IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1410.6408.html
   My bibliography  Save this paper

Asset Pricing in an Imperfect World

Author

Listed:
  • Gianluca Cassese

Abstract

In a model with no given probability measure, we consider asset pricing in the presence of frictions and other imperfections and characterize the property of coherent pricing, a notion related to (but much weaker than) the no arbitrage property. We show that prices are coherent if and only if the set of pricing measures is non empty, i.e. if pricing by expectation is possible. We then obtain a decomposition of coherent prices highlighting the role of bubbles. Eventually we show that under very weak conditions the coherent pricing of options allows for a very clear representation which allows, as in Breeden and Litzenberger, to extract the implied probability.

Suggested Citation

  • Gianluca Cassese, 2014. "Asset Pricing in an Imperfect World," Papers 1410.6408, arXiv.org.
    • Handle: RePEc:arx:papers:1410.6408
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1410.6408
    File Function: Latest version
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Napp, C., 2003. "The Dalang-Morton-Willinger theorem under cone constraints," Journal of Mathematical Economics, Elsevier, vol. 39(1-2), pages 111-126, February.
    2. 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.
    3. Jean-Luc Vila & Dimitri Vayanos, 1999. "Equilibrium interest rate and liquidity premium with transaction costs," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 13(3), pages 509-539.
    4. Christian Gilles & Stephen F. LeRoy, 1997. "Bubbles as payoffs at infinity (*)," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 9(2), pages 261-281.
    5. Gianluca Cassese, 2015. "Nonparametric Estimates of Option Prices Using Superhedging," Working Papers 293, University of Milano-Bicocca, Department of Economics, revised Feb 2015.
    6. De Long, J Bradford & Andrei Shleifer & Lawrence H. Summers & Robert J. Waldmann, 1990. "Noise Trader Risk in Financial Markets," Journal of Political Economy, University of Chicago Press, vol. 98(4), pages 703-738, August.
    7. Hugonnier, Julien, 2012. "Rational asset pricing bubbles and portfolio constraints," Journal of Economic Theory, Elsevier, vol. 147(6), pages 2260-2302.
    8. Elyès Jouini, 2001. "Arbitrage and investment opportunities," Finance and Stochastics, Springer, vol. 5(3), pages 305-325.
    9. Amihud, Yakov & Mendelson, Haim, 1986. "Asset pricing and the bid-ask spread," Journal of Financial Economics, Elsevier, vol. 17(2), pages 223-249, December.
    10. A. Chateauneuf & R. Kast & A. Lapied, 1996. "Choquet Pricing For Financial Markets With Frictions1," Mathematical Finance, Wiley Blackwell, vol. 6(3), pages 323-330, July.
    11. Owen A. Lamont & Richard H. Thaler, 2003. "Can the Market Add and Subtract? Mispricing in Tech Stock Carve-outs," Journal of Political Economy, University of Chicago Press, vol. 111(2), pages 227-268, April.
    12. repec:dau:papers:123456789/5630 is not listed on IDEAS
    13. Itzhak Gilboa & Fabio Maccheroni & Massimo Marinacci & David Schmeidler, 2010. "Objective and Subjective Rationality in a Multiple Prior Model," Econometrica, Econometric Society, vol. 78(2), pages 755-770, March.
    14. Vladimir Vovk, 2012. "Continuous-time trading and the emergence of probability," Finance and Stochastics, Springer, vol. 16(4), pages 561-609, October.
    15. Breeden, Douglas T & Litzenberger, Robert H, 1978. "Prices of State-contingent Claims Implicit in Option Prices," The Journal of Business, University of Chicago Press, vol. 51(4), pages 621-651, October.
    16. Bernard Bensaid & Jean‐Philippe Lesne & Henri Pagès & José Scheinkman, 1992. "Derivative Asset Pricing With Transaction Costs1," Mathematical Finance, Wiley Blackwell, vol. 2(2), pages 63-86, April.
    17. Gilles, Christian & LeRoy, Stephen F, 1992. "Bubbles and Charges," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 33(2), pages 323-339, May.
    18. Cerreia-Vioglio, S. & Maccheroni, F. & Marinacci, M., 2015. "Put–Call Parity and market frictions," Journal of Economic Theory, Elsevier, vol. 157(C), pages 730-762.
