Consider the SDE: dSt = 0.05 dt + 0.1dWt Suppose dWt is approximated by the following process: (a) Consider intervals of size = 1.

Consider the SDE:
dSt = 0.05 dt + 0.1dWt
Suppose dWt is approximated by the following process:

(a) Consider intervals of size Δ = 1. Calculate the values of St beginning from t = 0 to t = 3. Note that you need S0 = 100
(b) Let Δ = 0.5 and repeat the same calculations.
(c) Plot these two realizations.
(d) How would these graphs look if Δ = 0.01?
(e) Now multiply the variance of St by 3, let dt = 1, and obtain a new realization for St. (To generate any needed random variables, you can toss a coin.)

+A with probability 0.5 -A with probability 0.5 AW