The simplest model of currency banking

Economists start with central banking, an awfully incomplete model.  I make it simple.

The currency banker runs a savings and loan, for the member banks. The currency banker publishes its marginal gains or losses, as well as its volatility bounds, as well as the currency growth.   It examines the volatility of deposit balances and volatility of loan balances.  When these exceed the bounds, rates are computed backwards, each member bank taking gains and losses.  The currency banker takes gains and losses, and publishes its gain and lose history.

If the currency is growing in use, and operating within volatility, then the currency banker is taking regular losses; but prices are stable.  The currency banker has no bias, it follows the member bankers up and down.  Member banks are under some competition so exit and entry preserved.

Now, just define the volatility equation you want from the currency banker; then go do some Ito's calculus with the data.  If your currency banker equation is derived from the G based accounting identity, then your model is likely to be unstable, too much asymmetry.  G violates the entry-exit requirement for member banks.

And transaction costs are zero.  The cost of protecting the currency denominations, and shipping them around.  This ancillary cost  must be way below any real good flow variation.

In what good is the currency redeemable?

'Well the currency banker guarantees absolute honest account,mainly because it can be a spreadsheet function.  So the currency is redeemable because the futures price follows the safe rate rule, with published volatility bound.  It uses a well known futures pricing model, inverted, so it computes the safe rate.Your 'digits' are likely spendable with the many merchants who cause the bounded volatility.