Complex Economy (FMF170)
Matematisk Fysik seal LTH


Professor Thomas Guhr

The EXAM was written on Friday, December 16th, 2005.

Click here for the results.

If you could not take part, but you are interested in taking an exam, please contact me.

Why do banks, consulting firms and insurance companies hire more and more physicists? - Because the methods from statistical physics become increasingly important to model economical systems and, in particular, the capital markets. This course is an introduction to this quickly expanding field. It is often called Complex Economy or Econophysics.

This is how "the floor" looks when something truly exciting happens. The floor is the place in the stock exchange where the brokers meet and do the trading.

The stocks of companies are traded at stock exchanges. The people who do that professionally are called stock brokers. They buy or sell specific stocks because they expect them to go up or down in value. Thus, they have a certain market expectation. However, it is known that the value of a stock, as you see it in the chart below, can be modeled by a stochastic process. This does not mean that there is no ``deterministic'' reason for the value to change. It is very much like the motion of an oxygen molecule in the air: its motion is not random, but it can be modeled as a random process. Such considerations make it possible to apply the powerful machinery of statistical physics in the capital markets. For example, the Black and Scholes theory yields quantitative predictions for the values of financial derivatives, such as options.

This is a chart. It shows the value of a stock for a given company as a function of time. Here, the company is NOKIA, and you see its performance from end of May 2000 to end of May 2001 at the Stockholm stock exchange.

If you feel like looking at more charts like this one of stocks, options, indices, exchange rates, etc., comdirect provides a very useful service.

In this course, you will not learn how to get rich quickly. You will learn solid tools of statistical physics and how they are applied to the economy. However, because the field is so new, we will also discuss a few speculative models. You do not need a background in economics! - In the course, you will learn the basics that we need. The course is suitable for everybody who has a sufficient background in mathematics, as it is taught in the basic courses for physicists. Physics background is helpful, but not required. Thus, the course is also suitable for non-physicists.

The course is given in English. There is a kompendium which you can buy at a price of 100 SEK.

Content of the course:

  • some introductory remarks about statistical physics
  • basic concepts and mechanisms in the economy and in the capital markets: arbitrage, stocks, financial derivatives, options, portfolio, risk management
  • statistical models for stock markets: classes of Brownian motion, stochastic processes, probabilities and distributions, limit theorems, physics interpretation
  • Black and Scholes theory for options: diffusion equations, Ito's lemma, quantitative risk management, hedging
  • correlations between stocks: impact on risk management, random matrices, formal similarities to quantum chaotic systems in physics
  • controversial and speculative theories: can one predict market crashes? - are there similarities between market crashes and earth quakes?

The reference number of the course (kurskod) is FMF170. The course is given every second year, next time in Fall/Winter 2007, then Fall/Winter 2009 and so on.

Lectures are given Mondays from 10:00 to 12:00 o'clock and Wednesdays from 13:00 to 15:00 o'clock.
Exercises are offered Tuesdays from 8:00 to 10:00 o'clock.
The course starts on Monday, 24th of October 2005.
Lecture halls: week 44 everything in lecture hall B, week 45 to week 49 everything in lecture hall F.

** Written exam on December 16th, 2005, 8:00 till 13:00 o'clock **

For more information, send e-mail to or call 046 222 9087, Matematisk Fysik, Sölvegatan 14A, Lund.