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)

    in the mind of man,
    A motion and a spirit, that impels
    All thinking things, all objects of all thought,
    And rolls through all things.
    William Wordsworth (1770–1850)