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A new representation of the risk-neutral distribution and its applications

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  • Zhenyu Cui
  • Yuewu Xu

Abstract

This paper establishes a novel model-free representation of the risk-neutral density in terms of market-observed options prices by combining exact series representations of the Dirac Delta function and the Carr-Madan asset spanning formula. Compared to the widely used method for obtaining the risk-neutral densities via the Breeden–Litzenberger device, our method yields estimates of risk-neutral densities that are model-free, automatically smooth, and in closed-form. The closed-form feature of our new representation makes it ideal for many potential applications including a new model-free representation of the local volatility function in the Dupire's local volatility model. The validity of our method is demonstrated through simulation studies as well as an empirical application using S&P 500 index option data. Extension of the method to higher dimensions is also obtained by extending the spanning formula.

Suggested Citation

  • Zhenyu Cui & Yuewu Xu, 2022. "A new representation of the risk-neutral distribution and its applications," Quantitative Finance, Taylor & Francis Journals, vol. 22(5), pages 817-834, May.
    • Handle: RePEc:taf:quantf:v:22:y:2022:i:5:p:817-834
    DOI: 10.1080/14697688.2021.2013520
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    Cited by:

    1. Evgenii Vladimirov, 2023. "iCOS: Option-Implied COS Method," Papers 2309.00943, arXiv.org, revised Feb 2024.
    2. S'ebastien Bossu & St'ephane Cr'epey & Hoang-Dung Nguyen, 2024. "Spanning Multi-Asset Payoffs With ReLUs," Papers 2403.14231, arXiv.org.

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