Abstract: The Barrier option pricing problem is one of hot topics in modern finance, and also one of important fields in Mathematical finance. In this paper, the pricing problems of barrier options are discussed under the nonlinear Black-Scholes model. Firstly, the author uses the perturbation method of single-parameter to obtain asymptomatic formulae of barrier options pricing problems. Secondly, error estimates of these asymptotic solutions are illustrated by using the Feymann-Kac formula under the given condition. Finally, numerical experiments confirm the correctness of the proposed theoretical results as well as error estimation.

Key words: nonlinear Black-Scholes model, barrier options, asymptomatic pricing formulae, error estimates