Could banks move to continuous (rather than overnight) funding?

Question

The dominant frequencies for Money Market and FX instruments were 6m and 3m for a long time, and banks slowly moved to commercial trades at those frequencies but funding overnight. If this is a step in the direction of increasingly short-term funding as trade frequencies and volumes increase, could banks move to continuous funding? That is, the book is continuously balanced, excess lent continuously and funding performed continuously, with a continuously indexed swap instead of an Overnight Indexed Swap?

One can imagine an hourly or minute-to-minute fixing in FX already.

[Update Sep 2012]: Via Deus Ex Macchiato, this from the FSOC annual report:

Currently, triparty repo trades unwind every day, meaning that the clearing bank returns cash to the lender’s account and returns collateral to the borrower’s account. Trades are not settled until several hours later. For several hours each afternoon, dealers require funding of their entire triparty repo book that lenders do not provide. This $1.7 trillion funding need is provided by two clearing banks.

This is a potentially unstable situation.

This suggests that accounts are already balanced hourly or less.

Answer 1

Overnight funding is made through an auction, a fixing as you name it and it is achieved successfully (usually, i.e. when Lehman Brothers doesn't go bankrupt) because of the huge amounts on BOTH sides of this auction (i.e. liquidity).

If you do an auction every minute, you will have more volatility as prices will potentially vary every minute and there will be less liquidity, this is definitely not something Back Office should handle (because it's basically Trading). I cannot really imagine the situation if we add arbitrageurs in the middle of this, things would get really messy.