An SFP–FCC method for pricing and hedging early-exercise options under Lévy processes

Article


Chan, R. 2020. An SFP–FCC method for pricing and hedging early-exercise options under Lévy processes. Quantitative Finance.
AuthorsChan, R.
Abstract

This paper extends the singular Fourier–Padé (SFP) method proposed by Chan [Singular Fourier–Padé series expansion of European option prices. Quant. Finance, 2018, 18, 1149–1171] for pricing/hedging early-exercise options–Bermudan, American and discrete-monitored barrier options–under a Lévy process. The current SFP method is incorporated with the Filon–Clenshaw–Curtis (FCC) rules invented by Domínguez et al. [Stability and error estimates for Filon–Clenshaw–Curtis rules for highly oscillatory integrals. IMA J. Numer. Anal., 2011, 31, 1253–1280], and we call the new method SFP–FCC. The main purpose of using the SFP–FCC method is to require a small number of terms to yield fast error convergence and to formulate option pricing and option Greek curves rather than individual prices/Greek values. We also numerically show that the SFP–FCC method can retain a global spectral convergence rate in option pricing and hedging when the risk-free probability density function is piecewise smooth. Moreover, the computational complexity of the method is O((L−1)(N+1)( Ñ log Ñ)) with N, a (small) number of complex Fourier series terms, Ñ, a number of Chebyshev series terms and L, the number of early-exercise/monitoring dates. Finally, we compare the accuracy and computational time of our method with those of existing techniques in numerical experiments.

JournalQuantitative Finance
ISSN1469-7688
Year2020
PublisherTaylor & Francis
Accepted author manuscript
License
File Access Level
Anyone
Digital Object Identifier (DOI)doi:10.1080/14697688.2020.1736322
Web address (URL)https://doi.org/10.1080/14697688.2020.1736322
Publication dates
Online07 Apr 2020
Publication process dates
Accepted24 Feb 2020
Deposited05 May 2020
Copyright holder© 2020 Taylor & Francis
Copyright informationThis is an Accepted Manuscript of an article published by Taylor & Francis in Quantitative Finance on 07/04/2020, available online: http://www.tandfonline.com/10.1080/14697688.2020.1736322.
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