TABLE OF CONTENTS In this chapter, we look at some models for the underlying dynamics of correlations, and for correlation uncertainties [1]. This includes the time dependence of correlations. Our point of view is that correlations have an intrinsic meaning, independent of historical time series. As an analogy, volatility is often treated as a dynamical variable in stochastic volatility models, independent of historical time series. In a similar way, correlations can be treated as dynamical variables. In the last chapter, we were concerned with a different issue, namely given some correlations, to find ways to consistently stress the given correlations. Our purpose here is to investigate some possibilities for the underlying dynamics of the correlations themselves.
We start with the simple zero-correlation heuristic in three versions A, B, C [2].
Some people think that correlations should be set equal to zero if you cannot think of a rationale or reason that nonzero correlations should be present. What these people effectively have in mind is that scenarios should be put together for correlations. That is, if there is no motivation for a particular correlation to be nonzero, their scenario would be a default of zero correlation.
A good response to this attitude is that while correlation scenarios are indeed useful, real-world non-zero correlations exist whether or not we have an underlying theory to describe them. It is perhaps presumptuous and fallacious to think that we are...
