Here is a description of how the two-way pegging works quoted from Thorbinator on reddit:
A side chain holds no value of it's own, it uses whatever novel tech it has and the bitcoin market value.
How 2 way pegging works, the short version: magic, you can just use bitcoin or the alt chain interchangably.
The long version quoted:
To maintain the 21m coins promise, you start a side-chain with no in-chain mining subsidy, all bitcoin creation happens on bitcoin chain (as with 1-way peg). Reach a reasonable hash rate. (Other semantics than 1:1 peg should be possible, but this is the base case).
You move coins to the side-chain by spending them to a fancy script, which suspends them, and allows them to be reanimated by the production of an SPV proof of burn on the side-chain.
The side-chain has no mining reward, but it allows you to mint coins at no mining cost by providing an SPV proof that the coin has been suspended as in 2 on bitcoin. The SPV proof must be buried significantly before being used to reduce risk of reorganization. The side-chain is an SPV client to the bitcoin network, and so maintains a view of the bitcoin hash chain (but not the block data).
The bitcoin chain is firewalled from security bugs on the side chain, because bitcoin imposes the rule that no more coins can be reanimated than are currently suspend (with respect to a given chain).
To simplify what they hypothetical bitcoin change would need to consider and understand, after a coin is reanimated there is a maturity period imposed (say same as fresh mined coins). During the maturity period the reanimation script allows a fraud proof to spend the coins back. A fraud bounty fee (equal to the reanimate fee) can be offered by the mover to incentivize side-chain full nodes to watch reanimations and search for fraud proofs.
A fraud proof is an SPV proof with a longer chain showing that the proof of burn was orphaned.