| Summary: | 碩士 === 義守大學 === 財務金融學系 === 92 === Boyle and Lau discovered in 1994 that while evaluating continuous-time barriers option, the binomial tree model will produce big sharp evaluation errors and converge at low speed. In 1995, Ritchken proposed the method of pricing barrier option by using lattice. Late it was found the method converged too slow, when the initial underlying asset was close to the barrier. Boyle and Tian in 1998 used the explicit finite difference to determine the price of barrier option. The grid must be adjusted for the barrier pass all of them. However, this method cannot assure the initial underlying asset fall on the grid, nor can it directly obtain the accurate price of barrier option. Therefore, it is necessary to use quadratic interpolation to obtain the accurate price. In order to obtain the price of option directly, it is needed to adjust grids to assure both initial underlying asset and barrier pass the grid and then use implicit finite difference to evaluate the price of continuous-time barrier option. Both single and double barriers are discussed in the article. Numerical result, found by using implicit finite difference to evaluate the price of barrier option, shows the feature of monotone. Richardson extrapolation improves the efficiency and precision of calculation. Even if the price of initial underlying asset is extremely close to the barrier, implicit finite difference can still work properly.
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