A Finite Element Approach to Solving Leland Model for Options Pricing

Abstract

In this thesis work, the Leland model for pricing of European options is studied. Firstly, the derivation of the Leland model is introduced by using Ito’s lemma and synthesized replicate portfolio methodology. Then the model is transformed to a system of equations by change of variables to which the Galerkin finite element model canbeapplied. Crank-Nicolsonfinitedifferencemethodisadoptedtosolvetheresulting differential differential algebraic finite element system with data from literature. Some numerical solutions are presented by example.