Pricing of American Options

This thesis investigates the free boundary value problem of pricing American put options written on one underlying asset. In particular, attention is given to nd an accurate approximation of the critical ex- ercise boundary. The problem is approached using radial basis func- tions in the shape of Gaussian densities, and basis functions in the form of European put options. Furthermore, the domain is extended into the strike direction. Prices are computed for a range of strikes and maturities, and the critical strike prices are retrieved. Finally, the Merton Jump Diusion model is considered generating a partial integro dierential equation. Using Gaussian densities, prices and boundaries are computed on the extended domain