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The Binomial Tree Method and Explicit Difference Schemes for American Options with Time Dependent Coefficients

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  • Hyong-chol O
  • Song-gon Jang
  • Il-Gwang Jon
  • Mun-Chol Kim
  • Gyong-Ryol Kim
  • Hak-Yong Kim

Abstract

Binomial tree methods (BTM) and explicit difference schemes (EDS) for the variational inequality model of American options with time dependent coefficients are studied. When volatility is time dependent, it is not reasonable to assume that the dynamics of the underlying asset's price forms a binomial tree if a partition of time interval with equal parts is used. A time interval partition method that allows binomial tree dynamics of the underlying asset's price is provided. Conditions under which the prices of American option by BTM and EDS have the monotonic property on time variable are found. Using convergence of EDS for variational inequality model of American options to viscosity solution the decreasing property of the price of American put options and increasing property of the optimal exercise boundary on time variable are proved. First, put options are considered. Then the linear homogeneity and call-put symmetry of the price functions in the BTM and the EDS for the variational inequality model of American options with time dependent coefficients are studied and using them call options are studied.

Suggested Citation

  • 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.
    • Handle: RePEc:arx:papers:1505.04573
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    References listed on IDEAS

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    1. Hyong-Chol O & Yong-Gon Kim & Dong-Hyok Kim, 2013. "Higher Order Binaries with Time Dependent Coefficients and Two Factors - Model for Defaultable Bond with Discrete Default Information," Papers 1305.6868, arXiv.org, revised Jun 2013.
    2. Amin, Kaushik I, 1993. "Jump Diffusion Option Valuation in Discrete Time," Journal of Finance, American Finance Association, vol. 48(5), pages 1833-1863, December.
    3. He, Hua, 1990. "Convergence from Discrete- to Continuous-Time Contingent Claims Prices," The Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 523-546.
    4. Xiao Lan Zhang, 1997. "Numerical Analysis of American Option Pricing in a Jump-Diffusion Model," Mathematics of Operations Research, INFORMS, vol. 22(3), pages 668-690, August.
    5. Cox, John C. & Ross, Stephen A. & Rubinstein, Mark, 1979. "Option pricing: A simplified approach," Journal of Financial Economics, Elsevier, vol. 7(3), pages 229-263, September.
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    Cited by:

    1. 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.

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