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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.

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  • 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. 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..
    2. Damir Filipović & Eckhard Platen, 2009. "Consistent Market Extensions Under The Benchmark Approach," Mathematical Finance, Wiley Blackwell, vol. 19(1), pages 41-52, January.
    3. Eckhard Platen, 2024. "Benchmark-Neutral Pricing," Papers 2407.01542, arXiv.org.
    4. Eckhard Platen, 2025. "Information-minimizing stationary financial market dynamics," Papers 2507.18395, arXiv.org.
    5. Eckhard Platen & David Heath, 2006. "A Benchmark Approach to Quantitative Finance," Springer Finance, Springer, number 978-3-540-47856-0, October.
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