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Indifference Pricing of American Option Underlying Illiquid Stock under Exponential Forward Performance

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  • Xiaoshan Chen
  • Qingshuo Song
  • Fahuai Yi
  • George Yin

Abstract

This work focuses on the indifference pricing of American call option underlying a non-traded stock, which may be partially hedgeable by another traded stock. Under the exponential forward measure, the indifference price is formulated as a stochastic singular control problem. The value function is characterized as the unique solution of a partial differential equation in a Sobolev space. Together with some regularities and estimates of the value function, the existence of the optimal strategy is also obtained. The applications of the characterization result includes a derivation of a dual representation and the indifference pricing on employee stock option. As a byproduct, a generalized Ito's formula is obtained for functions in a Sobolev space.

Suggested Citation

  • Xiaoshan Chen & Qingshuo Song & Fahuai Yi & George Yin, 2011. "Indifference Pricing of American Option Underlying Illiquid Stock under Exponential Forward Performance," Papers 1201.0075, arXiv.org.
  • Handle: RePEc:arx:papers:1201.0075
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    References listed on IDEAS

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    1. A. Oberman & T. Zariphopoulou, 2003. "Pricing early exercise contracts in incomplete markets," Computational Management Science, Springer, vol. 1(1), pages 75-107, December.
    2. M. Musiela & T. Zariphopoulou, 2009. "Portfolio choice under dynamic investment performance criteria," Quantitative Finance, Taylor & Francis Journals, vol. 9(2), pages 161-170.
    3. 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.
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