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Indifference Pricing and Hedging in a Multiple-Priors Model with Trading Constraints

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  • Huiwen Yan
  • Gechun Liang
  • Zhou Yang

Abstract

This paper considers utility indifference valuation of derivatives under model uncertainty and trading constraints, where the utility is formulated as an additive stochastic differential utility of both intertemporal consumption and terminal wealth, and the uncertain prospects are ranked according to a multiple-priors model of Chen and Epstein (2002). The price is determined by two optimal stochastic control problems (mixed with optimal stopping time in the case of American option) of forward-backward stochastic differential equations. By means of backward stochastic differential equation and partial differential equation methods, we show that both bid and ask prices are closely related to the Black-Scholes risk-neutral price with modified dividend rates. The two prices will actually coincide with each other if there is no trading constraint or the model uncertainty disappears. Finally, two applications to European option and American option are discussed.

Suggested Citation

  • Huiwen Yan & Gechun Liang & Zhou Yang, 2015. "Indifference Pricing and Hedging in a Multiple-Priors Model with Trading Constraints," Papers 1503.08969, arXiv.org.
    • Handle: RePEc:arx:papers:1503.08969
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    References listed on IDEAS

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    1. 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.
    2. Duffie, Darrell & Epstein, Larry G, 1992. "Stochastic Differential Utility," Econometrica, Econometric Society, vol. 60(2), pages 353-394, March.
    3. Vicky Henderson, 2002. "Valuation Of Claims On Nontraded Assets Using Utility Maximization," Mathematical Finance, Wiley Blackwell, vol. 12(4), pages 351-373, October.
    4. Ying Hu & Peter Imkeller & Matthias Muller, 2005. "Utility maximization in incomplete markets," Papers math/0508448, arXiv.org.
    5. Zengjing Chen & Larry Epstein, 2002. "Ambiguity, Risk, and Asset Returns in Continuous Time," Econometrica, Econometric Society, vol. 70(4), pages 1403-1443, July.
    6. 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.
    7. Duffie, Darrel & Lions, Pierre-Louis, 1992. "PDE solutions of stochastic differential utility," Journal of Mathematical Economics, Elsevier, vol. 21(6), pages 577-606.
    8. Rama Cont, 2006. "Model Uncertainty And Its Impact On The Pricing Of Derivative Instruments," Mathematical Finance, Wiley Blackwell, vol. 16(3), pages 519-547, July.
    9. Marek Musiela & Thaleia Zariphopoulou, 2004. "An example of indifference prices under exponential preferences," Finance and Stochastics, Springer, vol. 8(2), pages 229-239, May.
    10. Duffie, Darrell & Epstein, Larry G, 1992. "Asset Pricing with Stochastic Differential Utility," The Review of Financial Studies, Society for Financial Studies, vol. 5(3), pages 411-436.
    11. Rama Cont, 2006. "Model uncertainty and its impact on the pricing of derivative instruments," Post-Print halshs-00002695, HAL.
    12. Michael Mania & Martin Schweizer, 2005. "Dynamic exponential utility indifference valuation," Papers math/0508489, arXiv.org.
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    Cited by:

    1. Gechun Liang & Zhou Yang, 2018. "Analysis of the optimal exercise boundary of American put options with delivery lags," Papers 1805.02909, arXiv.org, revised Dec 2020.
    2. Ling Wang & Kexin Chen & Mei Choi Chiu & Hoi Ying Wong, 2021. "Optimal Expansion of Business Opportunity," Papers 2112.06706, arXiv.org.
    3. Guohui Guan & Qitao Huang & Zongxia Liang & Fengyi Yuan, 2020. "Retirement decision with addictive habit persistence in a jump diffusion market," Papers 2011.10166, arXiv.org, revised Feb 2024.
    4. Zhou Yang & Hyeng Keun Koo, 2018. "Optimal Consumption and Portfolio Selection with Early Retirement Option," Mathematics of Operations Research, INFORMS, vol. 43(4), pages 1378-1404, November.
    5. Zixin Feng & Dejian Tian, 2021. "Optimal consumption and portfolio selection with Epstein-Zin utility under general constraints," Papers 2111.09032, arXiv.org, revised May 2023.
    6. Wang, Ling & Chen, Kexin & Chiu, Mei Choi & Wong, Hoi Ying, 2023. "Optimal expansion of business opportunity," European Journal of Operational Research, Elsevier, vol. 309(1), pages 432-445.
    7. Rohini Kumar & Frederick Forrest Miller & Hussein Nasralah & Stephan Sturm, 2024. "Risk-indifference Pricing of American-style Contingent Claims," Papers 2409.00095, arXiv.org.
    8. Zhou Yang & Gechun Liang & Chao Zhou, 2017. "Constrained portfolio-consumption strategies with uncertain parameters and borrowing costs," Papers 1711.02939, arXiv.org, revised Dec 2018.

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