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