Results in table 1 indicates that the algorithm in this paper yields the more accurate value for the shout options according to the indicator course grid error.
4.3 Performance Comparison of shout options in jump-diffusion model
In this part, performance of shout options in jump-diffusion model will be compared between the algorithm in this paper and two traditional finite element methods. The first one used an exponential time integration (ETI) [20] and the other employed a second-order backward differentiation formula (BDF-2) [19]. Parameters are\({\ S}_{0}=80,K=80,\sigma=0.25,T=1,r=0.03\) and the jump term parameters\(\ \lambda=1.2,\alpha=0.15,\gamma=0.3.\) The other parameters are \(\varphi=3\) and the number of time steps is twice that of spatial steps.
Table 2 shows that the accuracy of algorithm in this paper is much higher than that of finite element method in calculating shout options price. For example, when 480 spatial steps are used, the error of algorithm in this paper is only10-7, which is much smaller than that of finite element method10-3.
Table 2 Performance comparison on shout put options between algorithm in this paper and finite element algorithm in jump-diffusion model