Smoothing of initial conditions for high order approximations in option pricing
Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
In this article the Finite Difference method is used to solve the Black Scholes equation. A second order and fourth order accurate scheme is implemented in space and evaluated. The scheme is then tried for different initial conditions. First the discontinuous pay off function of a European Call option is used. Due to the nonsmooth charac- teristics of the chosen initial conditions both schemes show an order of two. Next, the analytical solution to the Black Scholes is used when t=T/2. In this case, with a smooth initial condition, the fourth order scheme shows an order of four. Finally, the initial nonsmooth pay off function is modified by smoothing. Also in this case, the fourth order method shows an order of convergence of four.
Place, publisher, year, edition, pages
2016. , 22 p.
TVE, 16029 maj
Finite Differences, Computational Finance, Black Scholes
Other Computer and Information Science
IdentifiersURN: urn:nbn:se:uu:diva-302322OAI: oai:DiVA.org:uu-302322DiVA: diva2:957102
Master Programme in Engineering Physics
von Sydow, Lina, Senior Lecturer
Sjödin, Martin, Professor