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Pricing methods for α-quantile and perpetual early exercise options based on Spitzer identities

Author

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  • C. E. Phelan
  • D. Marazzina
  • G. Germano

Abstract

We present new numerical schemes for pricing perpetual Bermudan and American options as well as α-quantile options. This includes a new direct calculation of the optimal exercise boundary for early-exercise options. Our approach is based on the Spitzer identities for general Lévy processes and on the Wiener–Hopf method. Our direct calculation of the price of α-quantile options combines for the first time the Dassios–Port–Wendel identity and the Spitzer identities for the extrema of processes. Our results show that the new pricing methods provide excellent error convergence with respect to computational time when implemented with a range of Lévy processes.

Suggested Citation

  • C. E. Phelan & D. Marazzina & G. Germano, 2020. "Pricing methods for α-quantile and perpetual early exercise options based on Spitzer identities," Quantitative Finance, Taylor & Francis Journals, vol. 20(6), pages 899-918, June.
    • Handle: RePEc:taf:quantf:v:20:y:2020:i:6:p:899-918
    DOI: 10.1080/14697688.2020.1718192
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    Cited by:

    1. Zhang, Meihui & Jia, Jinhong & Zheng, Xiangcheng, 2023. "Numerical approximation and fast implementation to a generalized distributed-order time-fractional option pricing model," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    2. Muto, Makoto & Saiki, Yoshitaka, 2024. "Synchronization analysis between exchange rates on the basis of purchasing power parity using the Hilbert transform," The North American Journal of Economics and Finance, Elsevier, vol. 74(C).
    3. Kontosakos, Vasileios E. & Mendonca, Keegan & Pantelous, Athanasios A. & Zuev, Konstantin M., 2021. "Pricing discretely-monitored double barrier options with small probabilities of execution," European Journal of Operational Research, Elsevier, vol. 290(1), pages 313-330.

    More about this item

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • D40 - Microeconomics - - Market Structure, Pricing, and Design - - - General
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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