ABSTRACT
In many cases, an option’s payoff may depend on several assets, e.g., swap options, quantos, basket options, etc. Therefore one has to model the dynamical behavior of several assets.
Definition 2.1.1 W = (W1, . . . ,Wd) is a d-dimensional Brownian motion with correlation matrix R if it is a continuous random vector starting at 0, with independent increments, and such that W (t) −W (s) ∼ Nd(0, R(t− s)), whenever 0 ≤ s ≤ t.
