Geometric Brownian Motion - Multivariate Geometric Brownian Motion

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 (1612–1680)

    It may be possible to do without dancing entirely. Instances have been known of young people passing many, many months successively, without being at any ball of any description, and no material injury accrue either to body or mind; Mbut when a beginning is made—when felicities of rapid motion have once been, though slightly, felt—it must be a very heavy set that does not ask for more.
    Jane Austen (1775–1817)