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Option pricing in an imperfect world

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  • 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 from which it is possible, as in the original work of Breeden and Litzenberger, to extract the implied probability. Eventually we test this conclusion empirically via a new non parametric approach.

Suggested Citation

  • Gianluca Cassese, 2014. "Option pricing in an imperfect world," Working Papers 277, University of Milano-Bicocca, Department of Economics, revised Jun 2014.
    • Handle: RePEc:mib:wpaper:277
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    1. P. Gagliardini & C. Gourieroux & E. Renault, 2011. "Efficient Derivative Pricing by the Extended Method of Moments," Econometrica, Econometric Society, vol. 79(4), pages 1181-1232, July.
    2. Napp, C., 2003. "The Dalang-Morton-Willinger theorem under cone constraints," Journal of Mathematical Economics, Elsevier, vol. 39(1-2), pages 111-126, February.
    3. Pedro Bordalo & Nicola Gennaioli & Andrei Shleifer, 2013. "Salience and Asset Prices," American Economic Review, American Economic Association, vol. 103(3), pages 623-628, May.
    4. Hugonnier, Julien, 2012. "Rational asset pricing bubbles and portfolio constraints," Journal of Economic Theory, Elsevier, vol. 147(6), pages 2260-2302.
    5. Ait-Sahalia, Yacine & Duarte, Jefferson, 2003. "Nonparametric option pricing under shape restrictions," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 9-47.
    6. Jackwerth, Jens Carsten & Rubinstein, Mark, 1996. "Recovering Probability Distributions from Option Prices," Journal of Finance, American Finance Association, vol. 51(5), pages 1611-1632, December.
    7. Dermody, Jaime Cuevas & Prisman, Eliezer Z., 1993. "No Arbitrage and Valuation in Markets with Realistic Transaction Costs," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 28(1), pages 65-80, March.
    8. Huang, Roger D & Stoll, Hans R, 1997. "The Components of the Bid-Ask Spread: A General Approach," The Review of Financial Studies, Society for Financial Studies, vol. 10(4), pages 995-1034.
    9. Harold Demsetz, 1968. "The Cost of Transacting," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 82(1), pages 33-53.
    10. 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.
    11. repec:dau:papers:123456789/5630 is not listed on IDEAS
    12. Hahn, F H, 1971. "Equilibrium with Transaction Costs," Econometrica, Econometric Society, vol. 39(3), pages 417-439, May.
    13. 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.
    14. 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.
    15. G.M. Constantinides & M. Harris & R. M. Stulz (ed.), 2003. "Handbook of the Economics of Finance," Handbook of the Economics of Finance, Elsevier, edition 1, volume 1, number 2, March.
    16. Heckman, James, 2013. "Sample selection bias as a specification error," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 31(3), pages 129-137.
    17. Gianluca Cassese, 2008. "Asset Pricing With No Exogenous Probability Measure," Mathematical Finance, Wiley Blackwell, vol. 18(1), pages 23-54, January.
    18. 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.
    19. Damir Filipović, 2008. "Optimal Numeraires For Risk Measures," Mathematical Finance, Wiley Blackwell, vol. 18(2), pages 333-336, April.
    20. Frank Riedel, 2011. "Finance Without Probabilistic Prior Assumptions," Papers 1107.1078, arXiv.org.
    21. Hansen, Lars Peter & Jagannathan, Ravi, 1991. "Implications of Security Market Data for Models of Dynamic Economies," Journal of Political Economy, University of Chicago Press, vol. 99(2), pages 225-262, April.
    22. 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.
    23. repec:crs:wpaper:9513 is not listed on IDEAS
    24. 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.
    25. 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.
    26. H. Yin & Y. Wang & L. Qi, 2009. "Shape-Preserving Interpolation and Smoothing for Options Market Implied Volatility," Journal of Optimization Theory and Applications, Springer, vol. 142(1), pages 243-266, July.
    27. Hasbrouck, Joel, 2002. "Stalking the "efficient price" in market microstructure specifications: an overview," Journal of Financial Markets, Elsevier, vol. 5(3), pages 329-339, July.
    28. repec:dau:papers:123456789/1850 is not listed on IDEAS
    29. 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.
    30. Daniel Kahneman & Amos Tversky, 2013. "Prospect Theory: An Analysis of Decision Under Risk," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 6, pages 99-127, World Scientific Publishing Co. Pte. Ltd..
    31. Bollen, Nicolas P. B. & Smith, Tom & Whaley, Robert E., 2004. "Modeling the bid/ask spread: measuring the inventory-holding premium," Journal of Financial Economics, Elsevier, vol. 72(1), pages 97-141, April.
    32. 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.
    33. Amihud, Yakov & Mendelson, Haim, 1986. "Asset pricing and the bid-ask spread," Journal of Financial Economics, Elsevier, vol. 17(2), pages 223-249, December.
    34. 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.
    35. G.M. Constantinides & M. Harris & R. M. Stulz (ed.), 2003. "Handbook of the Economics of Finance," Handbook of the Economics of Finance, Elsevier, edition 1, volume 1, number 1, March.
    36. E. Mammen & C. Thomas‐Agnan, 1999. "Smoothing Splines and Shape Restrictions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 26(2), pages 239-252, June.
    37. 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.
    38. 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.
    39. 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.
    40. Carr, Peter & Madan, Dilip B., 2005. "A note on sufficient conditions for no arbitrage," Finance Research Letters, Elsevier, vol. 2(3), pages 125-130, September.
    41. 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.
    42. Luttmer, Erzo G J, 1996. "Asset Pricing in Economies with Frictions," Econometrica, Econometric Society, vol. 64(6), pages 1439-1467, November.
    43. 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.
    44. Adonis Yatchew, 1998. "Nonparametric Regression Techniques in Economics," Journal of Economic Literature, American Economic Association, vol. 36(2), pages 669-721, June.
    45. repec:bla:jfinan:v:53:y:1998:i:2:p:499-547 is not listed on IDEAS
    46. 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.
    47. repec:dau:papers:123456789/1392 is not listed on IDEAS
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    More about this item

    Keywords

    Arbitrage; Bid/Ask spreads; Bubbles; Coherence; Risk-neutral probability; Transaction costs.;
    All these keywords.

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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