Multivariate Geometric Brownian Motion
GBM can be extended to the cast where there are multiple correlated price paths.
Each price path follows the underlying process
- ,
where the Wiener processes are correlated such that where .
For the multivariate case, this implies that
- .
Read more about this topic: Geometric Brownian Motion
Famous quotes containing the words geometric and/or motion:
“New York ... is a city of geometric heights, a petrified desert of grids and lattices, an inferno of greenish abstraction under a flat sky, a real Metropolis from which man is absent by his very accumulation.”
—Roland Barthes (19151980)
“When desire, having rejected reason and overpowered judgment which leads to right, is set in the direction of the pleasure which beauty can inspire, and when again under the influence of its kindred desires it is moved with violent motion towards the beauty of corporeal forms, it acquires a surname from this very violent motion, and is called love.”
—Socrates (469399 B.C.)