老师课堂留下的思考题是：
8. Assuming the stock price is driven by a mixed Poisson-Brownian motion with stock return
to be given by

with Levy measure to be given by

Let r = 8%,σ = 12%,μ j = 0,σ j = 10%,λ = 1,S 0 = 100.
(a) Generate a sample path for the stock price process S t on [0,3].
(b) Compute E[S t ], V ar(S t ) and the m.g.f. for S t .
(c) Compute E[(100 − S T ) + ],T = 3. (Using Monte Carlo simulation, and write down
the computer code)
(d) What is the probability for the stock price to exceed 105 at time 3? (Using Monte
Carlo simulation, and write down the computer code)