The forward-path method for pricing multi-asset American-style options under general diffusion processes

The forward-path method is one of the effective memory reduction approaches in pricing multi-asset American-style options by the Monte Carlo simulation. However, when the underlying assets follow a general diffusion process, it would be difficult to apply this method. In this paper we propose a simple and effective method, which applies the Milstein-Taylor explicit and implicit schemes and makes it possible to apply the forward-path method under general diffusion processes. It preserves the advantage of high reduction with relatively low cost of the forward-path method. Moreover, it works as a plug-in and one can flexibly substitute the schemes with different ones for different problems. It is proven that our method can conveniently restore the simulated path with strong convergence order 1.0. The numerical results indicate our method has high pricing accuracy and efficiency.