Pricing early-exercise and discrete barrier options by fourier-cosine series expansions |
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Authors: | F Fang C W Oosterlee |
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Institution: | 1.Delft Institute of Applied Mathematics,Delft University of Technology,Delft,The Netherlands;2.CWI, Centrum Wiskunde and Informatica,Amsterdam,The Netherlands |
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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. |
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