Radial Basis Function Solution for the LIBOR Market Model PDE

Abstract

This research paper is intended at analyzing the interpolation of LIBOR (London Inter Bank Offer Rate) Model PDE (Partial Differential Equation) in one and two dimensions using Radial Basis Functions (RBF) on full grids. The LIBOR Market model is considered an effective and standard approach for pricing the derivatives which is based on interest rates. In recent times, Monte Carlo methods are often used in practice to price derivatives instruments because of the high dimensionality of the model. This research paper highlights the applicability of the RBF method rather than Finite Difference Method (FDM) for solving the LMM PDE, LIBOR Market Model, with the Bermudan Swaption or Chooser Option as a boundary condition. The results have suggested faster convergence to reference value than FDM in one dimension. Also, the calculation of price is similar to FDM in two dimension.