The idea of triangular congruency possessing basic reductionist strength is apparent in nature, social interaction and by extension, market behaviour and transactions.

One market relationship which exhibits this property is the classic triangular currency arbitrage, which allows for the determination of the equilibrium cross-rates of three currencies. This necessarily invokes that most central tenet in arbitrage theories, the Law of One Price. And interestingly, some definitions have the Law of One Price as: "the resting place for an asset's price and arbitrage is the action that draws prices to that spot. The absence of arbitrage opportunities is consistent with equilibrium prices, wherein supply and demand is equal". Again this invariably leads back to the idea of a triangulated relationship between the two sides of demand and supply engaging to arbitrage/converge a plumb-line to the base of the equilibrium state/price.

The essential question in the financial markets of course, is in determining just how individual agents/traders’ market views (normally differing on many levels) transform or align into a herding market sentiment. Some interesting studies have used the percolation model (from the physical sciences) in accounting for how market views spread through a financial network topology; the crux lying in how network feedback builds and eventually escalates past the percolation threshold i.e. reaches criticality. A simple treatment utilizes a two-dimensional lattice of individual agent/trader interacting and inter-influencing neighbouring sites - reducing it to a pure geometrical percolation problem. And here the common triangular lattice is used as the basic building block for the network topology.





Speak your mind

1 Comment so far

  1. douglas roberts dimick on February 19, 2012 2:58 pm

    Systematics Not Sentiments

    I was rereading Don’s article on Triangular Congruency. Note his observation that “the idea of a triangulated relationship between the two sides of demand and supply engaging to arbitrage/converge a plumb-line to the base of the equilibrium state/price.”

    Victor’s published studies of electronics, when considering plumb-line correlations, indicates that trigometric calibration of price action is not consistently relative to data or indicator generated topologies. How about with transaction systematics? One may find that algo-quant applications, as Don indicates, often reduce given price sets into one or more models of a probability matrix, such as a geometric equation.

    The question then becomes one of efficacy with price to model sequencing. As with analyzing and distinguishing a legal issue, the topology of electronic exchange market systematics is analogous to fact, policy, and reason sequencing for modeling price action; it is ultimately governed by rules-based sequencing.

    Hence, consistency in mapping function and integration then would appear to focus on how to construct convergence/divergence gates for dynamic processing of order execution protocols. As in the law, here substance is often confused to be determinative “when” procedure actually functions in some way, shape, or form as condition precedent. Victor’s article on parallel circuitry for instance…



Resources & Links