Turbulence in the Financial Markets
Financial markets continuously evolve in a nonlinear, dynamic fashion, affected by destabilizing events and auto-reinforced mechanisms or memory effects. In spite of its complexities, the financial market is not entirely incomprehensible; although market cycles continuously change, their underlying mechanisms remain the same. This chapter provides an explanation of how fractal geometry helps us to understand the mechanisms underlying financial markets. One of the main features of financial markets is the alternation of periods of large price changes with periods of smaller changes. Fluctuations in volatility are unrelated to the predictability of future returns. This statement implies that there is autocorrelation structures dependence in the absolute values of returns. The multifractal model of asset returns combines the properties of L-stable processes (stationary and independent stable increments) and fractional Brownian Motions (tendency of price changes to be followed by changes in the same (or opposite) direction) to allow for long tails, correlated volatilities, and either unpredictability or long memory in returns.