Meshfree methods in option pricing
Independent thesis Advanced level (degree of Master (One Year)), 10 credits / 15 HE creditsStudent thesis
A meshfree approximation scheme based on the radial basis function methods is presented for the numerical solution of the options pricing model. This thesis deals with the valuation of the European, Barrier, Asian, American options of a single asset and American options of multi assets. The option prices are modeled by the Black-Scholes equation. The θ-method is used to discretize the equation with respect to time. By the next step, the option price is approximated in space with radial basis functions (RBF) with unknown parameters, in particular, we con- sider multiquadric radial basis functions (MQ-RBF). In case of Ameri- can options a penalty method is used, i.e. removing the free boundary is achieved by adding a small and continuous penalty term to the Black- Scholes equation. Finally, a comparison of analytical and finite difference solutions and numerical results from the literature is included.
Place, publisher, year, edition, pages
2011. , 59 p.
Financial Mathematics, option pricing, RBF, PDE, meshfree methods
Mathematics Discrete Mathematics
IdentifiersURN: urn:nbn:se:hh:diva-16383Local ID: IDE1124OAI: oai:DiVA.org:hh-16383DiVA: diva2:444783
Subject / course
2011-05-30, Wigforssallen, Halmstad University, Halmstad, 10:01 (English)
UppsokPhysics, Chemistry, Mathematics
Ehrhardt, Matthias, Professor Dr.
Bordag, Ljudmila A., Professor Dr.