Exercise 6.6 Let X be a jump-diffusion process of the Merton type with parameters = .08,

Exercise 6.6 Let X be a jump-diffusion process of the Merton type with parameters

μ = .08, σ = 0.22, λ = 100, γ = .05 and δ = .005. Suppose that the riskfree rate is 2%, and consider the change of measure defined by Ub,φ, where

φ(x) = 2 − 0.5x and b ∈ R.

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

(b) Under this change of measure, compute the new coefficients ˜μ, ˜σ, ˜ λ, ˜γ, and ˜δ.

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