The hyperbolic currency banker equation, reposted

The continuing work on currency banking.

Loan and deposit net balances are the objective function.  The currency banker always drives some fixed percentage of the economy through the banking system from the short end.  No matter what happens, bankers are forced to get involved, they can lever leave the scene of the crime.

Here I just through a cycle change in economic growth, and let the banker function recompute accumulation rates on deposits and balances. The ratio of short balances to total balances is 1/10, the net liability normalized to 1.0.  Accumulation rates are about 2% in this. So we see the currency banker balances shifted as much as 2% over the 15 period sequence (about four years). The driving function was simply an increase in bank activity. The response is white noise, and I am still looking at different driving functions.  The currency banker keeps one units of deposits more than loans, he keeps the member banks busy finding investments. So the banker activity should grow and shrink proportional to economic variance.


Accumulation rates  set deposits and loans balances for the forward period.  The currency banker wants net balances to sum to a normalized percentage of GDP, which I call 1.0. The actual cost of money is a derived value computed one period late.

The currency banker looks two periods ahead when setting rates. The equation becomes becomes:

D*(1+d)^2 - L*(1 - l)^2 = 1.0, where d,l are rates and D,L are liability and asset balances.  D for deposit and L for loan. So deposit liabilities minus loan assets are driven to a fixed percentage of GDP. Rates here are   accumulation functions.  The net balance is a currency banker liability to the economy.

Thus deposit balances accrue and loan balances decay..  Net balances are normalized to the unit percentage of GDP, at two look aheads over the term period is selected.  So we see how loan rate was redefined, it is an outstanding balance reduction at a fixed percentage. The banker makes the net balances come to a 1.0 at the look ahead.

The rates are set independently so that balances match.  Why did I pick a two period look ahead.  First, I know the hyperbolic form is correct, and second the banker wants to stay one step ahead of the economy.

At each step set: D = 1/(2d) and L = 1/(2l), and at equilibrium, D = L.  D and L will accumulate as agents react to economic changes, and the banker chooses the appropriate moment to reset rates. There is a scale factor in the balances, D,L. which is the percentage of debt allocated to the short end.  The currency banker takes losses during growth and takes gains during recessions, so prices will be stable around zero inflation.


What are these rates again?
The rate on deposit includes rate to be earned on current deposits . The rate on loans includes rates  to  decrease in loan balance.  Actual rate cost of money is backward derived from the previous period, not known to anyone at the moment.  This will produce the Black-Scholes no arbitrage result.

After accounting for rates paid in and out, the system always tries to project a net liability of the currency banker equal to some tiny portion of the economy.

Are currency banker term structure fixed?
The currency banker operates at the quarterly rate, likely.  Member banks are forewarned that rates may change quarterly, but they can always see the balances and know when and how.  If the economy engages in longer term invesing, then the rate variation will be small.

What about prices?
Inflation in this thing should be zero with a fixed variance. I have not quite verified this.  But the debt flow system should be no arbitrage and obeys the theory of everything.  Debt flow will of necessity be log additive so Lucas numbers will apply. Also, I am pretty sure this system eliminates the equity premium and r will equal g, mostly.

Anyway, this is what I am playing with on my spread sheet.  It makes no attempt at stimulus. But the net effect is bankers always off their butts doing something . I am pretty sure I have this right, I have confidence in hyperbolic banking.

How does this relate to Schramm-Loewner?

I would think the ratio of total debt to short end debt is the Schramm-Lowener index.  That ratio determines the dimensionality of motion of the economy. And that should also be related to the Compton spectral match between mass and wave.