# Probability of Hyperinflation as a function of Probability of Soverign Default

I'm looking for some academic research on modeling risk of hyperinflation. Specifically, I'm interested in modeling the probability of hyperinflation over some time interval (e.g., probability of hyperinflation in Argentina within the next year).

I'm familiar with numerous macroeconomic models which are related to inflation, but I'm looking for something a bit different. Clearly sovereign default hyperinflation are related, but I'd like to estimate some function to convert between the two. For example, we can infer probability of default from CDS rates. Then, I'd like to use that to determine probability of hyperinflation. Are there any problems with attempting to approach this problem using this method?

Any references or guidance would be appreciated. FWIW, my technical background in mathematics, stats, finance is relatively advanced. i.e., don't be discouraged from sharing any references using stochastic calculus, vector autoregression, etc.

Thanks!

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I think the problem is that, for countries with a sizeable risk of hyperinflation, you will not have deep and mature markets to extract market expectations from.

Argentina is a good example. Hyperinflation is just 'very big inflation', but you don't have inflation swaps in ARS. The CDS that you mention will pay in USD, and are therefore immune to ARS inflation. There are no quanto CDS on Argentina, as far as I know. You might want to extract information synthetically using bonds, but all Argentinean bonds are in USD, nobody wants Peso-denominated bonds. Perhaps you can look at the FX forward curve, as hyperinflation would cause ARS to collapse, but the market is not free-floating. Unless you have access to black market forward rates.

And even if you did, then you have to convert the risk neutral probabilities into actual ones.

Edit: There is academic research on the monetary aspects of hyperinflation, for example Cagan's 1956 paper in Milton Friedman's book. More refernces on Cagan's wiki page.

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Thank you for the link. Could you help me understand this sentence? "The CDS that you mention will pay in USD, and are therefore immune to ARS inflation." If ARS undergoes hyperinflation, then shouldn't the goverment be much less likely to be able to settle those USD-denominated credit instruments? Then, the implied default probability should take into consideration probability of hyperinflation. Where's the flaw in this logic? Could you provide a small example? Thanks! – Clark Henry Jul 30 '14 at 17:31
@nsw Sure. A CDS might reference Argentina but it is a contract between two separate parties, say banks Abc and Xyz: Abc buys a 5y CDS referencing Argentina from Xyz on a notional of USD10m at a price of 800bp. Abc pays USD400k every six months for 5 years to Xyz; if Argentina defaults within 5 years, then Xyz will pay Abc a fraction of USD10m (which is determined by a post-default auction of Argentine bonds). Argentina is not involved. Argentina is not involved at all in those exchanges, and hyperinflation would not affect them. – Kiwiakos Jul 30 '14 at 20:38
The hyperinflation would not affect that post-default price on Argentine bonds which determines the fraction of USD10m? – Clark Henry Jul 30 '14 at 20:41
@nsw A quanto CDS would be similar, but it would reference and pay in ARS instead of USD. The price might be 100bp instead of 800bp, that is to say, it costs only ARS50k every six months to insure ARS10m of Argentine debt. The price difference between the USD and the quanto reveals market expectation of the ARS depreciation following an Argentine default: if ARS will collapse post-default, then insuring ARS will be cheap. This implied FX shock can be potentially linked to hyperinflation. But unfortunately you don't have quantos on Argentina. – Kiwiakos Jul 30 '14 at 20:45
Thank you very much! Frankly, I've never heard of a quantos instrument, but your description is clear. Anyway that's something I will look into on my own or ask in another thread if necessary. FWIW, I think your last comment may be significant enough to include in your original answer. :) – Clark Henry Jul 30 '14 at 20:48

I wrote a hyperinflation simulator. With enough data and enough work I think it would be possible to tune the constants so that it did a reasonable job of matching real world hyperinflation evolution. With that you could then predict which countries were most at risk.

http://howfiatdies.blogspot.com/2013/03/simulating-hyperinflation.html

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Hi Vincent Cate, welcome to quant.SE! Can you tell us a bit more about the simulator. Ideally the answer is contained completely your post and not in an external resource. – Bob Jansen Jul 29 '14 at 4:49
I used the equation of exchange to calculate a price level. The velocity of money depends on inflation rate and interest rates. As inflation goes up people get out of bonds if the government is trying to peg interest rates. So the central bank ends up making a lot of new money and buying up bonds. But the more it buys up bonds the more inflation and the less anyone else wants to hold them. So you get a feedback loop and an explosion of new money. The setup conditions are lots of government debt, a large deficit, and central bank trying to control interest rates. Not more characters. – Vincent Cate Jul 29 '14 at 9:57
You can edit your answer, then you have plenty of characters:) – Bob Jansen Jul 29 '14 at 10:54