. The exponential function in Newton calculus has the unique property that it is the only function that is equal to its derivative so that f'($) = f
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. The exponential function in Newton calculus has the unique property that it is
the only function that is equal to its derivative so that f’($) = f (as) 4:} f (rs) = em
(up to a multiplicative constant). What deterministic equation does it satisfy?
Derive the It?) calculus exponential function using Ito Lemma. . The answer obtained in the previous step should be elm—it, with Wt the Wiener
process or the standard Brownian motion. Derive the stochastic differlential equa—
tion (SDE) whose solution is (2Wt and an SDE whose solution is raw“? . Simulate one path for eWt and, using the same path, for ewrit. 4. Using Monte Carlo simulation with 1000 paths, calculate and plot the moving average of each process at the 100 points on the interval [0, 1]; Le. At = 0.01.

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