Stochastic Correlation Models

Gunter Meissner

“I think correlation modelling is basically at the stage volatility modelling was about 15 years ago”

– Vladimir Piterbarg

In finance, many variables such as equities, bonds, commodities, exchange rates, interest rates and volatility are often modelled with a stochastic process. In addition, from our empirical Chapter 2, we derived that financial correlations behave somewhat erratic and random. Therefore, it seems like a good idea to model financial correlations with a stochastic process.

The modelling of financial correlation with a stochastic process is fairly new, but several promising approaches exist. We will discuss them, but, before we do, let’s look at some basics.


The reader who has made it all the way to this chapter has, hopefully, a good idea of what a stochastic process is. But let us have a closer look. Let’s start with a deterministic process. A deterministic process is a process with a known outcome. For example counting numbers by one and the movement of the sun are deterministic processes. The opposite of a deterministic process is a stochastic process, also called “random process”. Hence, heuristically (meaning non

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