分数阶CEV模型下未定权益的紧致差分法

Compact difference method with contingent claim under fractional CEV model

提出一种关于求解分数阶CEV模型下未定权益的紧致差分法.在时间上采用Caputo导数进行离散,在空间上采用4阶紧致差分格式进行离散.针对未定权益,得到一个时间2-α阶,空间4阶精度的紧致差分格式.并且运用傅里叶分析法和数学归纳法验证该方法的稳定性和收敛性.最后,通过数值实验验证该方法的有效性.

A compact difference scheme for solving contingent claim in fractional CEV models was proposed.In time,Caputo derivative was used for discretization,and in space,fourth order compact difference scheme was used for discretization.A compact difference scheme with time order 2-αand space order 4 precision was obtained for European contingent claim.Fourier analysis and mathematical induction were used to verify the stability and convergence of the proposed method.Finally,the effectiveness of the proposed method was verified by numerical experiments.