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Asset pricing theory for two price economies

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  • Dilip Madan

Abstract

We show that nonlinearly discounted nonlinear martingales are related to no arbitrage in two price economies as linearly discounted martingales were related to no arbitrage in economies satisfying the law of one price. Furthermore, assuming risk acceptability requires a positive physical expectation, we demonstrate that expected rates of return on ask prices should be dominated by expected rates of return on bid prices. A preliminary investigation conducted here, supports this hypothesis. In general we observe that asset pricing theory in two price economies leads to asset pricing inequalities. A model incorporating both nonlinear discounting and nonlinear martingales is developed for the valuation of contingent claims in two price economies. Examples illustrate the interactions present between the severity of measure changes and their associated discount rates. As a consequence arbitrage free two price economies can involve unique discount curves and measure changes that are however specific to both the product being priced and the trade direction. Furthermore the developed valuation operators call into question the current practice of Debt Valuation Adjustments. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • Dilip Madan, 2015. "Asset pricing theory for two price economies," Annals of Finance, Springer, vol. 11(1), pages 1-35, February.
    • Handle: RePEc:kap:annfin:v:11:y:2015:i:1:p:1-35
    DOI: 10.1007/s10436-014-0255-8
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    References listed on IDEAS

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    21. Dilip B. Madan & Wim Schoutens, 2012. "Tenor Specific Pricing," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 15(06), pages 1-21.
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    Citations

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    Cited by:

    1. Carr, Peter & Madan, Dilip B. & Melamed, Michael & Schoutens, Wim, 2016. "Hedging insurance books," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 364-372.
    2. Aziz Issaka & Indranil SenGupta, 2017. "Analysis of variance based instruments for Ornstein–Uhlenbeck type models: swap and price index," Annals of Finance, Springer, vol. 13(4), pages 401-434, November.
    3. Claudio Albanese & Simone Caenazzo & St'ephane Cr'epey, 2016. "Capital Valuation Adjustment and Funding Valuation Adjustment," Papers 1603.03012, arXiv.org.
    4. Florence Guillaume & Gero Junike & Peter Leoni & Wim Schoutens, 2019. "Implied liquidity risk premia in option markets," Annals of Finance, Springer, vol. 15(2), pages 233-246, June.
    5. Dilip B. Madan, 2016. "Benchmarking in two price financial markets," Annals of Finance, Springer, vol. 12(2), pages 201-219, May.
    6. Dilip B Madan, 2016. "Marking to two-price markets," Journal of Asset Management, Palgrave Macmillan, vol. 17(2), pages 100-118, March.
    7. Dilip B. Madan, 2016. "Adapted hedging," Annals of Finance, Springer, vol. 12(3), pages 305-334, December.
    8. Mehdi Vazifedan & Qiji Jim Zhu, 2020. "No-Arbitrage Principle in Conic Finance," Risks, MDPI, vol. 8(2), pages 1-34, June.
    9. Ilya Molchanov & Anja Mühlemann, 2021. "Nonlinear expectations of random sets," Finance and Stochastics, Springer, vol. 25(1), pages 5-41, January.
    10. Robert J. Elliott & Dilip B. Madan & Tak Kuen Siu, 2021. "Two price economic equilibria and financial market bid/ask prices," Annals of Finance, Springer, vol. 17(1), pages 27-43, March.
    11. Ilya Molchanov & Anja Muhlemann, 2019. "Nonlinear expectations of random sets," Papers 1903.04901, arXiv.org.
    12. Dilip B. Madan, 2018. "Financial equilibrium with non-linear valuations," Annals of Finance, Springer, vol. 14(2), pages 211-221, May.

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    More about this item

    Keywords

    Multi-curve discounting; Acceptable risks; Distorted expectations; Cliquets; Debt valuation adjustments; G10; G11; G13;
    All these keywords.

    JEL classification:

    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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