Making an arrow pen is very easy since you don't need a lathe. what you need is...
1. An arrow. I wouldn't use a new one.
2.a pen
3.A drill. (optional)
4.Knife.
5.pipe cutter.

Step 1: Measure.

make sure the pen is the size you want. what I do is use the pen as a size reference. measure from the back of the flecting on then mark it.

Step 2: Cut

take your pipe cutter and size it to the arrow and tighten but not too tight other wise it will turn out bad and you will get a fiber glass sliver. Then circle it arounmd the arrow and tighten slowly and softly until cut. when you hear little cracking noises tighten softer than before.

Step 3: Hallow.

If you use a drill at this part you would choose a bit that is large enough to chip a little bit away and small enough so that It won't eat away at the out side and only hallow out the length to where my finger is pointing in pic 7.then keep hallowing with larger bits until you have the desired thinness. number 2 pic is too small number 3 is too big. number 4 is just right. word to the wise dont hold the arrow where you are drilling too.