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A Note On Utility Indifference Pricing

Author

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  • JOHANNES GERER

    (University of Regensburg, Department of Finance, 93040 Regensburg, Germany)

  • GREGOR DORFLEITNER

    (University of Regensburg, Department of Finance, 93040 Regensburg, Germany)

Abstract

Utility-based valuation methods are enjoying growing popularity among researchers as a means to overcome the challenges in contingent claim pricing posed by the many sources of market incompleteness. However, we show that under the most common utility functions (including CARA and CRRA), any realistic and actually practicable hedging strategy involving a possible short position has infinitely negative utility. We then demonstrate for utility indifference prices (and also for the related so-called utility-based (marginal) prices) how this problem leads to a severe divergence between results obtained under the assumption of continuous trading and realistic results. The combination of continuous trading and common utility functions is thus not justified in these methods, raising the question of whether and how results obtained under such assumptions could be put to real-world use.

Suggested Citation

  • Johannes Gerer & Gregor Dorfleitner, 2016. "A Note On Utility Indifference Pricing," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(06), pages 1-17, September.
    • Handle: RePEc:wsi:ijtafx:v:19:y:2016:i:06:n:s0219024916500370
    DOI: 10.1142/S0219024916500370
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    References listed on IDEAS

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    1. Aytaç İlhan & Ronnie Sircar, 2006. "Optimal Static–Dynamic Hedges For Barrier Options," Mathematical Finance, Wiley Blackwell, vol. 16(2), pages 359-385, April.
    2. Svensson, Lars E. O. & Werner, Ingrid M., 1993. "Nontraded assets in incomplete markets : Pricing and portfolio choice," European Economic Review, Elsevier, vol. 37(5), pages 1149-1168, June.
    3. Benjamin Mohamed, 1994. "Simulations of transaction costs and optimal rehedging," Applied Mathematical Finance, Taylor & Francis Journals, vol. 1(1), pages 49-62.
    4. Merton, Robert C., 1971. "Optimum consumption and portfolio rules in a continuous-time model," Journal of Economic Theory, Elsevier, vol. 3(4), pages 373-413, December.
    5. (*), Thaleia Zariphopoulou & George M. Constantinides, 1999. "Bounds on prices of contingent claims in an intertemporal economy with proportional transaction costs and general preferences," Finance and Stochastics, Springer, vol. 3(3), pages 345-369.
    6. Becherer, Dirk, 2003. "Rational hedging and valuation of integrated risks under constant absolute risk aversion," Insurance: Mathematics and Economics, Elsevier, vol. 33(1), pages 1-28, August.
    7. Sara Biagini & Marco Frittelli, 2005. "Utility maximization in incomplete markets for unbounded processes," Finance and Stochastics, Springer, vol. 9(4), pages 493-517, October.
    8. L. Rogers & José Scheinkman, 2007. "Optimal exercise of executive stock options," Finance and Stochastics, Springer, vol. 11(3), pages 357-372, July.
    9. Julien Hugonnier & Dmitry Kramkov, 2004. "Optimal investment with random endowments in incomplete markets," Papers math/0405293, arXiv.org.
    10. Mark P. Owen & Gordan Žitković, 2009. "Optimal Investment With An Unbounded Random Endowment And Utility‐Based Pricing," Mathematical Finance, Wiley Blackwell, vol. 19(1), pages 129-159, January.
    11. Freddy Delbaen & Peter Grandits & Thorsten Rheinländer & Dominick Samperi & Martin Schweizer & Christophe Stricker, 2002. "Exponential Hedging and Entropic Penalties," Mathematical Finance, Wiley Blackwell, vol. 12(2), pages 99-123, April.
    12. Grasselli, Matheus & Henderson, Vicky, 2009. "Risk aversion and block exercise of executive stock options," Journal of Economic Dynamics and Control, Elsevier, vol. 33(1), pages 109-127, January.
    13. Vicky Henderson, 2002. "Valuation Of Claims On Nontraded Assets Using Utility Maximization," Mathematical Finance, Wiley Blackwell, vol. 12(4), pages 351-373, October.
    14. Sethi, Suresh P. & Taksar, Michael, 1988. "A note on Merton's "Optimum Consumption and Portfolio Rules in a continuous-Time Model"," Journal of Economic Theory, Elsevier, vol. 46(2), pages 395-401, December.
    15. Julien Hugonnier & Dmitry Kramkov & Walter Schachermayer, 2005. "On Utility‐Based Pricing Of Contingent Claims In Incomplete Markets," Mathematical Finance, Wiley Blackwell, vol. 15(2), pages 203-212, April.
    16. Jan Kallsen & Christoph Kühn, 2004. "Pricing derivatives of American and game type in incomplete markets," Finance and Stochastics, Springer, vol. 8(2), pages 261-284, May.
    17. Tim Leung & Ronnie Sircar, 2009. "Accounting For Risk Aversion, Vesting, Job Termination Risk And Multiple Exercises In Valuation Of Employee Stock Options," Mathematical Finance, Wiley Blackwell, vol. 19(1), pages 99-128, January.
    18. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    19. Halil Mete Soner & Guy Barles, 1998. "Option pricing with transaction costs and a nonlinear Black-Scholes equation," Finance and Stochastics, Springer, vol. 2(4), pages 369-397.
    20. Merton, Robert C, 1969. "Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case," The Review of Economics and Statistics, MIT Press, vol. 51(3), pages 247-257, August.
    21. Vicky Henderson, 2005. "The impact of the market portfolio on the valuation, incentives and optimality of executive stock options," Quantitative Finance, Taylor & Francis Journals, vol. 5(1), pages 35-47.
    22. Ying Hu & Peter Imkeller & Matthias Muller, 2005. "Utility maximization in incomplete markets," Papers math/0508448, arXiv.org.
    23. M. R. Grasselli & T. R. Hurd, 2007. "Indifference Pricing and Hedging for Volatility Derivatives," Applied Mathematical Finance, Taylor & Francis Journals, vol. 14(4), pages 303-317.
    24. Duffie, Darrell & Fleming, Wendell & Soner, H. Mete & Zariphopoulou, Thaleia, 1997. "Hedging in incomplete markets with HARA utility," Journal of Economic Dynamics and Control, Elsevier, vol. 21(4-5), pages 753-782, May.
    25. Michael Mania & Martin Schweizer, 2005. "Dynamic exponential utility indifference valuation," Papers math/0508489, arXiv.org.
    26. Yuri M. Kabanov & Christophe Stricker, 2002. "On the optimal portfolio for the exponential utility maximization: remarks to the six‐author paper," Mathematical Finance, Wiley Blackwell, vol. 12(2), pages 125-134, April.
    27. Aytaç Ílhan & Mattias Jonsson & Ronnie Sircar, 2005. "Optimal investment with derivative securities," Finance and Stochastics, Springer, vol. 9(4), pages 585-595, October.
    28. Richard Rouge & Nicole El Karoui, 2000. "Pricing Via Utility Maximization and Entropy," Mathematical Finance, Wiley Blackwell, vol. 10(2), pages 259-276, April.
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    Cited by:

    1. Alet Roux & Zhikang Xu, 2019. "Optimal investment and contingent claim valuation with exponential disutility under proportional transaction costs," Papers 1909.06260, arXiv.org, revised May 2021.

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