Near instant trades can happen “off-chain”, which is how centralized exchanges work on bitcoin today (e.g. btc-e, or bitstamp). The exchange could maintain a share reserve from deposits, and would enable very fast trades. Then, there could be settlement to the blockchain on either some regular basis, and/or when people “cashed out” from the exchange.
The asset or security (or whatever else) in question would just be another Counterparty token, much like XCP, LTBCOIN, SWARM, SJCX (StorjCoin), and others that already exist today. The legal and regulatory framework around it may vary (i.e. a token representing a corporate stock security, vs a token representing a small business crowdsale), but the underlying technical specifics would be the same.
And — if it was permissible by law — the digital token/asset could even be traded on the same exchanges that the Bitcoin community uses and trusts today (such as Bitstamp, Mintpal, OKCoin, and more), as an alternative to totally “trust-less”, decentralized trading on Counterparty’s DEx (decentralized exchange). This is exactly how things work with XCP (the Counterparty currency) today.