Rational Spectral Collocation Method for Pricing American Vanilla and Butterfly Spread Options
We present a rational spectral collocation method for pricing American vanilla and butterfly spread options. Due to the early exercise possibilities, free boundary conditions are associated with both of these PDEs. The problem is first reformulated as a variational inequality. Then, by adding a penalty term, the resulting variational inequality is transformed into a nonlinear advection-diffusion-reaction equation on fixed boundaries. This nonlinear PDE is discretised in asset (space) direction by means of rational interpolation using suitable barycentric weights and transformed Chebyshev points. This gives a system of stiff nonlinear ODEs which is then integrated using an implicit fourth-order Lobatto time-integration method. We carried out extensive comparisons with other results obtained by using some existing methods found in literature and observed that our approach is very competitive.
KeywordsAmerican options Butterfly spread options Rational spectral collocation method
E. Pindza and E. Ngounda acknowledge the financial support from the Agence Nationale des Bourses du Gabon. Patidar’s research was also supported by the South African National Research Foundation.