Consider the SDE:

dSt = .05dt + .1dWt.

Suppose dWt, is approximated by the following process:

(a) Consider Intervals of size ? = 1. Calculate the values of S_t, beginning from t = 0 to t = 3. Note that you need S₀ = 1.

(b) Let ? = .5 and repeat the same calculations.

(c) Plot these two realizations.

(d) How would these graphs look if ? = .01?

(e) Now multiply the variance of S_t, by 3, let dt = 1, and obtain a new realization for S_t.

(To generate any needed random variables you can toss a coin.)

with probability 5 SW, +4 with probability 5.