Applications of A Spectral Element Method

Abstract: Spectral methods are mostly used for computations in fluid dynamics. In this talk, we will introduce their applications to financial engineering. First, we will learn the high efficiency of a Spectral Element Method(SEM) to pricing European options under the one-dimensional and two-dimensional Black-Scholes (BS) model, Merton=92s jump diffusion (JD) model, and Heston=92s stochastic volatility (SV) model. I will show that the method is stable, and it gives "exponential convergence" in both the solution and its Greeks. Then, we will look at the SEM's application to Nonlinear Regression through a real-world example in energy market, i.e., Weather-Normalizing the power load. We will see that the SEM approach overcomes the problems in the regular polynomial fit.