MSci Project Proposal Form 2009-2010
Project Code: CMTH-Vvedensky-4
Project title: Hierarchical Model of Market Crashes
Supervisor: Prof. Dimitri D. Vvedensky
Assessor:
Telephone: Ex. 7 605
Telephone:
E-mail: d.vvedensky
E-mail:
Research Group: Condensed Matter Theory
Research Group:
Project Summary:
Recent economic events, including the dramatic falls in the shares of individual companies (especially
financial institutions) and in composite indices such as the Dow Jones and FTSE have highlighted the
volatility of financial markets. Comparisons with previous events, such as the stock market crashes of
1929 and Black Monday (October 19, 1987), indicate that such seismic shifts of the market, although
rare, are devastating. In this era of globalization, there is no safe haven from the current economic
turbulence. One of the goals of the quantitative analysis of financial markets is the assessment of the
likelihood of large adverse changes and the prediction of crashes.
Traditional models of market fluctuations that rely on random walks fail to account for the frequency
and characteristics of market crashes. Most notable among such models is the Black-Scholes model
for the pricing of options and derivatives.
An alternative approach that focuses on crowd behavior is based what is called a ‘hierarchical’ model,
which is an Ising-like model, but with different connectivities between neighboring sites that are
meant to mimic imitation and crowd behavior. There are three aspects to this project:

The first is programming the hierarchical model and to become familiar with its behavior as
the parameters that determined the extent of imitation between market traders. No previous
programming experience is required. Indeed, this project could serve as a vehicle for
attaining programming proficiency.

An accompanying analytic calculation that provides a justification for the characteristic
precursors to market crashes.

The results of the simulations and analytic calculations can be used to analyze real market
crashes in various markets to identify similarities and differences between different crashes.
Historical data for various markets is readily available.
Experimental component:
0%
Computational component: 50–70 %
Theoretical component:
30–50 %
Is the MSci Project eligible for students on the MSci
Physics with Theoretical Physics Degree: YES
Suggested reading:
D. Sornette and A. Johansen, ‘A hierarchical model of financial crashes,’ Physica A 261, 581–598.
A. A. Farhadi and D. D. Vvedensky, ‘Risk, randomness, crashes, and quants,’ Contemporary Physics 44, 237–
257 (2003).
Imperial College of Science, Technology, and Medicine