Pricing exotic options with L-stable Padé schemes

In this paper we develop a strongly stable (L-stable) and highly accurate method for pricing exotic options. The method is based on Padé schemes and also utilizes partial fraction decomposition to address issues regarding accuracy and computational efficiency. Due to non-smooth payoffs, which cause discontinuities in the solution (or its derivatives), standard A-stable methods are prone to produce large and spurious oscillations in the numerical solutions which would mislead to estimating options accurately. The proposed method does not suffer these drawbacks while being easy to implement on concurrent processors. Numerical results are presented for digital options, butterfly spread and barrier options in one and two assets. In addition, the methods are tested on the Heston stochastic volatility model.