American put option gives the holder the right to sell a unit of stock at prespecified strike price before or at maturity. Unlike the European option, the pricing problem has been an intriguing issue because the analytical solution may not exist. The valuation of the option has been resorted to numerical methods or quasi-analytical methods. In this thesis, the pricing problem is formulated as a free boundary problem differential equation. Using the front-fixing technique and finite difference method, the free boundary PDE can be solved by a numerical scheme in a fixed domain. The scheme is proved to have five desirable properties, which are consistent with the exact solution. However, due to the fact that the temporal derivatives is unbounded near maturity, the scheme fails to be consistent....[ Read more ]

American put option gives the holder the right to sell a unit of stock at prespecified strike price before or at maturity. Unlike the European option, the pricing problem has been an intriguing issue because the analytical solution may not exist. The valuation of the option has been resorted to numerical methods or quasi-analytical methods. In this thesis, the pricing problem is formulated as a free boundary problem differential equation. Using the front-fixing technique and finite difference method, the free boundary PDE can be solved by a numerical scheme in a fixed domain. The scheme is proved to have five desirable properties, which are consistent with the exact solution. However, due to the fact that the temporal derivatives is unbounded near maturity, the scheme fails to be consistent. Nevertheless, it can be shown that the convergence of the scheme is at least of 1/2-order in time and 1st order in space if the truncation errors at each layer are aggregated.