C++ code for pricing options under Feller-Levy models using the Finite Element Method
The arbitrage-free price of financial products with payoff at time
, is given by
.
The stock price process follows , where
is an
-stable Lévy process, and hence the stock price is a jump process.
Using the Feynman-Kac theorem, the fractional partial differential equation governing the price of the option is given by
where the risk free interest rate, and
the payoff.
Finally, the finite element method is applied to the above equation to solve for the option price process. However, a special numerical treatment is required for the discretization of the fractional laplace operator given by
, and that is taken care of in this project.