Slobodan Milovanovic: Radial Basis Function generated Finite Differences for Multidimensional PDEs in Finance
Tid: To 2017-10-12 kl 14.15 - 15.00
Föreläsare: Slobodan Milovanovic, Uppsala University
Plats: Room F11, Lindstedtsvägen 22, våningsplan 2, F-huset, KTH Campus.
The aim is to use radial basis function generated finite differences (RBF-FD) to solve multidimensional PDEs that arise from multi-factor models or multi-asset financial derivatives. Being mesh-free while generating a sparse differentiation matrix, this method exploits the best properties from both finite difference (FD) methods and radial basis function (RBF) methods. Moreover, RBF-FD is expected to be advantageous for high-dimensional problems compared to: Monte Carlo (MC) methods which converge slowly, global RBF methods since they produce dense matrices, and FD methods because they require regular grids. A recent progress in research related to RBF-FD showed the benefits of using polyharmonic splines (PHS) as RBFs augmented with polynomials. This has sparked a great potential for applying the method in financial engineering. The performance of the method together with the new implementational features will be shown, such as smoothing of the terminal condition while pricing European and American basket options under the standard Black-Scholes-Merton model with up to three underlying assets. The results highlight RBF-FD as a sparse method, capable of achieving high accuracy within a reasonable computational time.