A lot of hope is being placed on regulatory equivalence - a concept that potentially allows businesses from a non-EU country to trade in some EU markets under its home country rules, rather than complying with (foreign) EU requirements. This might look like an attractive option for the UK since, at the point of a Brexit, the UK's rules are at least equivalent to the EU's.
However, as this article points out, one of the supposed benefits of a Brexit is parliamentary sovereignty - necessarily suggesting a divergence in standards. While we could become stricter than the minimum EU standard, as we can now, I think the only political suggestion is that we will 'cut red tape' by reducing regulation (and losing equivalence).
Even if we move forward in parallel with EU legislation for a certain time, the coverage of the equivalence concept is extremely light within EU financial services legislation - there are a lot of gaps. Equivalence seems to me to be a stopgap measure that might smoothly shepherd the UK to a different, future regime. However, achieving a more blanket coverage for equivalence is going to cost something during the Brexit negotiations. Let's not pretend this is a perfect alternative to passporting when weighing up that cost.
This allows companies from markets that are deemed to have “equivalent” regulatory standards to trade freely across borders with each others’ customers under their home country’s laws and regulations.