Dynamic Correlation Model

[Nonius]

not really, because I am lazy and also because it suffers from mathematicianisis. it's too complicated, the math would be too involved, the dimensions too large, and the return, no pun intended, would be almost surely zero. but, to summarize a summary, let's start with covariance. covariance matrices live in a space that is naturally identified with a symmetric space given by the quotient space of an action of O(n) (orthogonal matrices, ie, matrices that have the property that their inverses are equal to the transpose) on the space of all invertible matrices, ie, GL(N). since it's a symmetric space, it's a manifold equipped with a metric, ie, a riemannian manifold, and there's a bunch of symmetries afforded by the action of the action O(n). since it's a riemannian manifold, there is associated with it a heat kernel. to every heat kernel on a riemannian manifold, there is a notion of brownian motion, there are heat type PDEs floating around, and if one extended the notion of hedging to manifolds, one could probably write down what Black Scholes means in this context. (I note that MJ once pointed out that hedging in a manifold context might be dicey because of certain types of singularities that would occur) but it would be complicated. and the dimensions, as mentioned, would be large, ie, n(n+1)/2. in the case of correlation, it is worse, because, even though there is still an identification of correlation matrices with orbits of an action of the orthogonal group on some matrices, the orbit space is no longer a manifold. rather, it is an orbifold, ie, it is a disjoint union of pieces that look like manifolds, but it could all, in theory, that is, all the heat equation shit, be extended. I think. This sounds very N.

[deeds]

Thank you so much for the little summary, Nonius.