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Speculative and Hedging Interaction Model in Oil and U.S. Dollar Markets III - Phase Transition

Michael Campbell and David Carfi

posted on 19 January 2017

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We show that there is a phase transition in the bounded rational Carfi-Mussolino speculative and hedging model. This model has two types of operators: a real economic subject (Air) and one or more investment banks (Bank). It also has two markets: oil spot market and US dollar futures. We consider the Bank agents' behavior to equilibrate much more quickly than that of Air, as they react to the move of Air in the typical manner that speculators equilibrate markets. In this sense, Air is an acting external agent due to its longer-term investing, whereas the action of the banks is `annealed' -- i.e., equilibrates before Air makes its next transaction.

This model constitutes a potential game with a non-convex potential, and in the spirit of the Sonnenschein-Mantel-Debreu theorem, there are two equilibriums at lower temperatures due to a market-exchange symmetry in the potential. When the longer-term investing Air remains in the oil futures market (nonzero field), the speculating Bank agents prefer the oil spot market and their behavior is more stable, as is reflected by finite spatial volatility. Bank agents also prefer the oil spot market immediately after a relatively slow divestment of Air from the oil futures market. When Air makes no purchases of oil futures as a hedge (zero field), then as Bank agents become more rational (thermal cooling), they will ``crowd'' or ``herd'' their preferences into one market or the other at a critical temperature, which is spontaneous symmetry breaking of the market exchange symmetry. Thus we see that spontaneous symmetry breaking refines the potential and signifies the emergence of a market preference among speculators. The spatial volatility diverges at this critical temperature, indicating a less stable situation when longer-term investing is absent.

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