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.

WHAT IS A STOCHASTIC PROCESS?

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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