Boom and bust research links: superexponential growth and crashes

Given the rapidity of today’s gap higher in the S&P 500, it would seem to be an appropriate time to repost some research related to the boom and bust cycle. Certainly it would seem we are near a phase transition of sorts in the stock market. For most of 2015 the market has been range-bound, but as of recently we have been skirting along yearly highs. Many have been waiting for the next leg higher, but some have been calling for a correction or even a crash. Who is right? Are we in a bubble?

One promising line of research for modeling financial bubbles is the Log-periodic growth model, sometimes called superexponential growth. The basic idea is that in a bubble, assets will grow at faster and faster rates of return until they reach the top, which are known as singularities because the model was born from physical models of phase changes.

Here is a TED talk from one of the model’s most vocal proponents, Didier Sornette, giving a high level overview of the concept:

For those interested in delving deeper into the subject, you will want to check out these papers:

Predicting Financial Crashes Using Discrete Scale Invariance

We present a synthesis of all the available empirical evidence in the light of recent theoretical developments for the existence of characteristic log-periodic signatures of growing bubbles in a variety of markets including 8 unrelated crashes from 1929 to 1998 on stock markets as diverse as the US, Hong-Kong or the Russian market and on currencies. To our knowledge, no major financial crash preceded by an extended bubble has occurred in the past 2 decades without exhibiting such log-periodic signatures

Bubbles and anti-bubbles in Latin-American, Asian and Western stock markets: An empirical study

Twenty-one signicant bubbles followed by large crashes or severe corrections in Latin-American and Asian stock markets are identied. We nd that, with very few exceptions, these speculative bubbles can be quantitatively described by a rational expectation model of bubbles predicting a specic power law acceleration as well as so-called log-periodic geometric patterns. This considerably extends the applicability

Financial bubbles: mechanisms and diagnostics

We define a financial bubble as a period of unsustainable growth, when the price of an asset increases ever more quickly, in a series of accelerating phases of corrections and rebounds. More technically, during a bubble phase, the price follows a faster-than-exponential power law growth process, often accompanied by log-periodic oscillations. This dynamic ends abruptly in a change of regime that may be a crash or a substantial correction. Because they leave such specific traces, bubbles may be recognised in advance, that is, before they burst…

And for more current research on the subject, make sure to visit ETH’s great link-fest on Bubble Theory.

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Lead image licensed under CC BY 2.0 from leighklotz

2 replies »

  1. Sornette attempted to forecast a prolonged series of depression like stock market “down years” after either the 2000 tech crash or 2008 financial crisis ( don’t remember which ) utilizing some kind of mathematics used in calculating “spirals” and “geologic” shocks. He was foiled .. Same with John Mauldin, using different esoteric methods and projections… 2 authors form completely different backrounds. …


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