The dynamics of the continuous-time stochastic processes X = (Xt) and Y =

(Yt) are given by dXt = Xt [μX dt + σX dz1t], dYt = μY dt + ρσY dz1t +

'

1 − ρ2σY dz2t, where z1 and z2 are independent standard Brownian motions, and μX, σX,μY, ρ, σY are constants with σX, σY ≥ 0 and ρ ∈ [−1, 1].

(a) State the conditional expectation and variance of the increments of the two processes, that is state Et[dXt], Vart[dXt], Et[dYt], and Vart[dYt]. State the conditional covariance and correlation between the increments of the two processes, that is Covt[dXt, dYt] and Corrt[dXt, dYt].

Define a process W = (Wt) by Wt = XteYt .

(b) Determine the dynamics of W, that is find dWt. Describe what type of process W is.