(Nazarbayev University School of Science and Technology, 2016-05-09) Zhexembay, Laila; Pak, Andrey
The main purpose of our Capstone project is to study the Risk-Adjusted
Pricing Methodology (RAMP) Black-Scholes model and to find the finite
element solutions of the nonlinear Black-Scholes equation. The RAPM
is one of the many nonlinear models in option pricing considering factors
which affect the volatility in the original Black-Scholes equation. This
model can be simplifed to a nonlinear parabolic equation in a new vari-
able which equals the product of Gamma and the price of the underlying
asset. Galerkin nite element method is applied to the parabolic equation.
Two types of solutions will be presented: one using the linear elements
and the other using quadratic elements. Local finite element equations
for the linear and quadratic elements are derived with some specifc inter-
polations of the nonlinear terms. Numerical solutions are obtained and
compared to the results in literature. The explanation of the discrepancies
will be given together with the future goals of this study.