The numerical method of pricing up-and-out call Parision Option based on the Black-Scholes model is focused in this article. The two-point compact scheme with second-order accuracy is used. A technique to remove the singularity of the pay-offf unction is used to make the result more accurate,more effective and more stable.The influence of the delaying time and the barrier on the option price is discussed.
In this paper, the method with high-order accuracy was presented for a kind ofnonlinear sigular perturbation problems. The numerical tests demonstrate that only afew grid points are enough for the numerical results with high-order accuracy in ourmethod.
