Free Lunches with Vanishing Risks Most Likely Exist

2025/08/09 by Eckhard Platen, Platen, Eckhard, Kevin Fergusson +1
Economics, Econometrics and Finance · #60G35 #62P05 #62P20 #FOS: Economics and business #Financial Markets and Investment Strategies #Financial Risk and Volatility Modeling #Mathematical Finance (q-fin.MF) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2508.07108

openalex publication_date 2025/08/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Information-minimizing stationary financial market dynamics
• Less-Expensive Valuation of Long Term Annuities Linked to Mortality, Cash and Equity
• A Theory for the Term Structure of Interest Rates

Related

• Free Lunch
• A Penny Saved is a Penny Earned: Less Expensive Zero Coupon Bonds
• Robust no-free lunch with vanishing risk, a continuum of assets and proportional transaction costs
• Benchmark-Neutral Pricing
• Self-Financing, Replicating Hedging Strategies, an incomplete thermodynamic analogy