Monday, April 24, 2017

Can the pits do a better government default

John Cochrane answered a related question about using inflation to whither away government debt. I think statistically, dumping time we can get closer answers.

One version, out of many, will default a tiny portion of government debt across the curve, favoring the deposits that most match the final outcome.  One algorithm: When the variation between savings and loans drops below 1%, the central banks defaults a tenth of a point of government debt.  That is, the central bank, rather than be hedged, the central bank forces the hedge on the economy, requiring a 1% or more price variation, in anticipation of the defaults.

Now the central bank and the bankers  have equal visibility of the trade book and the ability to make asynchronous bets, from a queue. The central bank will never hit its target, just float around it.  Time plotters will observe a 1% short term rate, but the currency risk is bouncing around that term length; time plotters have time error.

The economy, meanwhile,  is doing entry and exit, however, and I am sorry about that.  Firms unable to meet the cost of defaults, drop out; or use an alternative currency.   The overall gain is actually quite nice.  Firms not easily taxed and most harmed by government costs go off the system, and their cost to government and the economy drops.  Various government expenses across the programs become more visible.

The math

Look at John's equations, the series on the left.  It is the infinite sum of returns.  We use compact distributions, and that is a finite  series with computed window length, simply the sum accumulated up the matching tree, that is, the pay off strike prices.  The prices will be quantized accumulations up the tree of  the 2% induced price variation.  The  more we default, the lower the tree rank, the lower the economic complexity, and the more utilization of alternative currencies.

The problem soled is separating currency risk from the cost of entry and exit, the TBTF problem. Currently, TBTF includes the accumulating bit error, it is not visible, the nickels and dimes stack up.  The implied cost is in all the inflation adjustments, and price fixes across the programs.

Entry and exit need to be priced. The Cochrane systems handles default fine, random events with replacement. But the actuality is that some of those mis-pricings have to be absorbed by the pit boss, as they represent accumulated price errors, the market liquidity to 'make the market'.  Currency error are not observable by anyone, are not an assignable cost, have no pricing surface by definition.  This is different from price variations which are expected.  Being purely untradable, bit errors need to be accumulated if currency is conserved.

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