Paper: arXiv 2407.01542

Authors: Eckhard Platen

Abstract

The paper introduces benchmark-neutral pricing and hedging for long-term contingent claims. It employs the growth optimal portfolio of the stocks as numeraire and the new benchmark-neutral pricing measure for pricing. For a realistic parsimonious model, this pricing measure turns out to be an equivalent probability measure, which is not the case for the risk-neutral pricing measure. Many risk-neutral prices of long-term contracts are more expensive than necessary. Benchmark-neutral pricing identifies the minimal possible prices of contingent claims, which is illustrated with remarkable accuracy for a long-term zero-coupon bond.

Complexity vs Empirical Score

  • Math Complexity: 8.0/10
  • Empirical Rigor: 4.5/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper introduces a mathematically sophisticated alternative to traditional risk-neutral pricing by using the Growth Optimal Portfolio as a numeraire, proving that many long-term derivatives are overpriced under standard frameworks. While the theoretical derivations and mathematical proofs are advanced and novel, the empirical application is limited to a stylized long-term zero-coupon bond illustration rather than extensive historical backtesting.

Research Flowchart

  flowchart TD
    A["Research Goal: Price & hedge long-term contingent claims efficiently"] --> B["Inputs: Stock market data & long-term zero-coupon bond claims"]
    B --> C["Methodology: Select Growth Optimal Portfolio (GOP) as numeraire"]
    C --> D["Process: Apply numeraire change to derive Benchmark-Neutral Pricing Measure"]
    D --> E["Finding: Measure is an Equivalent Probability Measure (unlike risk-neutral)"]
    E --> F["Outcome: Identifies minimal correct prices, avoiding overpricing"]

Cited References (22)

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  4. A BENCHMARK APPROACH TO FINANCE (2006) — link
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  7. A New Interpretation of Information Rate (1956) — link
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and 14 more
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  2. The fundamental theorem of asset pricing for unbounded stochastic processes (1998) — link
  3. Hedging for the long run (2012) — link
  4. CONSISTENT MARKET EXTENSIONS UNDER THE BENCHMARK APPROACH — link
  5. BENCHMARKED RISK MINIMIZATION (2014) — link
  6. A Benchmark Approach to Quantitative Finance (2006) — link
  7. The numéraire portfolio in semimartingale financial models (2007) — link
  8. The leverage effect puzzle: Disentangling sources of bias at high frequency (2013) — link
  9. Changes of numéraire, changes of probability measure and option pricing (1995) — link
  10. Empirical Evidence on Student-tLog-Returns of Diversified World Stock Indices (2008) — link
  11. APPROXIMATING THE GROWTH OPTIMAL PORTFOLIO AND STOCK PRICE BUBBLES (2020) — link
  12. Moment explosions in stochastic volatility models (2006) — link
  13. Less-expensive long-term annuities linked to mortality, cash and equity (2022) — link
  14. Portfolio Theory and Arbitrage (2021) — link

0 of 22 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.