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研究马氏状态转换的Lévy模型下的期权定价问题.假定资产价格过程为At=exp∫t0rsds,St=S0exp∫0tμs-21σs2ds+∫0tσsdBs+∫R0log(1+k(x))N(t,dx),其中(Bt,0≤t≤T)是标准Brown运动,N(t,.)是一Poisson随机测度,(Xt,0≤t≤T)是开关马氏过程,且它们三者相互独立;μs=〈Xs,μ〉,σs=〈Xs,σ〉,rs=〈Xs,r〉均受开关马氏过程的影响.对此模型,作Esscher测度变换,得到一个等价鞅测度,该测度可使定义的相关熵达到最小.在该测度下给出了欧式期权定价的一般方法.推广了Elliott等人的结论.
We study the option pricing problem under the Lévy model with state transition of Markov. Suppose the asset price process is At = exp∫t0rsds, St = S0exp∫0tμs-21σs2ds + ∫0tσsdBs + ∫R0log (1 + k (x)) N (t, dx) , Where (Bt, 0≤t≤T) is a standard Brownian motion, N (t,.) Is a Poisson random measure, (Xt, 0≤t≤T) is a switched Markov process and their three are independent; μs = , σs = , rs = are all affected by the switching Markov process. For this model, the Esscher measure transformation is used to obtain an equivalent martingale measure. The defined entropy can be minimized, and the general method of European option pricing is given under this measure, which generalizes the conclusion of Elliott et al.