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

Authors:
F. Fang;C. W. Oosterlee
Affiliations:
Delft University of Technology, Delft Institute of Applied Mathematics, Delft, The Netherlands;CWI, Centrum Wiskunde and Informatica, Amsterdam, The Netherlands
Venue:
Numerische Mathematik
Year:
2009

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Abstract

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 ($${{\rm{C}}^{\infty}[a,b]\in\mathbb {R}}$$) 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.