meshfree approximation methods with matlab

Various numerical methods have been applied to option pricing, including tree models ( Shreve 2004), finite difference methods ( Duffy 2006), and Monte Carlo simulations ( Jäckel 2002), among others. PDEs seldom have analytical solutions and hence, numerical procedures are essential to calculate option premiums. Therefore, from the numerical experiments, this study concludes that the fractional step method is more appropriate than the radial basis functions for solving a PDE with a mixed derivative. The fractional step method calculates the option premium more accurately and much faster than the radial basis functions. The numerical results show that the both methods calculate premiums with high accuracy in the presence of mixed derivatives.

Numerical experiments are conducted by applying these methods to exchange option pricing exchange options are selected because the exchange option premium has an analytical form. This study applies the fractional step method and the radial basis functions to solve a PDE with a mixed derivative, and investigates the efficiency of these numerical methods. The aim of this study is to find out which numerical method would be appropriate to solve PDEs with mixed derivatives based on the accuracy of the solutions and the computation time.

Alternating direction implicit (ADI) finite difference methods are popular for solving a PDE with more than two space dimensions however, it is not straightforward to employ the ADI method for solving a PDE with mixed derivatives. In option pricing models with correlated stochastic processes, an option premium is commonly a solution to a partial differential equation (PDE) with mixed derivatives in more than two space dimensions.

Meshfree approximation methods with matlab