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When everybody with the same opinion are connected to each other, it would be more difficult for them to change their opinion. In the simulation results, we measure the degree of connectedness and the volatility. The plot of the inverse of conectedness corresponds strongly to the plot for volatility. Meaning: the less connected you are, the higher your fluctuation will be. The "closed network" represent the snapshot of the system with minimum volatility. While the "open network" represent the system with the maximum volatility.

The benefit of having a model in Econophysics

Is there a correlation between volatility clustering and trend changes in price? The graph below is generated using a simple Ising Model. The nice thing about this model is that we can easily vary the volatility clustering. Hence finding its correlation to the trend changes. One benefit of having models in Econophysics is the ability to vary the outcomes as we like it. A feature that obviously a bit hard to come by in real life ...

Mensimulasi Sistem Kompleks

Pertama tama, econophysics mencoba mempelajari perilaku ekonomi dari sudut pandang systemic. Mengenai crash, Didier Sornette (Seorang econophysicist dalam buku Why Stock Market Crash: Critical Events in Complex Financial Systems. Princeton University Press, Princeton, 2003.) mengatakan: "A crash occurs because the system has entered an unstable phase. Any small disturbance or process will create dramatic changes or even a collapse. The collapse is fundamentally due to the unstable phase of the system. The instantaneous cause of the collapse in the form of the disturbances is secondary. The real process that leads to the unstable phase may take a very long time."

Jadi penyebab primer dari krisis ekonomi adalah perilaku dari sistem itu sendiri, sedangkan apa yang seringkali disebut sebagai "penyebab" di dalam berbagai artikel, itu adalah penyebab sekunder. Semacam "trigger" yang mendorong sistem yang memang sudah dalam keadaan kritis untuk memasuki "crash". Kedua, perilaku sistem adalah hasil dari perilaku kolektif dari semua pelaku yang mengambil berbagai keputusan, mulai dari yang paling "irrasional" hingga yang paling "rasional". Para pengamat sering berbicara tentang satu unsur dalam pengambilan keputusan pelaku pasar. Memang merupakan unsur yang penting, tetapi perilaku pasar sangat sulit dijelaskan hanya berdasarkan satu atau dua faktor saja. Ketiga, kata "fisika" di dalam ekonofisika menuntut bahwa semuanya diawali dari analisa data empiris dan kembali kepada analisa data empiris. Data empiris dalam bentuk "historical data" dalam waktu yang panjang memperlihatkan semacam "universalitas" dalam perilaku sistem ekonomi. Ada kesamaan yang menakjubkan antara perilaku complex system dalam ekonomi. biologi, dan fisika. Manusia sebagai individu memang sulit dipahami dan cenderung unpredictable. Namun suatu complex system yang tersusun atas banyak individu yang saling berinteraksi ternyata akan menghasilkan collective behavior yang dapat diukur dan cukup sederhana. Kita dapat menyusun model sederhana yang memuat beberapa simple rules yang mengatur interaksi antar individu, interaksi dengan environment dst. Kita lalu dapat membuat simulasi yang hasilnya dapat dibandingkan atau difit dengan data empiris. Simulasi diperlukan untuk "menciptakan" collective behavior. Simple rules saja (yang memuat kuantifikasi interaksi antar individu, misalnya) tidak cukup. Pertanyaan yang sering diajukan adalah: Bagaimana simulasi dapat memperhitungkan sifat manusia yang complex, unpredictable, dan kerap kali bersifat irrasional? Jawab: meskipun setiap individu bersifat complex, sulit dipahami, bahkan "dark", namun collective behaviornya ternyata merupakan "emergent simplicity"! Perlu dicatat bahwa kita tidak secara langsung mensimulasikan manusia, tetapi mensimulasikan konsekuensi dari keputusan-keputusan yang dibuat manusia. Contoh sederhana: simulasi traffic network. Di dalam simulasi ini, kita mensimulasikan pergerakan mobil mobil pada sebuah jaringan jalan raya. Parameter simulasi dapat diatur mulai dari kondisi di mana setiap mobil bergerak secara acak, hingga kondisi di mana sebagian besar mobil bergerak ke arah yang sama (sehingga menimbulkan kemacetan). Perhatikan bahwa setiap mobil dikendarai oleh seorang manusia, yang mengambil keputusan berdasarkan kondisi individual yang sangat kompleks. Namun, kompleksitas itu tidak relevan bagi simulasi tersebut karena kita toh hanya berurusan dengan berbagai kemungkinan pergerakan kolektif dari mobil mobil itu. Contoh lain: pergerakan harga saham. Fluktuasi harga saham diplot sebagai fungsi dari waktu. Fluktuasi itu terjadi akibat keputusan kolektif dari banyak pelaku yang mengambil keputusan akibat interaksi satu sama lain, plus informasi tentang kondisi global dari pasar. Pertimbangan dari setiap pelaku pasti sangat kompleks dan tidak sepenuhnya rasional. Namun sama halnya seperti simulasi traffic network, yang kita simulasikan adalah pergerakan obyek obyeknya (pergerakan harga saham atau pergerakan mobil) dan bukan mensimulasikan manusianya.

