A Model Reference Type Algorithm Using Importance Resampling

We describe a new version of Model Reference Adaptive Search algorithm which uses a sampling importance resampling phase. This method has in background a sequence of reference distributions introduced mainly for theoretical purposes - at each step is considered the closest distribution to the corresponding reference distribution. Our main contribution is to resample using this references, i.e., these distributions are involved in the calculus of the weights for the resampling stage. As an alternative, resampling with natural weights are also compared with the standard algorithm. These two techniques are tested on pricing bermudan options under three different models for stock price dynamics: the geometric Brownian, the normal jump diffusion, and a relatively new framework - an asymmetric double-exponentially jump diffusion model. Our algorithm performs almost twice as fast as the standard algorithm having same standard errors - this means that our method is a reliable and faster method. The accuracy of the results and the speed of the algorithm is enhanced by implementing a Gibbs sampler combined with a Metropolis Chain, hence avoiding the time costly accept-reject method for generating samples from a truncated multivariate normal distribution.