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An example of indifference prices under exponential preferences

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  • Marek Musiela

    ()

  • Thaleia Zariphopoulou

    ()

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    Abstract

    The aim herein is to analyze utility-based prices and hedging strategies. The analysis is based on an explicitly solved example of a European claim written on a nontraded asset, in a model where risk preferences are exponential, and the traded and nontraded asset are diffusion processes with, respectively, lognormal and arbitrary dynamics. Our results show that a nonlinear pricing rule emerges with certainty equivalent characteristics, yielding the price as a nonlinear expectation of the derivative’s payoff under the appropriate pricing measure. The latter is a martingale measure that minimizes its relative to the historical measure entropy. Copyright Springer-Verlag Berlin/Heidelberg 2004

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    Bibliographic Info

    Article provided by Springer in its journal Finance and Stochastics.

    Volume (Year): 8 (2004)
    Issue (Month): 2 (05)
    Pages: 229-239

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    Handle: RePEc:spr:finsto:v:8:y:2004:i:2:p:229-239

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    Related research

    Keywords: Incomplete markets; indifference prices; nonlinear asset pricing;

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    Cited by:
    1. Xu, Wei & Odening, Martin & Musshoff, Oliver, 2007. "Indifference Pricing of Weather Insurance," 101st Seminar, July 5-6, 2007, Berlin Germany 9267, European Association of Agricultural Economists.
    2. Ilhan, Aytaç & Jonsson, Mattias & Sircar, Ronnie, 2009. "Optimal static-dynamic hedges for exotic options under convex risk measures," Stochastic Processes and their Applications, Elsevier, vol. 119(10), pages 3608-3632, October.
    3. Michael Mania & Marina Santacroce, 2010. "Exponential utility maximization under partial information," Finance and Stochastics, Springer, vol. 14(3), pages 419-448, September.
    4. Erhan Bayraktar & Virginia R. Young, 2007. "Pricing Options in Incomplete Equity Markets via the Instantaneous Sharpe Ratio," Papers math/0701650, arXiv.org, revised Jul 2007.
    5. Antoon Pelsser, 2011. "Time-Consistent Actuarial Valuations," Papers 1109.1751, arXiv.org.
    6. Michael Mania & Marina Santacroce, 2008. "Exponential Utility Maximization under Partial Information," ICER Working Papers - Applied Mathematics Series 24-2008, ICER - International Centre for Economic Research.
    7. Gang-Zhi Fan & Ming Pu & Seow Ong, 2012. "Optimal Portfolio Choices, House Risk Hedging and the Pricing of Forward House Transactions," The Journal of Real Estate Finance and Economics, Springer, vol. 45(1), pages 3-29, June.
    8. Chen, Mi & Peng, Xiaofan & Guo, Junyi, 2013. "Optimal dividend problem with a nonlinear regular-singular stochastic control," Insurance: Mathematics and Economics, Elsevier, vol. 52(3), pages 448-456.
    9. Schwartz, Eduardo S & Tebaldi, Claudio, 2004. "Illiquid Assets and Optimal Portfolio Choice," University of California at Los Angeles, Anderson Graduate School of Management qt7q65t12x, Anderson Graduate School of Management, UCLA.
    10. Claudia Ceci & Anna Gerardi, 2011. "Utility indifference valuation for jump risky assets," Decisions in Economics and Finance, Springer, vol. 34(2), pages 85-120, November.
    11. Mingxin Xu, 2006. "Risk measure pricing and hedging in incomplete markets," Annals of Finance, Springer, vol. 2(1), pages 51-71, January.
    12. Vicky Henderson & Gechun Liang, 2014. "Pseudo Linear Pricing Rule for Utility Indifference Valuation," Papers 1403.7830, arXiv.org.
    13. Akuzawa, Toshinao & Nishiyama, Yoshihiko, 2013. "Implied Sharpe ratios of portfolios with options: Application to Nikkei futures and listed options," The North American Journal of Economics and Finance, Elsevier, vol. 25(C), pages 335-357.
    14. Stadje, M.A. & Pelsser, A., 2014. "Time-Consistent and Market-Consistent Evaluations (Revised version of 2012-086)," Discussion Paper 2014-002, Tilburg University, Center for Economic Research.
    15. Michail Anthropelos & Nikolaos E. Frangos & Stylianos Z. Xanthopoulos & Athanasios N. Yannacopoulos, 2008. "On contingent claims pricing in incomplete markets: A risk sharing approach," Papers 0809.4781, arXiv.org, revised Feb 2012.
    16. David German, 2010. "Overview of utility-based valuation," Papers 1003.5712, arXiv.org.
    17. Srdjan Stojanovic, 2006. "Pricing and Hedging of Multi Type Contracts under Multidimensional Risks in Incomplete Markets Modeled by General Itô SDE Systems," Asia-Pacific Financial Markets, Springer, vol. 13(4), pages 345-372, December.
    18. Pelsser, A. & Stadje, M.A., 2012. "Time-Consistent and Market-Consistent Evaluations (Revised version of CentER DP 2011-063)," Discussion Paper 2012-086, Tilburg University, Center for Economic Research.
    19. Pauline Barrieu & Nicole El Karoui, 2005. "Inf-convolution of risk measures and optimal risk transfer," LSE Research Online Documents on Economics 2829, London School of Economics and Political Science, LSE Library.

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