In this question, you need to evaluate the accuracy of Ito's lemma. Suppose thatXfollows an arithmetic Brownian motion,dX=.1dt+.25dzwith initial valueX0= 2 andf(X) =X2.For t=.1, .01, .001, .0001,calculate the mean and the standard deviation of the error from Ito's approxi- mation of fas well as the ratio of the standard deviation of the error to the standard deviation of f.

(Hint: Construct a grid of 999 equispaced points from 0.001 to 0.999. Use these points as an argument

in the inverse standard normal distribution function. Multiplying these numbers by

values fordz. For each value ofdz, computeX(t+t),f[X(t+t)], the actual f, the approximation of ffrom Ito's lemma and the error resulting from Ito's approximation, f(actual)f(Ito).)