Hedging and pricing early-exercise options with complex fourier series expansion |
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| Affiliation: | 1. School of Economic Mathematics, Southwestern University of Finance and Economics, 555 Liutai Boulevard, Wenjiang, Chengdu 611130, PR China;2. Department of Economics and Management, Sichuan Vocational and Technical College of Communications, Chengdu 611130, PR China;1. Chulalongkorn University, Sasin Graduate Institute of Business Administration, Bangkok, Thailand;2. Chulalongkorn University, College of Population Studies, Bangkok, Thailand;3. Pennsylvania State University, School of Graduate Professional Studies, Malvern, PA, USA;1. Division of Economics, Nanyang Technological University, Singapore 639805, Singapore;2. School of Economics and Commerce, South China University of Technology, China;3. Research Center of Financial Engineering, South China University of Technology, China |
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| Abstract: | We introduce a new numerical method called the complex Fourier series (CFS) method proposed by Chan (2017) to price options with an early-exercise feature—American, Bermudan and discretely monitored barrier options—under exponential Lévy asset dynamics. This new method allows us to quickly and accurately compute the values of early-exercise options and their Greeks. We also provide an error analysis to demonstrate that, in many cases, we can achieve an exponential convergence rate in the pricing method as long as we choose the correct truncated computational interval. Our numerical analysis indicates that the CFS method is computationally more comparable or favourable than the methods currently available. Finally, the superiority of the CFS method is illustrated with real financial data by considering Standard & Poor’s depositary receipts (SPDR) exchange-traded fund (ETF) on the S&P 500® index options, which are American options traded from November 2017 to February 2018 and from 30 January 2019 to 21 June 2019. |
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| Keywords: | American option Bermuda option Barrier option complex Fourier series early-exercise options Lévy processes |
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