How much should I pay my friend to photograph my wedding if he is insisting on not charging me?

Honestly, if he isn't a professional photographer, accept the photos as his wedding gift to you. If he IS a professional, then you can accept them as a gift or pay him up to or beyond the rates he charges other clients based on the number and size of prints you're getting.  Or offer to pay the going rate for the prints and accept the "photography" as a gift.

Look at comparative costs, and work it out

Treat your friend's services as a wedding gift. Just like gifts of cookware and linens, you express appreciation with a handwritten thank you letter or note. 

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maybe you can buy him a gift for doing that

You can offer him whatever the going rate is in your area, but if he insists on doing it for free, don't fight him.

Is he a professional wedding photographer? Then get some estimates from other wedding photographers give him at least half that.

Not a professional? Give a little less?? You could get him a gift card. 

Or can you repay with a skill of your own? 

Do not tell him his services are in replacement of a gift!  Rude!  No one owes you a wedding gift. It is optional. Never expect a gift. 

Really think about asking him.  As a close friend allow  him to relax and be a guest at your wedding.  Instead of working it. Not being able to join in on the fun.

maybe it's his wedding present to you. 

Tell him you will accept his offer as a wedding present to you and your bride.