Date Added: Jun 2009
The authors price multi-asset options by solving their price partial differential equations using a meshfree approach with radial basis functions under jump-diffusion and geometric Brownian motion frameworks. In the geometric Brownian motion framework, they propose an effective technique that breaks the multi-dimensional problem to multiple 3D problems. They solve the price PDEs or PIDEs with an implicit meshfree scheme using thin-plate radial basis functions. Meshfree approach is very accurate, has high order of convergence and is easily scalable and adaptable to higher dimensions and different payoff profiles. They also obtain closed form approximations for the option Greeks. They test the model on American crack spread options traded on NYMEX.