Changing a Periodic Tenancy to Fixed-Term in Wales

I'm a residential landlord based in Wales. A property of mine has been rented through a letting agent. The tenant has been in situ for 14 months, so their contract has rolled over to a periodic one following the initial fixed 12-month term. I've just taken the property off the agent's hands and intend to manage it myself. I have my Rent Smart Wales landlord licence.  
 
My tenant wants another 12-month fixed contract rather than continuing the periodic. I'm happy to give him the extra security he requires. My questions are:   
 
Can I convert the current periodic contract back to a fixed-term one?  
If not, is the only way to cancel the periodic contract to do so with both party's agreement and set up a new contract? I'd rather not have to do this.  
If that were the case, would the deposit have to be cancelled and returned and a new one created, or can it stay as it is or be transferred?