Category Financial Econometrics and Empirical Market Microstructure

Modeling Financial Market Using Percolation Theory

Anastasiya Byachkova and Artem Simonov

Abstract Econophysics is a relatively new discipline. It is one of the most interesting and promising trends in modeling complex economic systems such as financial markets. In this paper we use the approach of econophysics to explain various mechanisms of price formation in the stock market. We study a model, which was proposed by Jean-Philippe Bouchaud and Dietrich Stauffer (Bouchaud 2002; Chang et al. 2002; Stauffer 2001; Stauffer and Sornette 1990), and used to describe the agents’ cooperation in the market. The most important point of this research is the calibration of the model, using real market conditions to proof the model’s possibility of setting out a real market pricing process.

Keywords Agent modeling • Econophysics • Financial market...

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Multifractal Formalism for Stochastic Processes

Original definition of fractal was proposed by Mandelbrot with respect to sets. He defined fractal as a mathematical set with fractal dimension is strictly larger than its topological dimension (Mandelbrot 1975,1982). Later he extends this definition, calling a fractal any kind of self-similar structure (Mandelbrot 1985).

For the stochastic processes the notion of fractality is based on the defini­tion of self-affine processes—processes that keep statistical properties under any affine transformations. Being more strict, a stochastic process X = {X (t); t > 0; X (0) = 0} is called self-affine, if for 8 c > 0 and time moments ti,…,tk > 0, the following expression holds:

{X(ctl),…,X(c tk)} = {cHX (ti) ,…,0HX (tk)}, (3)

where H is a constant named self-affine index and symbol “=” stands fo...

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Adaptive Learning

Risk management is a core discipline in a rapidly changing world. From finance to ecology, we face unprecedented systemic risks from increasingly coupled global systems. Non-linearities render long term predictions futile, and require considera­tion of many possible paths. Indeed we’ve seen a paradigm shift from “Command and Control” to “Sense and Respond” (Haeckel 2004). As in an ocean sailing race, organizations must navigate changing conditions using dynamic steering (Robertson 2010) with continuous feedback. “Managing Uncertainty” has replaced “Change

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Fig. 25 Macro and micro polarity management. Source: Laubsch (2010a, b)

Management” in leadership seminars (change management makes no sense if the direction of change is not clear).

Figure 25 shows how we can sp...

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Benchmarking

The website www. rogovindex. com was created in 2012-2013 to allow for viewing and, if desired, exporting into spreadsheet files the history of hourly, daily, weekly, monthly, or annual (the user may choose to define time zone lag) quotations of global risk factor indices, starting from January 1, 1957 at 1:00 a. m. (GMT).

A market of space weather index derivatives (Hyman (2001), (Rogov 2002) could be developed. For example, the RogovIndex© indices may be used as base assets for new index forwards and options. For this purpose, the website enables the users to build up portfolios of any combination of derivatives and offers analysis tools.

Already, every user of the website can upload to the database his or her own time series of any risk frequency indicators...

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Jumps Identification

Before a price jump can be accounted for in an estimation stage, it first has to be identified. Surprisingly, but the literature up to now does not offer a consensus on how to identify price jumps properly. Jumps are identified with various techniques that yield different results.

Generally, a price jump is commonly understood as an abrupt price movement that is much larger when compared to the current market situation. But this definition is too general and hard to define and test. The best way to treat this definition is to define the indicators for price jumps that fit the intuitive definition.

The most frequent approach in the literature is based on the assumption that the price of asset St follows stochastic differential equation, where the two components contribute to volatility:

dS[...

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European Divergence Case Study

The European Divergence Scenario illustrates the Adaptive Stress Testing frame­work well. With the introduction of the Euro, credit spreads converged for all member countries and started an unsustainable cycle of credit growth in high inflation countries like Greece, Italy, Portugal, and Spain. The artificial stability of the Euro currency was a classic Minsky case of stability breeding instability. As hidden imbalances continued to build up in the Euro periphery, Innovators like GaveKal Research analyzed the unsustainability of “PIGS” borrowing levels, and launched a European Divergence Fund in November 2007:

For ten years, investors have made money on convergence trades (i. e., Italian rates falling to meet German rates)...

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