Great fortunes are made and lost on Wall Street with the power of mathematics. Quantitative or “quant” modeling is akin to an arms race among banks. The conventional wisdom is that a bank that has superior models can better exploit market inefficiencies and manage risk competitively.
Many of the modeling techniques and ideas were borrowed from mathematics and physics. In hard sciences, a mathematical law always describes a truth of nature, which can be verified precisely by repeatable experiments. In contrast, financial models are nothing more than toy representations of reality—it is impossible to predict the madness of the crowd consistently, and any success in doing so is often unrepeatable. It really is pseudoscience, not precise science. The danger for a risk manager is in not being able to tell the difference.
Empirical studies have shown that the basic model assumptions of being independent and identically distributed (i.i.d.), stationarity, and Gaussian thin-tailed distribution are violated under stressful market conditions. Market prices do not exhibit Brownian motion like gas particles. Phenomena that are in fact observed are fat-tailness and skewness of returns, and evidence of clustering and asymmetry of volatility. In truth, the 2008 crisis is one expensive experiment to debunk our deep-rooted ideas.
This chapter discusses the causes and effects of the market “anomalies” that disrupt the VaR measure. Due to its failings, ...