Waaaaaay back in the day, I showed how to simulate correlated random walks using copulas….
I was really thinking about the application to pairs trading back then… which was fine, because one of the limitations was that the method could only simulate two random variables at a time.
If you wanted to do some large universe like the S&P 500 you had to do everything pairwise, and then you weren’t really capturing any higher dimension relationships within the market.
Luckily, I found a solution in another, more intuitive model: the KDE. I put together a notebook on my Github Pages account to walk through the full process of simulating the components of the S&P 500. In the notebook I also investigate how to visualize the correlation structure of the market.
For the full notebook click here: Simulating Correlated Random Walks for the S&P 500
The notebook has content that I can’t display on wordpress such as interactive D3 network graphs of S&P 500 components: