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Variational inequality for perpetual American option price and convergence to the solution of the difference equation

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  • Hyong-chol O
  • Song-San Jo

Abstract

A variational inequality for pricing the perpetual American option and the corresponding difference equation are considered. First, the maximum principle and uniqueness of the solution to variational inequality for pricing the perpetual American option are proved. Then the maximum principle, the existence and uniqueness of the solution to the difference equation corresponding to the variational inequality for pricing the perpetual American option and the solution representation are provided and the fact that the solution to the difference equation converges to the viscosity solution to the variational inequality is proved. It is shown that the limits of the prices of variational inequality and BTM models for American Option when the maturity goes to infinity do not depend on time and they become the prices of the perpetual American option.

Suggested Citation

  • Hyong-chol O & Song-San Jo, 2019. "Variational inequality for perpetual American option price and convergence to the solution of the difference equation," Papers 1903.05189, arXiv.org.
    • Handle: RePEc:arx:papers:1903.05189
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    References listed on IDEAS

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    12. Hyong-chol O & Song-gon Jang & Il-Gwang Jon & Mun-Chol Kim & Gyong-Ryol Kim & Hak-Yong Kim, 2015. "The Binomial Tree Method and Explicit Difference Schemes for American Options with Time Dependent Coefficients," Papers 1505.04573, arXiv.org, revised Aug 2018.
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