given n correlated assets, S_1 to S_n, is it somehow possible to relate the transition density S_1(t),...,S_n(t) --> S_1(T),...,S_n(T) to a geodesic on the manifold, with metric related to the correlation matrix?cheers, Frido

Yes it is. See Pierre Henry-Labordere's book.

Do you have a reference to his book, please?

Yes, this is the content of the classic theorem by Varadhan which states roughly the following. The transition probability is given asymptotically (in the limit where the time ) by . Here is the geodesic distance between the points on the state space with respect to a suitable Riemannian metric (involving the correlations bewteen the Brownians and diffusion coefficients). You can easily find more on Varadhan's theorem by searching the web.QuoteOriginally posted by: frolloosgiven n correlated assets, S_1 to S_n, is it somehow possible to relate the transition density S_1(t),...,S_n(t) --> S_1(T),...,S_n(T) to a geodesic on the manifold, with metric related to the correlation matrix?cheers, Frido

thank you for the replies and references, will look into the articles & book you mentioned.

Analysis, Geometry, and Modelling in Finance, Chapman & HallHowever most of the stuff can be found in working papers.