This thesis analyzes the performance of two numerical methods (Adaptive Mesh Model and QUAD) to value options. Most derivatives securities do not have closed-form solutions and must be priced by numerical techniques. But these numerical models contain “distribution error” and “nonlinearity error” producing large errors even with thousands of time steps and millions of node calculations. Proved to be the successful approaches that reduce these errors, Adaptive Mesh Model (AMM, 1999) and QUAD (2003) have a wide methodological difference in developing numerical procedures. So there are comparative merits and demerits in accuracy and efficiency in valuing options according to pay-off scheme, time dependency and observation continuity.
