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.