Option Pricing Under Lévy Model With Markov Regime Switching

This paper investigates option pricing under Levy model with Markov Regime Switching.We suppose that the price of assets follow the processwhere (B_t, 0≤t≤T)is standard Brown motion ,N(t,·)is stochastic measure ,(X_t, 0≤t≤T)is markov process,and all of them are independent with each other,μ_s =< X_s,μ>,σ_s =< X_s,σ>,γ_s =< X_s,γ>are all affected by markov regime switching . In chapter 3,we suppose the Levy measure of Possion stochastic measure v(·)is not affected by the Markov regime switching. Firstly,we use Esscher transform to get a equal martingal measure ,and then prove this measure minmises the relative entropy. Finally we get the common method of european option pricing under the measure which have got .In chapter 4,we suppose that the Levy measure of Possion stochastic measure v(·)is affected by the Markov regime switching. We get the similar result with chapter 3.We extend the result in [16]and[17],respectively.