Thread by @TerribleQuant

A thread on Copula trading in 2022:

I previously mentioned the use of CDS pricing literature for alternative copula distributions, and for bringing assumptions to the higher dimensions without using vines.

Continuing, this topic I'll go through some other methods/tricks:

For optimizing copulas the easiest method is to use a heuristic method and then brute force the lower dimensions. This is usually bivariate only, but with smaller asset universes trivariate is possible. From there you just test all permutations that include...
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your established pair or triplet. To solve for the weights you can do this with standard methods. Another note is that since copulas are effectively conditional probabilities and vine copulas form chains, the Baum Welch algorithm can be adapted with use of non-gaussian...
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distributions that handle more than bivariate dimensionalities, since Markov Chains are still conditional probabilities. There is plenty of literature for this and it isn't very hard to do so. Gaussian Mixture models can be adapted to provide even more flexibility...

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but there is not the same level of bias you gain from other copula approaches. Since your vines can be canonical to a single asset, you can cluster by industry or with unsupervised methods, and then use LASSO to induce sparsity between the connections...
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using a little bit of graph theory can help, but sparse PCA does a fine job for most approaches. With your reduced asset series, you can now fit your paths to whichever asset is canonical.
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The issue is that there is usually not a single canonical node so when optimizing do so for each node in your sample with the goal of inducing sparsity relative to it as the central node. Do not worry if your connections are multivariate, although this will...
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drastically increase the computational complexity, hence why I originally brought up the use of heuristic methods. Since we are trying to induce sparsity using SPCA we can effectively replicate this with semi-definite programming using the matrix norm penalty.
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The matrix norm penalty is effective equivalent to SPCA on the resultant matrix and frankly, either/both can be used. Thus is makes sense to either apply SPCA to the greedy solution (non-convex) or matrix norm penalty to the SDP (convex) solution.
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