CEV跳-扩散模型中期权定价研究

考虑了CEV与Kou双指数跳-扩散组合模型中的期权定价问题.首先,运用Ito公式和期权定价的无套利原理,得到了模型下期权价格所满足的偏积-微分方程.然后,运用中心差分和Lagrange线性插值,分别对偏积-微分方程中的微分项和积分项进行离散化处理,再由Euler法,最终得了偏积-微分方程的有限差分格式,并且对差分方法的误差和收敛性进行了分析.最后数值实验验证了该算法是一个稳定且收敛的算法.

Study on the Pricing Convertible Bond with Paris Option Feature under Jump-diffusion Structure

In this paper,we consider the issue of option pricing under the CEV double exponential jump-diffusion process.Firstly,we establish the option pricing model,and derive the partial-integral differential equation satisfied by the options pricing model based the Ito formula and no-arbitrage principle.Then,we obtain the concrete discretization difference scheme of the differential equation,by using center finite difference discretization for the spatial derivative term together with zeroth-order term and Lagrange linear interpolation for integral term,Error and stability are also discussed in the paper.Lastly,numerical experiments also show that the algorithm is a stable and effective algorithm.