With the upcoming hard fork will there be a fixed exchange rate between Bitcoin Unlimited and Bitcoin? As you know, there might be an upcoming hard fork of BTC to enlarge the block size. 

Will the new currency Bitcoin Unlimited be a different currency or will it be compatible with Bitcoin with a fixed exchange rate between the new and the old currency?
If the two projects both persist, they would be freely traded one for the other. A fixed price could only be established if someone with unlimited funds guaranteed an exchange rate, which naturally can't happen because there is a limited number of tokens.

If the hardfork occurs you will have whatever Bitcoin you had on both these chain-tips.

Note, that to Bitcoin Unlimited nodes as it's currently implemented the Bitcoin chain would still appear valid, and if the latter ever grows longer after the chain split, BU nodes would reorganize back to the Bitcoin chain. This could of course be prohibited by setting BU nodes to require one of the blocks created after the chain split to be part of their longest chain.