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A functional analysis approach to the static replication of European options

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  • Sébastien Bossu
  • Peter Carr
  • Andrew Papanicolaou

Abstract

The replication of any European contingent claim by a static portfolio of calls and puts with strikes forming a continuum, formally proven by Carr and Madan [Towards a theory of volatility trading. In Volatility: New Estimation Techniques for Pricing Derivatives, edited by R.A. Jarrow, Vol. 29, pp. 417–427, 1998 (Risk books)], is part of the more general theory of integral equations. We use spectral decomposition techniques to show that exact payoff replication may be achieved with a discrete portfolio of special options. We discuss applications for fast pricing of vanilla options that may be suitable for large option books or high frequency option trading, and for model pricing when the characteristic function of the underlying asset price is known.

Suggested Citation

  • Sébastien Bossu & Peter Carr & Andrew Papanicolaou, 2021. "A functional analysis approach to the static replication of European options," Quantitative Finance, Taylor & Francis Journals, vol. 21(4), pages 637-655, April.
    • Handle: RePEc:taf:quantf:v:21:y:2021:i:4:p:637-655
    DOI: 10.1080/14697688.2020.1810857
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    Citations

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    Cited by:

    1. Vikranth Lokeshwar Dhandapani & Shashi Jain, 2023. "Data-driven Approach for Static Hedging of Exchange Traded Options," Papers 2302.00728, arXiv.org, revised Jan 2024.
    2. Vikranth Lokeshwar Dhandapani & Shashi Jain, 2024. "Neural Networks for Portfolio-Level Risk Management: Portfolio Compression, Static Hedging, Counterparty Credit Risk Exposures and Impact on Capital Requirement," Papers 2402.17941, arXiv.org.
    3. Purba Banerjee & Srikanth Iyer & Shashi Jain, 2023. "Multi-period static hedging of European options," Papers 2310.01104, arXiv.org, revised Oct 2023.
    4. Carlo Marinelli, 2021. "On certain representations of pricing functionals," Papers 2109.05564, arXiv.org.
    5. Lucio Fernandez‐Arjona & Damir Filipović, 2022. "A machine learning approach to portfolio pricing and risk management for high‐dimensional problems," Mathematical Finance, Wiley Blackwell, vol. 32(4), pages 982-1019, October.
    6. Navratil, Robert & Taylor, Stephen & Vecer, Jan, 2022. "On the utility maximization of the discrepancy between a perceived and market implied risk neutral distribution," European Journal of Operational Research, Elsevier, vol. 302(3), pages 1215-1229.

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