New model uses the laws of molecular fluid dynamics to aid the analysis of financial markets

May 27, 2014
New model uses the laws of molecular fluid dynamics to aid the analysis of financial markets
Misako Takayasu and colleagues have created a new model describing the fluctuations in an order-book for financial markets, using the laws of Brownian motion exhibited by particles in a fluid. The centre colloid particle (green and yellow) rests at the mid-price of a set of transactions. The range of price fluctuation is described by surrounding molecules (red and blue) which knock the mid-price up or down.

A new model to aid the analysis of financial markets uses the laws of molecular fluid dynamics to describe order-book transactions.

The laws of mathematics and physics are often used to describe areas of complex statistics, such as the transactions in global financial markets. In particular, fractals - self-similar patterns that replicate the same detailed structures at many scales - can be used to help describe fluctuations in many different scenarios, including business transactions between millions of companies and the dynamics of internet traffic.

Misako Takayasu, associate professor at the Tokyo Institute of Technology, has dedicated her career to modelling such complex systems. Now, Takayasu and her colleagues in Japan and Switzerland have developed a novel way of describing the dynamics of the order books of financial markets, by linking the transaction patterns to the random motion of particles in a fluid.

"We were asked to analyze the order book data of foreign exchange markets, specifically the US dollar-Japanese yen market," explains Takayasu. "To help understand such a massively complex data set we turned to ."

The order book of a describes all orders, buying and selling, and includes all shifts in prices and volumes. Market prices are determined through these interactions. When a pair of buy and sell orders are of equal value, the transaction completes and the pair disappears from the order book - rather like the annihilation that occurs when particles meet their antiparticles.

"The database shows the creation and annihilation of detailed orders - a vast amount of information," explains Takayasu. "With layers of data to deal with, imagining the order-book as molecules of data moving randomly, similar to particles in fluid following the laws of Brownian motion, helped us to make sense of the data."

The researchers introduced a concept based on an imaginary colloid particle suspended in a fluid, at a location wherein the particle centre represents the mid-price of transactions (see image). The spread of possible prices for transactions are, in turn, represented by the surrounding fluid molecules. Whenever new orders are placed, the molecules change configuration and the main colloid particle shifts position.

The team completed their molecular analogy by implementing the laws that govern Brownian motion to observe and describe fluctuations in the market.

"Molecular fluid dynamics also helped us to characterize the stability of market, which has never been discussed in economics before," describes Takayasu. "We used drag coefficients to determine the 'viscosity' of the market, and the so-called Knudsen number to describe the market continuity. The smaller the drag coefficient the less stable the market is, and the larger the Knudsen number, the more likely the market price could behave erratically, as in the case of a crash."

Further development of this approach could help market analysts to describe how and why major incidents such as crashes occur.

Explore further: Blueprint of a trend: How does a financial bubble burst?

More information: Yoshihiro Yura, Hideki Takayasu, Didier Sornette, and Misako Takayasu, "Financial Brownian Particle in the Layered Order-Book Fluid and Fluctuation-Dissipation Relations." Phys. Rev. Lett. 112, 098703 – Published 7 March 2014

Related Stories

Blueprint of a trend: How does a financial bubble burst?

May 2, 2011

A joint study by academics in Switzerland, Germany and at Boston University sheds new light on the formation of financial bubbles and crashes. Wild fluctuations in stock prices caused by bubbles bursting have had a dramatic ...

Spurious switching points in traded stock dynamics

May 15, 2012

Physicists have rebuffed the existence of power laws governing the dynamics of traded stock volatility, volume and intertrade times at times of stock price extrema. They did this by demonstrating that what appeared as "switching ...

Recommended for you

CERN collides heavy nuclei at new record high energy

November 25, 2015

The world's most powerful accelerator, the 27 km long Large Hadron Collider (LHC) operating at CERN in Geneva established collisions between lead nuclei, this morning, at the highest energies ever. The LHC has been colliding ...

'Material universe' yields surprising new particle

November 25, 2015

An international team of researchers has predicted the existence of a new type of particle called the type-II Weyl fermion in metallic materials. When subjected to a magnetic field, the materials containing the particle act ...

Exploring the physics of a chocolate fountain

November 24, 2015

A mathematics student has worked out the secrets of how chocolate behaves in a chocolate fountain, answering the age-old question of why the falling 'curtain' of chocolate surprisingly pulls inwards rather than going straight ...


Please sign in to add a comment. Registration is free, and takes less than a minute. Read more

Click here to reset your password.
Sign in to get notified via email when new comments are made.