This paper adapts the hybrid method, a combination of the Laplace transformation and the finite-difference approach, to the pricing of barrier-style options. The hybrid method eliminates the time steps and provides a highly accurate and precise numerical solution that can be rapidly obtained. This method is superior to lattice methods when trying to solve barrier-style options. Previous studies have tried to solve barrier-style options; however, there have continually been several disadvantages. Very small time steps and stock node spaces are needed to avoid undesirable numerically induced oscillations in the solution of barrier option. In addition, all the intermediate option prices must be computed at each time step, even though one may be only interested in the terminal price of barrier-style complex options. The hybrid method may also solve more complex problems concerning barrier-style options with various boundary constraints such as options with a time-varying rebate. In order to demonstrate the accuracy and efficiency of the proposed scheme, we compare our algorithm with several well-known pricing formulas of barrier-type options. The numerical results show that the hybrid method is robust, and provides a highly accurate solution and fast convergence, regardless of whether or not the initial asset prices are close to the barrier.
