Multi-asset options: a numerical study

Abstract

This thesis compares three methods for numerically pricing multi-asset options, as- suming the underlying assets follow a multi-dimensional geometric Brownian motion with constant coeffcients. The considered methods are the binomial pricing model, the Monte Carlo method, and the finite element method (FEM) applied to the pric- ing PDE (the PDE method). It is shown that the binomial model can be used to price both European and American multi-asset options. It is also concluded that the binomial model has a rather fast convergence rate and the results can be fur- ther improved by using adaptive mesh refinements. However, the binomial model performs worse for large volatilities. Furthermore, it is found that the Monte Carlo method converges very fast and that the results can be improved by using variance reduction techniques. This method also works well for pricing Asian options due to its simple formula. Even though the Monte Carlo method is shown to be the fastest and most reliable out of the three methods, it does not perform well for larger volatilities. While the binomial pricing model and the Monte Carlo method seem to underestimate the price for large volatilities, the PDE method is shown to be the only method out of the three that gives reliable estimates. However, the method also has the slowest convergence rate out of the three methods when the volatilities are low. This method also needs the most adaptation for each new option.