Econophysics

Economic crisis have been puzzling people for quite sometimes. Looking at the empirical data, people cannot help but wonder if there are patterns in those crises. The above figure is the logarithmic returns for the SP500 price index during the period from january 3, 1950 to September 3, 2013. Some important dates are included in the figures.

Des 6, 1974 Market Crash, Oil Crisis; Oct 19, 1987 Black Monday; May 21, 1998 Asian Financial Crisis; Dec 31, 2008 USA crisis. (Data Source: Yahoo Finance).

Here, we are easily tempted to say that there are some sort of periodicities or cycles of crises being showed in that figure. But things are not that simple. In fact, the crises do not have any apparent regularity. On the other hand, It's been known for quite sometimes that price fluctuation contains important information about the behavior of the financial market.

The simplest economics model treats the behavior of the system through a "representative agent" approach where the heterogeneous preferences of the individual agents are replaced by average preference curve. Agents determine their action in isolation, with no reference whatsoever to the decision of others. In other word, interactions between agents are neglected.

The need to account for interaction, however, is quite compelling. Imitation and social pressure effect must be responsible for the appearance of trends, fads and fashion, or mass panic, that would be difficult if agents were really insensitive to the behavior of others In our approach, interactions between agents are very important. The definition of a "system" actually include the interaction between the agents. Because of that, crises, crashes, and bubbles, are inherently the natural property of the system itself. We avoid giving one explanation for "normal" economy, and another for "anomalous" one. There is only one explanation that encompass all states of the system.

The “physics” part of the “econophysics” emphasis the correlations between models and empirical data. We, therefore, treat an economical system as if it is a physical system where any explanation should be validated by empirical data. The figure below shows the comparison of our simulations to the S&P 500 data,

Physics

To see the connections between.seemingly different phenomena, to try to get a glimpse of the big picture and to present the simplest possible mathematical description of a phenomena that includes as many links as are necessary, but no more. McCauley

Morphology and Dynamics

In most of our simulations we know how to control the output of the simulations, hence the basic explanations of the results are known by design. What is not so obvious is the correlation between the morphology of the system and its dynamics. The rules that govern the simulations are part of the fundamental explanations. But they are far from sufficient. The correlations between the morphology and dynamics provides us with the correlations between one observable to the other. Quite simply, the dynamics of the system is explained by the morphology of the system. A dramatic change of the dynamics, therefore, is explained by a dramatic change in morphology.

Today's reading

#econophysics

Simulation Research Design

Background Reading

Preliminary Simulations

Formulating the Problems

Simulation Design

Running and Collecting data

Data analysis (1) numerical

Data analysis (2) physical

Data analysis (3) theoretical

What is the purpose of doing the simulation?

Well, what is the purpose of any research? Research is a process to find new knowledge. And science is a quest to understand. So in this case, simulations' goal is to understand. The question is: "How do we understand anything by simulations?"

#econophysics

Getting Started

Individuals appear and disappear. One way to do the simulation is by making only one individual appear or disappear at each Monte Carlo step. This is not exactly what happens in nature, of course. To correct that, we use MCSS instead of MCS, as our time unit.

We set up the simulations in many different way. One way is to drive them by a Hamiltonian and let it obey the detailed balance etc, the other way is by a set of simulation rules.

Now remember that "Monte Carlo" means "doing something with probability". Individuals are distributed (or taken away) from the system with a probability, individuals are also interacting with each other, with a probability.

Each individual has properties. The simplest property of an individual is just to exist. Such individual can be found in Ising model simulations where we can define an individual as spin-up (when it exists) or spin-down (when it doesn't exist). An individual could have a more complex set of properties. This "individual" can be a species, a language, or an agent in financial market. In this case we need to include the properties of the individual in the simulation. One way to do that by using a bit string for each individual. Now, what are the ingredients of the simulation? - The rule for the materialization or de-materialization of individuals - The rule for displacements of individuals. - The rule for population growth or shrink toward an equilibrium or fixed points

- The rule for independent mutation of each individual, and the rule for mutation by interaction with each other.

Next, of course, is running the simulation and getting the measurement results.

#econophysics

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