(BQ) Part 2 book "The statistical mechanics of financial markets" has contents: Turbulence and foreign exchange markets, derivative pricing beyond black–scholes, microscopic market models, theory of stock exchange crashes, risk management, economic and regulatory capital for financial institutions. | 6. Turbulence and Foreign Exchange Markets The preceding chapter has shown that, when looking at financial time series in fine detail, they are more complex than what would be expected from simple stochastic processes such as geometric Brownian motion, L´vy flights e or truncated L´vy flights. One of the main differences to these stochastic e processes is the heteroscedasticity of financial time series, ., the fact that their volatility is not a constant. While this has given rise to the formulation of the ARCH and GARCH processes [48, 49] briefly mentioned in Chap. , we here pursue the analogy with physics and consider phenomena of increased complexity. Important Questions The flow properties of fluids are such an area. In this chapter, we will discuss the following questions: • How do fluid flows change as, ., their velocity is increased? • Is there a phase transition between a slow-flow (laminar) and a fast-flow (turbulent) regime? • What are the hallmarks of turbulence? What are its statistical properties? • Are there models of turbulence? • Are there similarities in the time series and in the statistical properties between turbulence and financial assets? • Are the models of turbulence useful to formulate models for financial markets? • Are there benchmark financial assets which are particularly well suited to study statistical and time series properties? • Is there a relation to geometrical constructions such as fractals and multifractals, and is it useful? Turbulent Flows A good introduction to the field of turbulence has been written by Frisch [134]. We first introduce turbulence in a phenomenological way. In a second step, we discuss time series analysis of turbulent signals. 174 6. Turbulence and Foreign Exchange Markets Phenomenology The basic question is: how do fluids flow? The answer is not clear-cut, and depends on a control parameter, the Reynolds number R= Lv . ν () Here, L is a typical length scale, v a typical velocity, ., v
