Approximating European Options By Rebate Barrier Options

When the underlying stock price is a strict local martingale process under an equivalent local martingale measure, Black-Scholes PDE associated with an European option may have multiple solutions. In this paper, the authors study an approximation for the smallest hedging price of such an European option. The results show that a class of rebate barrier options can be used for this approximation, when its rebate and barrier are chosen appropriately. An asymptotic convergence rate is also achieved when the knocked-out barrier moves to infinity under suitable conditions.