Pricing early-exercise and discrete barrier options by fourier-cosine series expansions

We present a pricing method based on Fourier-cosine expansions for early-exercise and discretely-monitored barrier options. The method works well for exponential Lévy asset price models. The error convergence is exponential for processes characterized by very smooth (C^∞[a, b] ∈ ℝ) transitional probability density functions. The computational complexity is O((M - 1)N log N) with N a (small) number of terms from the series expansion, and M, the number of early-exercise/monitoring dates. This paper is the follow-up of (Fang and Oosterlee in SIAM J Sci Comput 31(2):826-848, 2008) in which we presented the impressive performance of the Fourier-cosine series method for European options.