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

By Fang Fang, Cornelis W. Oosterlee. Numerische Mathematik, 2009

302 citations recorded by the source corpus.

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.

Subfields: Finance

View Paper: https://www.semanticscholar.org/paper/f8521b17f5c80f09913b516104af84d1b52b6d56

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Citations in the corpus

An iterative method for pricing American options under jump-diffusion models (2011, unknown): “One alternative approach to PIDEs is to employ a riskneutral valuation formula and evaluate it quickly using FFT (Fast Fourier Transform) [11, 18].”
A Novel Pricing Method for European Options Based on Fourier-Cosine Series Expansions (2008, methodology): “The generalization of the COS method for options with early-exercise features, like Bermudan and American options, is on its way; see [12].”
Extension of stochastic volatility equity models with the Hull–White interest rate process (2012, methodology): “The COS method can achieve an exponential convergence rate for European, Bermudan and barrier options for affine models whose probability density function is in C∞[a, b], with nonzero derivatives [14; 15].”