High-order accurate implicit methods for barrier option pricing

This paper deals with a high‐order accurate implicit finite‐difference approach to the pricing of barrier options. In this way various types of barrier options are priced, including barrier options paying rebates, and options on dividend‐paying‐stocks. Moreover, the barriers may be monitored either continuously or discretely. In addition to the high‐order accuracy of the scheme, and the stretching effect of the coordinate transformation, the main feature of this approach lies on a probability‐based optimal determination of boundary conditions. This leads to much faster and accurate results when compared with similar pricing approaches. The strength of the present scheme is particularly demonstrated in the valuation of discretely monitored barrier options where it yields values closest to those obtained from the only semi‐analytical valuation methods available. The scheme is also applied to the analysis of Greeks data such as Delta and Gamma.