Exercise 6.8 Let X be a jump-diffusion process of the Kou type with parameters = .08,

Exercise 6.8 Let X be a jump-diffusion process of the Kou type with parameters μ =

.08, σ = 0.22, λ = 100, p = 0.7, η1 = 125, and η2 = 100. Suppose that the risk-free rate is 2%, and consider the change of measure defined by Ub,φ, where

φ(x) = (ζ01 + ζ11x)I(x > 0) + (ζ02 + ζ12x)I(x ≤ 0), and b ∈ R.

(a) Under this change of measure, the new parameters of the pure-jump part are ˜λ = 500, ˜p = 0.9, ˜η1 = 250, and ˜η2 = 400. Find φ.

(b) Find b so that the associated measure is a martingale measure.

(c) Give the old and new parameters under the weighted-symmetric representation of the jumps, i.e., find ω, ˜ω, δ, and ˜δ.

(d) Simulate 500 daily observations under this equivalent martingale measure.