Risk, randomness, crashes and quants
Market movements, whether short-term fluctuations, long-term trends, or sudden surges or crashes, have an immense and widespread economic impact. These movements are suggestive of the complex behaviour seen in many non-equilibrium physical systems. Not surprisingly, therefore, the characterization of market behaviour presents an inviting challenge to the physical sciences and, indeed, many concepts and methods developed for modelling non-equilibrium natural phenomena have found fertile ground in financial settings. In this review, we begin with the simplest random process, the random walk, and, assuming no prior knowledge of markets, build up to the conceptual and computational machinery used to analyse and model the behaviour of financial systems. We then consider the evidence that calls into question several aspects of the random walk model of markets and discuss some ideas that have been put forward to account for the observed discrepancies. The application of all of these methods is illustrated with examples of actual market data.