| Summary: | 碩士 === 國立成功大學 === 工業管理學系 === 89 === Most models for pricing barrier options assume continuous monitoring of the barrier; under this assumption, the option can often be priced in closed form. Many real contracts with barrier provisions specify discrete monitoring instants; there are essentially no closed-form solutions for pricing these options. The lattice and simulation pricing approaches can lead to significant pricing errors even with a large number of time-steps. The reason is that when the barrier is closing to the current price of the underlying asset, the lattice method is difficult to achieve convergence. When the numerical analytical approach is adopted, it become either computationally intensive or produce less accurate estimation as the dimension increases. Aiming to resolve the preceding problems, we propose an analytical methodology that satisfies the partial differential equation and initial condition that characterize the discrete barrier option problem. The objectives of this thesis are as follows. First, we derive the P.D.E. valuation methodology to price discrete barrier down-and-out barrier options. Second, the thesis analyzes the impact of the numbers of partition and the integral interval upon the size of the absolute and relative pricing errors, the proper numbers of partition and the range of integration are also recommended.
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