A comparison of numerical methods for pricing single and double barrier options

Barrier options are the most popular and traded derivatives in the financial market because of their lower prices. Many studies have been conducted to develop the methods of pricing barrier options. Barrier option prices can be calculated using the classical binomial tree method, but it is time-consuming when we have a large number of time periods. Muroi and Yamada have developed a new fast algorithm to obtain the prices of barrier options by using the spectral expansion approach. We implement and check this algorithm by doing more extensive numerical experimental studies and showing that the same prices calculated using the binomial tree method can also be obtained using the spectral binomial tree approach with a higher computational speed