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Unspanned stochastic volatility in the multifactor CIR model

Author

Listed:
  • Damir Filipović
  • Martin Larsson
  • Francesco Statti

Abstract

Empirical evidence suggests that fixed‐income markets exhibit unspanned stochastic volatility (USV), that is, that one cannot fully hedge volatility risk solely using a portfolio of bonds. While Collin‐Dufresne and Goldstein (2002, Journal of Finance, 57, 1685–1730) showed that no two‐factor Cox–Ingersoll–Ross (CIR) model can exhibit USV, it has been unknown to date whether CIR models with more than two factors can exhibit USV or not. We formally review USV and relate it to bond market incompleteness. We provide necessary and sufficient conditions for a multifactor CIR model to exhibit USV. We then construct a class of three‐factor CIR models that exhibit USV. This answers in the affirmative the above previously open question. We also show that multifactor CIR models with diagonal drift matrix cannot exhibit USV.

Suggested Citation

  • Damir Filipović & Martin Larsson & Francesco Statti, 2019. "Unspanned stochastic volatility in the multifactor CIR model," Mathematical Finance, Wiley Blackwell, vol. 29(3), pages 827-836, July.
    • Handle: RePEc:bla:mathfi:v:29:y:2019:i:3:p:827-836
    DOI: 10.1111/mafi.12193
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    Cited by:

    1. Backwell, Alex, 2021. "Unspanned stochastic volatility from an empirical and practical perspective," Journal of Banking & Finance, Elsevier, vol. 122(C).
    2. Damir Filipović, 2023. "Discount models," Finance and Stochastics, Springer, vol. 27(4), pages 933-946, October.
    3. Hölzermann, Julian, 2020. "Pricing Interest Rate Derivatives under Volatility Uncertainty," Center for Mathematical Economics Working Papers 633, Center for Mathematical Economics, Bielefeld University.
    4. Yuecai Han & Fengtong Zhang, 2024. "Pricing fixed income derivatives under a three-factor CIR model with unspanned stochastic volatility," Review of Derivatives Research, Springer, vol. 27(1), pages 37-53, April.
    5. Julian Holzermann, 2020. "Pricing Interest Rate Derivatives under Volatility Uncertainty," Papers 2003.04606, arXiv.org, revised Nov 2021.
    6. Damir Filipovic, 2023. "Discount Models," Papers 2306.16871, arXiv.org, revised Jul 2023.

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