Paper: arXiv 2508.07108

Authors: 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.

Complexity vs Empirical Score

  • Math Complexity: 7.0/10
  • Empirical Rigor: 6.5/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper directly challenges the foundational FTAP assumption in quantitative finance by attempting to empirically falsify the non-existence of FLVRs using historical S&P 500 and Treasury data. It combines sophisticated continuous-time financial mathematics (Benchmark Approach) with empirical hypothesis testing on extreme-maturity zero-coupon bond hedging.

Research Flowchart

  flowchart TD
    A[Research Goal: Test existence of Free Lunches with Vanishing Risk - FLVR - in real markets] --> B[Data Inputs: Stock Market Total Return Index & Savings Account Rate]
    B --> C[Methodology: Benchmark Approach & Dynamic Portfolio Management]
    C --> D[Computational Step: Accurate hedging of an extreme-maturity Zero-Coupon Bond]
    D --> E[Outcome: Portfolio starts with $0 initial wealth and yields strictly positive wealth at maturity]
    E --> F[Key Finding: Reject No-FLVR Hypothesis; FLVRs exist and fit within Benchmark Approach]

Cited References (17)

  1. Information-minimizing stationary financial market dynamics — → 2507.18395
  2. Managing the shortfall risk of target date funds by overfunding (2024) — link
  3. Less-Expensive Valuation of Long Term Annuities Linked to Mortality, Cash and Equity (2017) — link
  4. An Introduction to Mathematical Statistics (2017) — link
  5. CONSISTENT MARKET EXTENSIONS UNDER THE BENCHMARK APPROACH (2009) — link
  6. A Benchmark Approach to Quantitative Finance (2006) — link
  7. A Theory for the Term Structure of Interest Rates (2004) — link
  8. The fundamental theorem of asset pricing for unbounded stochastic processes (1998) — link
and 9 more
  1. The Logic of Scientific Discovery (1988) — link
  2. S&P500, Total Return Indices, Gross of Dividends (2025)
  3. 3-Month Treasury Bill Secondary Market Rate, Discount Basis [DTB3] (2025)
  4. Benchmark-neutral pricing. Technical report (2024)
  5. Continuous-Time Asset Pricing Theory (2021) — link
  6. Numerical Solution of Stochastic Differential Equations (2015)
  7. Methods of Mathematical Finance (2010) — link
  8. Continuous Martingales and Brownian Motion (3rd ed.) (1999)
  9. IFRS Foundation (2022

1 of 17 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.