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.
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Fang, F., Oosterlee, C.W. Pricing early-exercise and discrete barrier options by fourier-cosine series expansions. Numer. Math. 114, 27–62 (2009). https://doi.org/10.1007/s00211-009-0252-4
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DOI: https://doi.org/10.1007/s00211-009-0252-4