The hope of getting a model for bubble formation in financial markets is such a grand prize in the current state of human knowledge of what makes markets and prices move since they affect the seven billion and since for a century we have followed Bachelier to a brick wall of a fortress in terms of any scientific understanding of the markets that moves away from the English Utilitarians only breached slightly by the genius of Benoit Mandelbrot but not conquered. Onsager’s very simple explanation of vortex formation in turbulent fluid movement by negative temperature states is much more than a simple analogy for technical fidgeting and trial and error. Volatility is like temperature of a bubbling cauldron of human emotions literally if you ask the market participants who speak of the market with an awe and devotion that in the ancient times might have been reserved only for a Dionysus or an Apollo. It is too easy to say that people anthropomorphise that they cannot conquer in nature as some deity or other that is a component of the strange relation of humans with powers they do not control or cannot see clearly. But there is the issue of the empirical effects of finance to seven billion that need a science in ways infinitely more urgent than Emile Durkheim’s project of seeking a science of sociology of religion of modern western man in terms of indigenous religions as primitive models during the time when British Empire scientists was surveying the peoples of the world which were essentially their conquests before Hiroshima when the entire worl belonged to the winners of that game on the global board. Therefore I am reading and trying to decipher in baby steps the science of Onsager’s hydrodynamic model. I am not an expert on it by any means but I have the means to become one specializing in the connection between this scientific theory, analyzing it to sufficient depth to understand the mathematics, and then try to conceptualize a model for financial markets that is empirical rather than based on Ito calculus of Brownian motion. There exists a stochastic integral for fractional Brownian motion as well but it is unknown to me whether this calculus without a simple Ito formula can reproduce the arbitrage-free theory that came with the martingale risk-neutral measure ideas that have been used in actual markets with success. Of course success in the market is powerful but as obviously bad scientific theories or perhaps better stated, scientific theories that are imperfect match to all available known empirical features are like the scientific paradigms of Thomas Kuhn and survive till some set of conditions trigger a paradigm shift. Empirical problems are not sufficient. New paradigms must promise also new concepts, considtency and completeness and so on. Such a new paradigm would result if a long memory VARFIMA model covariance matrix can be enrichened with concepts that provide a mathematical link — and by mathematical link I mean in terms of mathematical structures and not by claiming exact identifications. In what way is volume like temperature and in what way is it not like temperature in substantive terms is my preoccupation after if any links can allow us to take the literal explanation of Onsager of how vortices are formed and map it to bubbles in volatility?

kinetic-theory-onsager-2D-vortex-formation

Alan Greenspan has shown the expanse of his understanding of economic phenomena in his relatively recent autobiography and his estimates as the man who held the seat of chair for many years at the Fed sheds light on the current objective thinking in the Fed scientifically. In fact Alan Greenspan is quite the renaissance scholar and has some amateur but significant interest and understanding of nuclear physics from intellectual curiosity and for formative years in his intellectual youth. He has positive ideas there for some of the characteristics of bubbles which are sophisticated but one phrase of his that illuminates his view is ‘irrational exhuberance’ and optimism of plebian mobs in the markets, extremely high valuation of tech stocks prompted the phrase and of course the tech valuations are still obscenely high if evaluated by any measure traditional corporate analysts would use in the markets, the so called ‘fundamentalists’ among financial traders. Since the quants, mathematicians and physicists have entered the fray since early 1990s the old fundamentalist/technicals division was modified by a new class of sophisticated mathematical and statistical models that developed from the Markovian school with the success and failure of Long-Term Capital Management. The fixed income quant models of Heath-Jarrow-Morton (I used to work for Andrew Morton for my first job) are based on the Markov approach but to entire yield curves rather than the spot rate. Recall that fixed income simply refers to debt instruments rather than commodities such as gold and oil or stocks. These models were tools that Lehman Brothers where I worked and elsewhere sought to evaluate the fair cost of complex deals made of promises to buy or sell in the future various objects, a simple example being a swap of Treasury 3Month + 50 basis points for some Corporate AAA rated debt. In this example 50 basis points is 0.5% and called the risk premium of the Corporate debt. So these yield curve models were essentially methods of diffusing yield curves into the future and calculating expected present values of future transactions. The measure used for the expectations had some theory behind it assuming that the motion is Markov. The theory produced a ‘risk-neutral measure’ which is a construct of the theory and which is a martingale with respect to the Brownian filtration. Markov models dominate the parctice and claimes the seat of paradigm as scientific theory so long memory models are not considered yet ripe for a new paradigm. One important lesson learned from Long-Term Capital’s collapse is that Markov models of this type severely underestimates risks of turbulent blow-ups, very similar in a way of misunderstanding the potential of losing one’s home when one has a decent job and a good education and good skills. Turbulence is common in financial markets. Irrational exhuberence is not limited to tech in Bay Area; it was common throughout history of trade and commerce and public markets.

on May 19, 2015 at 10:03 pm |ReaderIntriguing. If you can develop a theory I would be interested.

on May 21, 2015 at 6:00 pm |ReaderSince you seem to be taking interest once more in quant finance-related topics, I’m wondering if you’d like to work with me on the sovereign wealth fund project? (The time is now, the moment has come.)