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Free Lunches with Vanishing Risks Most Likely Exist

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  • Eckhard Platen
  • Kevin Fergusson

Abstract

The hypothesis that there do not exist free lunches with vanishing risk (FLVRs) in the real market underpins the popular risk-neutral pricing and hedging methodology in quantitative finance. The paper documents the fact that this hypothesis can be safely rejected. It performs extremely accurately the hedging of an extreme-maturity zero-coupon bond (ZCB). This hedge is part of a portfolio that starts with zero initial wealth and invests dynamically in a total return stock market index and the savings account to generate at the maturity date of the extreme-maturity ZCB a strictly positive amount with strictly positive probability, which represents an FLVR. The fact that FLVRs naturally exist in the real market can be accommodated theoretically under the benchmark approach.

Suggested Citation

  • Eckhard Platen & Kevin Fergusson, 2025. "Free Lunches with Vanishing Risks Most Likely Exist," Papers 2508.07108, arXiv.org.
    • Handle: RePEc:arx:papers:2508.07108
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    References listed on IDEAS

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    1. Damir Filipović & Eckhard Platen, 2009. "Consistent Market Extensions Under The Benchmark Approach," Mathematical Finance, Wiley Blackwell, vol. 19(1), pages 41-52, January.
    2. Eckhard Platen, 2006. "A Benchmark Approach To Finance," Mathematical Finance, Wiley Blackwell, vol. 16(1), pages 131-151, January.
    3. Eckhard Platen, 2025. "Information-minimizing stationary financial market dynamics," Papers 2507.18395, arXiv.org.
    4. Eckhard Platen, 2024. "Benchmark-Neutral Pricing," Papers 2407.01542, arXiv.org.
    5. Eckhard Platen & David Heath, 2006. "A Benchmark Approach to Quantitative Finance," Springer Finance, Springer, number 978-3-540-47856-0, April.
    6. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 5, pages 129-164, World Scientific Publishing Co. Pte. Ltd..
    7. Fergusson, Kevin & Platen, Eckhard, 2023. "Less-expensive long-term annuities linked to mortality, cash and equity," Annals of Actuarial Science, Cambridge University Press, vol. 17(1), pages 170-207, March.
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