Consider again the situation described in Exercise 15 of Sec 12 2 Suppose that Wu has the Laplace distribution with parameters 0 and 0 1u1 2 See Eq (10 7 5) for the p d f a Prove that the m g f of Wu is (t) (1 t2u 100)1, for 10u1 2 t 10u1 2 b Let r 0 06 be the risk free interest rate Simulate a lar...

a The mgf of a Laplace distribution with parameters 0 and is The integral from to 0 is finite if and ...

Consider again the situation described in Exercise 15 of Sec. 12.2. Suppose that Wu has the Laplace

Question:

Consider again the situation described in Exercise 15 of Sec. 12.2. Suppose that Wu has the Laplace with parameters θ = 0 and σ = 0.1u1/2. See Eq. (10.7.5) for the p.d.f.
a. Prove that the m.g.f. of Wu is
ψ(t) = (1− t2u/100)−1, for −10u−1/2 < t < 10u−1/2.
b. Let r = 0.06 be the risk-free interest rate. Simulate a large number v of values of Wu with u = 1 and use these to estimate the price of an option to buy one share of this stock at time u = 1 in the future for the current price S0. Also compute the simulation standard error.
c. Use importance sampling to improve on the simulation in part (b). Instead of simulating Wu values directly, simulate from the conditional of Wu given that Su > S0. How much smaller is the simulation standard error?
Distribution
The word "distribution" has several meanings in the financial world, most of them pertaining to the payment of assets from a fund, account, or individual security to an investor or beneficiary. Retirement account distributions are among the most...