基于跳-扩散过程的多阶段因果复合期权定价

目的假定在多重突发事件的冲击影响下标的资产价格变动服从跳一扩散过程，把多期投资项目的价值评估问题用多阶段因果复合期权去解决。方法运用已有的金融数学知识，建立了基于跳一扩散过程的多阶段因果复合期权定价模型，然后利用随机微分方程和偏微分方程去求解该模型。结果建立了基于跳一扩散过程的多阶段因果复合期权定价模型，继而得到了拥有封闭解的数学公式。结论第i阶段的因果复合期权的价值求解通式为：F（ti-1）=e^-rti∑N1=0^∞…∑Nn=1^∞P（N1,N2…,N1）Emax（S（ti）-K0,0｜（N1,N2,…,Ni）].

The pricing method of multi-stage causal compound option following jump-diffusion process

Aim To use the multi-stage causal compound option to make an evaluation of multi- phase investment project by assuming that the appointed capital＂ price fluctuation follows the jump-dif- fusion process under the affection of multiple emergencies＂ impactions. Methods By using the existed financial mathematics knowledge, the pricing model of multi-stage causal compound option following jump-diffusion process is established to solve this model with the stochastic differential equation and partial differential equation. Results The pricing model of multi-stage causal compound option follow- ing jump-diffusion process is established, thus obtaining the mathematical formula with closed-form solution. Conclusion The general formula for making the valuation of the causal compound option at i stage is F（ti-1）=e^-rti∑N1=0^∞…∑Nn=1^∞P（N1,N2…,N1）Emax（S（ti）-K0,0｜（N1,N2,…,Ni）].