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Pricing And Valuation Under The Real-World Measure

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  • GABRIEL FRAHM

    (Department of Mathematics/Statistics, Chair for Applied Stochastics and Risk Management, Helmut Schmidt University, Germany)

Abstract

In general it is not clear which kind of information is supposed to be used for calculating the fair value of a contingent claim. Even if the information is specified, it is not guaranteed that the fair value is uniquely determined by the given information. A further problem is that asset prices are typically expressed in terms of a risk-neutral measure. This makes it difficult to transfer the fundamental results of financial mathematics to econometrics. I show that the aforementioned problems evaporate if the financial market is complete and sensitive. In this case, after an appropriate choice of the numéraire, the discounted price processes turn out to be uniformly integrable martingales under the real-world measure. This leads to a Law of One Price and a simple real-world valuation formula in a model-independent framework where the number of assets as well as the lifetime of the market can be finite or infinite.

Suggested Citation

  • Gabriel Frahm, 2016. "Pricing And Valuation Under The Real-World Measure," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(01), pages 1-39, February.
    • Handle: RePEc:wsi:ijtafx:v:19:y:2016:i:01:n:s0219024916500060
    DOI: 10.1142/S0219024916500060
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    References listed on IDEAS

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    Cited by:

    1. Gabriel Frahm & Ferdinand Huber, 2019. "The Outperformance Probability of Mutual Funds," JRFM, MDPI, vol. 12(3), pages 1-29, June.
    2. Gabriel Frahm, 2018. "Corrigendum: “Pricing And Valuation Under The Real-World Measure”," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(04), pages 1-4, June.
    3. Gabriel Frahm, 0. "Arbitrage Pricing Theory In Ergodic Markets," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(05), pages 1-28.
    4. Gabriel Frahm, 2020. "Statistical properties of estimators for the log-optimal portfolio," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 92(1), pages 1-32, August.
    5. Gabriel Frahm & Alexander Jonen & Rainer Schüssler, 2019. "The Fundamental Theorems Of Asset Pricing And The Closed-End Fund Puzzle," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(05), pages 1-31, August.

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