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Making No-Arbitrage Discounting-Invariant: A New FTAP Beyond NFLVR and NUPBR

Author

Listed:
  • Dániel Ágoston Bálint

    (ETH Zurich)

  • Martin Schweizer

    (ETH Zürich and Swiss Finance Institute)

Abstract

In general multi-asset models of financial markets, the classic no-arbitrage concepts NFLVR and NUPBR have a serious shortcoming — they depend crucially on the way prices are discounted. To avoid this unnatural economic behaviour, we introduce a new idea for defining “absence of arbitrage”. It rests on the new notion of strongly index weight maximal strategies, which allows us to generalise both NFLVR (by dynamic index weight efficiency) and NUPBR (by dynamic index weight viability). These new no-arbitrage concepts do not change when we look at discounted or undiscounted prices, and they can be used in open-ended models under very weak assumptions on asset prices. We establish corresponding versions of the FTAP, i.e., dual characterisations of our concepts in terms of martingale properties. A key new feature is that as one expects, “properly anticipated prices fluctuate randomly”, but with an endogenous discounting process which is not a priori chosen exogenously. We also illustrate our results by a wide range of examples. In particular, we show that the classic Black–Scholes model on [0,1) is arbitrage-free in our sense if and only if its parameters satisfy m−r ε {0, σ²} or, equivalently, either bond-discounted or stock-discounted prices are martingales.

Suggested Citation

  • Dániel Ágoston Bálint & Martin Schweizer, 2018. "Making No-Arbitrage Discounting-Invariant: A New FTAP Beyond NFLVR and NUPBR," Swiss Finance Institute Research Paper Series 18-23, Swiss Finance Institute, revised Mar 2018.
    • Handle: RePEc:chf:rpseri:rp1823
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    References listed on IDEAS

    as
    1. Mark Loewenstein & Gregory A. Willard, 2000. "Local martingales, arbitrage, and viability," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 16(1), pages 135-161.
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    11. Koichiro Takaoka & Martin Schweizer, 2014. "A note on the condition of no unbounded profit with bounded risk," Finance and Stochastics, Springer, vol. 18(2), pages 393-405, April.
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    Cited by:

    1. Jan Obłój & Johannes Wiesel, 2021. "A unified framework for robust modelling of financial markets in discrete time," Finance and Stochastics, Springer, vol. 25(3), pages 427-468, July.

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    More about this item

    Keywords

    no arbitrage; maximal strategies; semimartingales; discounting; NFLVR; NUPBR; FTAP; o-martingale deflator; strongly index weight maximal; dynamically index weight viable; Black–Scholes model;
    All these keywords.

    JEL classification:

    • C00 - Mathematical and Quantitative Methods - - General - - - General
    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)

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