Working papers 2007

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Number 2007/01 - Professor R Bowden and Dawn Lorimer - June 2007

• pdf277KBMonetary Policy and the exchange rate: The Kiwi that had to fly

Abstract:

June 2007 saw the first serious attempt by the Reserve Bank of New Zealand to exercise its currency intervention powers, in an attempt to put a cap on the soaring NZ dollar. Sceptics pointed out that this was inconsistent with the comfort to the foreign exchange carry trade conveyed by signals that the official cash rate would remain high or even tightened further, and intervention attempts could even perversely drive the currency higher. The problem for monetary policy has been that in an incomplete debt market, the only real channel for the official cash rate to impact on fixed rate home mortgage rates is via the indirect feedback from offshore NZ interest rates. This means that the exchange rate becomes the vector. We argue on the basis of forward interest rates that the problem is fixing itself, and from here on will only be hindered by currency intervention or further tightening signals from the central bank.

Number 2007/02 - Professor R Bowden - May 2007

• pdf241 KBInformation, measure shifts and distribution diagnostics

Summary: Reflexive shifting of a given distribution, using its own distribution function, can reveal information. The shifts are changes in measure accomplished via simple Radon-Nikodym derivatives. The separation of the resulting left and right unit shifted distributions reveals the binary entropy of location. Recombining the shifts via convex combinations yields information-based asymmetry and spread metrics as well as insight into latent structure. The resulting diagnostics are applicable even for long tail densities where distributional moments may not exist, and independently also of benchmarks such as the Gaussian.

Number 2007/03 - Professor R Bowden - May 2007

• pdf270 KBDirectional entropy and tail uncertainty, with applications to financial hazard and investments

Abstract:

“Mine is a long and sad tale”, said the Mouse, turning to Alice and sighing. “

It is a long tail certainly,” said Alice, looking down with wonder at the Mouse’s tail; “but why do you call it sad ?” And she kept on puzzling about it while the mouse was speaking…

Contexts such as value at risk or venture capital require local uncertainty measures, as distinct from properties of the entire distribution such as differential entropy. Applications such as value at risk and options pricing can be illuminated by means of a regime-specific concept of directional entropy. The latter enables a change of measure to an equivalent logistic distribution, one that has the same total and directional entropies at the given marker, e.g. value at risk critical point or option strike price. This is done via a scaling function that can be interpreted as a Radon-Nikodym derivative and used in its own right as a risk metric. Value at risk rescaling adjusts the critical probability to capture the long tail risk. Directional entropy can be used to identify regions of maximal exposure to new information, which can actually increase entropy rather than collapse it.