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:
“In mathematics he was greater
Than Tycho Brahe, or Erra Pater:
For he, by geometric scale,
Could take the size of pots of ale;
Resolve, by sines and tangents straight,
If bread and butter wanted weight;
And wisely tell what hour o th day
The clock doth strike, by algebra.”
—Samuel Butler (16121680)
“A field of water betrays the spirit that is in the air. It is continually receiving new life and motion from above. It is intermediate in its nature between land and sky.”
—Henry David Thoreau (18171862)