Pricing American Options using Monte Carlo Method - Wu, Z (University of Oxford;Mathematical Institute, 2012)
This thesis reviewed a number of Monte Carlo based methods for pricing American options. The least-squares regression based Longstaff-Schwartz method (LSM) for approximating lower bounds of option values and the Duality approach through martingales for estimating the upper bounds of option values were implemented with simple examples of American put options. The effectiveness of these techniques and the dependencies on various simulation parameters were tested and discussed. A computing saving technique was suggested to reduce the computational complexity by constructing regression basis functions which are orthogonal to each other with respect to the natural distribution of the underlying asset price. The orthogonality was achieved by using Hermite polynomials. The technique was tested for both the LSM approach and the Duality approach. At the last, the Multilevel Mote Carlo (MLMC) technique was employed with pricing American options and the effects on variance reduction were discussed. A smoothing technique using artificial probability weighted payoff functions jointly with Brownian Bridge interpolations was proposed to improve the Multilevel Monte Carlo performances for pricing American options.