    19. Bruno Bouchard, 2006. "No-arbitrage in Discrete-time Markets with Proportional Transaction Costs and General Information structure," Finance and Stochastics, Springer, vol. 10(2), pages 276-297, April.
    20. Brown, Donald J & Ross, Stephen A, 1991. "Spanning, Valuation and Options," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 1(1), pages 3-12, January.
    21. Bruno Bouchard, 2006. "No-arbitrage in Discrete-time Markets with Proportional Transaction Costs and General Information structure," Finance and Stochastics, Springer, vol. 10(2), pages 276-297, April.
    22. Frank Riedel, 2015. "Financial economics without probabilistic prior assumptions," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 38(1), pages 75-91, April.
    23. 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.
    24. Prisman, Eliezer Z, 1986. "Valuation of Risky Assets in Arbitrage Free Economies with Frictions," Journal of Finance, American Finance Association, vol. 41(3), pages 545-557, July.
    25. Lintner, John, 1969. "The Aggregation of Investor's Diverse Judgments and Preferences in Purely Competitive Security Markets," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 4(4), pages 347-400, December.
    26. Gianluca Cassese, 2008. "Asset Pricing With No Exogenous Probability Measure," Mathematical Finance, Wiley Blackwell, vol. 18(1), pages 23-54, January.
    27. Kreps, David M., 1981. "Arbitrage and equilibrium in economies with infinitely many commodities," Journal of Mathematical Economics, Elsevier, vol. 8(1), pages 15-35, March.
    28. Damir Filipović, 2008. "Optimal Numeraires For Risk Measures," Mathematical Finance, Wiley Blackwell, vol. 18(2), pages 333-336, April.
    29. Alexander Cox & David Hobson, 2005. "Local martingales, bubbles and option prices," Finance and Stochastics, Springer, vol. 9(4), pages 477-492, October.
    30. repec:dau:papers:123456789/5591 is not listed on IDEAS
    31. Loewenstein, Mark & Willard, Gregory A., 2000. "Rational Equilibrium Asset-Pricing Bubbles in Continuous Trading Models," Journal of Economic Theory, Elsevier, vol. 91(1), pages 17-58, March.
    32. 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.
    33. Luttmer, Erzo G J, 1996. "Asset Pricing in Economies with Frictions," Econometrica, Econometric Society, vol. 64(6), pages 1439-1467, November.
    34. Teemu Pennanen, 2011. "Arbitrage and deflators in illiquid markets," Finance and Stochastics, Springer, vol. 15(1), pages 57-83, January.
    35. Shleifer, Andrei & Vishny, Robert W, 1997. "The Limits of Arbitrage," Journal of Finance, American Finance Association, vol. 52(1), pages 35-55, March.
    36. repec:crs:wpaper:9513 is not listed on IDEAS
    37. 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.
    38. Owen A. Lamont & Richard H. Thaler, 2003. "Anomalies: The Law of One Price in Financial Markets," Journal of Economic Perspectives, American Economic Association, vol. 17(4), pages 191-202, Fall.
    39. V. Martins-da-Rocha & Yiannis Vailakis, 2010. "Financial markets with endogenous transaction costs," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 45(1), pages 65-97, October.
    40. repec:dau:papers:123456789/1850 is not listed on IDEAS
    41. Banz, Rolf W & Miller, Merton H, 1978. "Prices for State-contingent Claims: Some Estimates and Applications," The Journal of Business, University of Chicago Press, vol. 51(4), pages 653-672, October.
    42. Roux, Alet, 2011. "The fundamental theorem of asset pricing in the presence of bid-ask and interest rate spreads," Journal of Mathematical Economics, Elsevier, vol. 47(2), pages 159-163, March.
    43. Black, Fischer, 1972. "Capital Market Equilibrium with Restricted Borrowing," The Journal of Business, University of Chicago Press, vol. 45(3), pages 444-455, July.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Gianluca Cassese, 2015. "Nonparametric Estimates of Option Prices Using Superhedging," Working Papers 293, University of Milano-Bicocca, Department of Economics, revised Feb 2015.
    2. Gianluca Cassese, 2021. "Complete and competitive financial markets in a complex world," Finance and Stochastics, Springer, vol. 25(4), pages 659-688, October.
    3. Matteo Burzoni & Frank Riedel & H. Mete Soner, 2021. "Viability and Arbitrage Under Knightian Uncertainty," Econometrica, Econometric Society, vol. 89(3), pages 1207-1234, May.
