() {
     if (Input.GetKey (fireButton) && charge < chargeMax) {//pulling the arrow back
         loadArrow ();
     }
     if (Input.GetKeyUp (fireButton)) {//fire the arrow
         fireArrow ();
     }
 }

}

If anyone has any suggestions I would be very appreciative, thanks