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Benchmarking in two price financial markets

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  • Dilip B. Madan

    (University of Maryland)

Abstract

No arbitrage for two price economies with no locally risk free asset implies that suitably benchmarked prices are nonlinear martingales. However, both the benchmarking asset and the measure change depend on the process being benchmarked. Further assumptions allow the nonlinear martingales in discrete time to become expectations with respect to a nonadditivity probability. Such nonlinear expectations are imminently reasonable given the lack of experience with tail events on both sides of the gain loss spectrum. Continuous time extensions employ measure distortions. The general valuation of economic activities and the leveraging of stability in benchmarked price processes is then addressed. Traditional asset pricing questions and investigations are then reopened for benchmarked prices. In particular, the analytics for benchmarked option pricing and the asset pricing theory for benchmarked prices in a limiting stationary state are developed.

Suggested Citation

  • Dilip B. Madan, 2016. "Benchmarking in two price financial markets," Annals of Finance, Springer, vol. 12(2), pages 201-219, May.
    • Handle: RePEc:kap:annfin:v:12:y:2016:i:2:d:10.1007_s10436-016-0278-4
    DOI: 10.1007/s10436-016-0278-4
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    References listed on IDEAS

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    1. Jouini Elyes & Kallal Hedi, 1995. "Martingales and Arbitrage in Securities Markets with Transaction Costs," Journal of Economic Theory, Elsevier, vol. 66(1), pages 178-197, June.
    2. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
    3. repec:dau:papers:123456789/9300 is not listed on IDEAS
    4. Bakshi, Gurdip & Madan, Dilip & Panayotov, George, 2010. "Returns of claims on the upside and the viability of U-shaped pricing kernels," Journal of Financial Economics, Elsevier, vol. 97(1), pages 130-154, July.
    5. N. El Karoui & S. Peng & M. C. Quenez, 1997. "Backward Stochastic Differential Equations in Finance," Mathematical Finance, Wiley Blackwell, vol. 7(1), pages 1-71, January.
    6. Przemysław Rola, 2015. "Arbitrage in markets with bid-ask spreads," Annals of Finance, Springer, vol. 11(3), pages 453-475, November.
    7. Ernst Eberlein & Dilip Madan & Martijn Pistorius & Wim Schoutens & Marc Yor, 2014. "Two price economies in continuous time," Annals of Finance, Springer, vol. 10(1), pages 71-100, February.
    8. Cohen, Samuel N. & Elliott, Robert J., 2010. "A general theory of finite state Backward Stochastic Difference Equations," Stochastic Processes and their Applications, Elsevier, vol. 120(4), pages 442-466, April.
    9. Yuri Kabanov, 2009. "Markets with Transaction Costs. Mathematical Theory," Post-Print hal-00488168, HAL.
    10. Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December.
    11. Kabanov, Yu. M. & Stricker, Ch., 2001. "The Harrison-Pliska arbitrage pricing theorem under transaction costs," Journal of Mathematical Economics, Elsevier, vol. 35(2), pages 185-196, April.
    12. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    13. Riedel, Frank, 2004. "Dynamic coherent risk measures," Stochastic Processes and their Applications, Elsevier, vol. 112(2), pages 185-200, August.
    14. repec:dau:papers:123456789/5630 is not listed on IDEAS
    15. Ross, Stephen A, 1978. "A Simple Approach to the Valuation of Risky Streams," The Journal of Business, University of Chicago Press, vol. 51(3), pages 453-475, July.
    16. Dilip Madan, 2015. "Asset pricing theory for two price economies," Annals of Finance, Springer, vol. 11(1), pages 1-35, February.
    17. Jocelyne Bion-Nadal, 2008. "Dynamic risk measures: Time consistency and risk measures from BMO martingales," Finance and Stochastics, Springer, vol. 12(2), pages 219-244, April.
    18. Harrison, J. Michael & Kreps, David M., 1979. "Martingales and arbitrage in multiperiod securities markets," Journal of Economic Theory, Elsevier, vol. 20(3), pages 381-408, June.
    19. Harrison, J. Michael & Pliska, Stanley R., 1981. "Martingales and stochastic integrals in the theory of continuous trading," Stochastic Processes and their Applications, Elsevier, vol. 11(3), pages 215-260, August.
    20. Fabio Mercurio, 2010. "Modern Libor Market Models: Using Different Curves For Projecting Rates And For Discounting," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 13(01), pages 113-137.
    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.
    22. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
    23. Paolo Guasoni & Emmanuel Lépinette & Miklós Rásonyi, 2012. "The fundamental theorem of asset pricing under transaction costs," Finance and Stochastics, Springer, vol. 16(4), pages 741-777, October.
    24. Walter Schachermayer, 2004. "The Fundamental Theorem of Asset Pricing under Proportional Transaction Costs in Finite Discrete Time," Mathematical Finance, Wiley Blackwell, vol. 14(1), pages 19-48, January.
    25. Andrea Pallavicini & Marco Tarenghi, 2010. "Interest-Rate Modeling with Multiple Yield Curves," Papers 1006.4767, arXiv.org.
    26. Dilip B. Madan & Alexander Cherny, 2010. "Markets As A Counterparty: An Introduction To Conic Finance," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 13(08), pages 1149-1177.
    27. Alexander Cherny & Dilip Madan, 2009. "New Measures for Performance Evaluation," The Review of Financial Studies, Society for Financial Studies, vol. 22(7), pages 2371-2406, July.
    28. Bion-Nadal, Jocelyne, 2009. "Bid-ask dynamic pricing in financial markets with transaction costs and liquidity risk," Journal of Mathematical Economics, Elsevier, vol. 45(11), pages 738-750, December.
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    Cited by:

    1. Dilip B. Madan & Wim Schoutens & King Wang, 2017. "Measuring And Monitoring The Efficiency Of Markets," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(08), pages 1-32, December.
    2. Dilip B. Madan, 2018. "Financial equilibrium with non-linear valuations," Annals of Finance, Springer, vol. 14(2), pages 211-221, May.
    3. Dilip B. Madan & Martijn Pistorius & Wim Schoutens, 2017. "Conic Trading In A Markovian Steady State," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(02), pages 1-22, March.

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    More about this item

    Keywords

    Acceptable risks; Nonlinear expectations; Nonadditive probability; Distorted expectation;
    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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