    4. Lorenzo Bastianello & Alain Chateauneuf & Bernard Cornet, 2022. "Put-Call Parities, absence of arbitrage opportunities and non-linear pricing rules," Papers 2203.16292, arXiv.org.
    5. Gianluca Cassese, 2019. "Nonparametric Estimates Of Option Prices And Related Quantities," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(07), pages 1-29, November.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Gianluca Cassese, 2014. "Option Pricing in an Imperfect World," Papers 1406.0412, arXiv.org, revised Sep 2016.
    2. Lorenzo Bastianello & Alain Chateauneuf & Bernard Cornet, 2022. "Put-Call Parities, absence of arbitrage opportunities and non-linear pricing rules," Papers 2203.16292, arXiv.org.
    3. Alain Chateauneuf & Bernard Cornet, 2022. "Submodular financial markets with frictions," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 73(2), pages 721-744, April.
    4. Cerreia-Vioglio, S. & Maccheroni, F. & Marinacci, M., 2015. "Put–Call Parity and market frictions," Journal of Economic Theory, Elsevier, vol. 157(C), pages 730-762.
    5. Lim, Terence & Lo, Andrew W. & Merton, Robert C. & Scholes, Myron S., 2006. "The Derivatives Sourcebook," Foundations and Trends(R) in Finance, now publishers, vol. 1(5–6), pages 365-572, April.
    6. repec:dau:papers:123456789/5374 is not listed on IDEAS
    7. M. Dempster & I. Evstigneev & M. Taksar, 2006. "Asset Pricing and Hedging in Financial Markets with Transaction Costs: An Approach Based on the Von Neumann–Gale Model," Annals of Finance, Springer, vol. 2(4), pages 327-355, October.
    8. Matteo Burzoni & Frank Riedel & H. Mete Soner, 2021. "Viability and Arbitrage Under Knightian Uncertainty," Econometrica, Econometric Society, vol. 89(3), pages 1207-1234, May.
    9. Emy Lécuyer & Victor Filipe Martins da Rocha, 2022. "Convex Asset Pricing," Working Papers hal-03916844, HAL.
    10. Martin Brown & Tomasz Zastawniak, 2020. "Fundamental Theorem of Asset Pricing under fixed and proportional transaction costs," Annals of Finance, Springer, vol. 16(3), pages 423-433, September.
    11. Aloisio Araujo & Alain Chateauneuf & José Heleno Faro & Bruno Holanda, 2019. "Updating pricing rules," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 68(2), pages 335-361, September.
    12. Araujo, Aloisio & Chateauneuf, Alain & Faro, José Heleno, 2018. "Financial market structures revealed by pricing rules: Efficient complete markets are prevalent," Journal of Economic Theory, Elsevier, vol. 173(C), pages 257-288.
    13. Jouini, Elyes & Kallal, Hedi & Napp, Clotilde, 2001. "Arbitrage and viability in securities markets with fixed trading costs," Journal of Mathematical Economics, Elsevier, vol. 35(2), pages 197-221, April.
    14. Jouini, Elyes, 2001. "Arbitrage and control problems in finance: A presentation," Journal of Mathematical Economics, Elsevier, vol. 35(2), pages 167-183, April.
    15. Napp, Clotilde, 2001. "Pricing issues with investment flows Applications to market models with frictions," Journal of Mathematical Economics, Elsevier, vol. 35(3), pages 383-408, June.
    16. Maria Arduca & Cosimo Munari, 2020. "Fundamental theorem of asset pricing with acceptable risk in markets with frictions," Papers 2012.08351, arXiv.org, revised Apr 2022.
    17. Tomasz R. Bielecki & Igor Cialenco & Rodrigo Rodriguez, 2012. "No-Arbitrage Pricing for Dividend-Paying Securities in Discrete-Time Markets with Transaction Costs," Papers 1205.6254, arXiv.org, revised Jun 2013.
    18. Alet Roux, 2007. "The fundamental theorem of asset pricing under proportional transaction costs," Papers 0710.2758, arXiv.org.
    19. Robert A. Jarrow, 2015. "Asset Price Bubbles," Annual Review of Financial Economics, Annual Reviews, vol. 7(1), pages 201-218, December.
    20. John Y. Campbell, 2000. "Asset Pricing at the Millennium," Journal of Finance, American Finance Association, vol. 55(4), pages 1515-1567, August.
    21. Maria Arduca & Cosimo Munari, 2023. "Fundamental theorem of asset pricing with acceptable risk in markets with frictions," Finance and Stochastics, Springer, vol. 27(3), pages 831-862, July.

    More about this item

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:1410.6408. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.