4.2 Performance Comparison of shout options with no jumps
The first example is carried out for the jump-diffusion model with the parameter\(\ \lambda=0\), that is, the underlying asset follows geometric Brownian motion only. For comparison, we also include results in [2] and [4] for the same shout options. The result in [4] were obtained using numerical PDE method and in [2] using a similarity reduction and an explicit difference method.
Parameters are used \(\sigma=0.20,r=0.10,K=\$100,T=5yr\) In Table 1.The Reference solution using asset grid nodes=\(n\), time steps=\(n\). Result in [4]: time steps=\(n\), asset grid nodes=\(2n-1\).The error given is for the course grid and was estimated using the converged answer at the finest level as an approximation for the exact solution.