Risk Finance Modeling and Dependence
Dependence arises because financial prices and events depend on one another, on latent and common macroeconomic factors, on other assets, on other securities, and on a broad array and many types of information. In some cases, events may also feed each other, leading to complex feedback relationships and to a contagion (for example, a contagion of defaulting loans, bank runs, the meltdown of financial markets and their security prices, etc.). Generally, dependence implies that assets tend to move in directions that are observed more or less to be concurrent—some movements may be causal, other spurious. Dependence may also be a signal and a symptom of common risk sources (such as macroeconomic factors affecting assets in a given portfolio) or result from real or statistical covariations between assets. Although dependence is fundamental for finance, it is loosely used, implying far more than is implied by a simple (noncausal) statistical covariation of asset prices and economic factors. The definition of financial models that seek to structure causally the dependence of financial prices are therefore important and are central to financial modeling, financial theory, and risk engineering in general. The purpose of this chapter is to focus attention to a number of approaches for quantitatively modeling dependence. This chapter seeks to motivate the student to appreciate the fact that dependence is complex and extremely important ...