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Numerical Valuation of Discrete Barrier Options with the Adaptive Mesh Model and Other Competing Techniques

This thesis develops an Adaptive Mesh Model for pricing discrete double barrier options. Adaptive Mesh Model is a kind of trinomial tree lattice that applying higher resolution to where nonlinearity errors occur. After the Adaptive Mesh Model for discrete single barrier options was proposed in 1999 by Ahn, Figlewski, and Gao, there is no further research has been done in Adaptive Mesh Model for discrete barriers. Furthermore, numerical data are also scarce in the paper of Ahn et al.. This thesis bases on the lattice structure of Ahn et al. and extends the Adaptive Mesh Model to price discrete double barrier options. Besides, there is no close-form solution for discrete barrier options such that many methods have been suggested and declared to price discrete barrier options fast and accurately but no one can tell exactly that what method is the best. We also make a complete comparisons of the Adaptive Mesh Model with other methods no matter in accuracy or in efficiency. Our numerical data shows that the Adaptive Mesh Model is generally surpassed the other tree lattice methods and the BGK formula approach, and exceed the quadrature method in efficiency with accurate enough outcomes.