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American option valuation under stochastic interest rates

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  • San-Lin Chung

Abstract

By applying Ho, Stapleton and Subrahmanyam's (1997, hereafter HSS) generalised Geske–Johnson (1984, hereafter GJ) method, this paper provides analytic solutions for the valuation and hedging of American options in a stochastic interest rate economy. The proposed method simplifies HSS's three-dimensional solution to a one-dimensional solution. The simulations verify that the proposed method is more efficient and accurate than the HSS (1997) method. We illustrate how the price, the delta, and the rho of an American option vary between the stochastic and non-stochastic interest rate models. The magnitude of this effect depends on the moneyness of the option, interest rates, volatilities of the underlying asset price and the bond price, as well as the correlation between them. Copyright Kluwer Academic Publishers 2000

Suggested Citation

  • San-Lin Chung, 2000. "American option valuation under stochastic interest rates," Review of Derivatives Research, Springer, vol. 3(3), pages 283-307, October.
    • Handle: RePEc:kap:revdev:v:3:y:2000:i:3:p:283-307
    DOI: 10.1023/A:1009694721959
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    References listed on IDEAS

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    1. Ho, Thomas S Y & Lee, Sang-bin, 1986. "Term Structure Movements and Pricing Interest Rate Contingent Claims," Journal of Finance, American Finance Association, vol. 41(5), pages 1011-1029, December.
    2. Bunch, David S & Johnson, Herb, 1992. "A Simple and Numerically Efficient Valuation Method for American Puts Using a Modified Geske-Johnson Approach," Journal of Finance, American Finance Association, vol. 47(2), pages 809-816, June.
    3. Hull, John & White, Alan, 1990. "Pricing Interest-Rate-Derivative Securities," The Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 573-592.
    4. Rabinovitch, Ramon, 1989. "Pricing Stock and Bond Options when the Default-Free Rate is Stochastic," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 24(4), pages 447-457, December.
    5. Farshid Jamshidian, 1993. "Option and Futures Evaluation With Deterministic Volatilities1," Mathematical Finance, Wiley Blackwell, vol. 3(2), pages 149-159, April.
    6. Jamshidian, Farshid, 1989. " An Exact Bond Option Formula," Journal of Finance, American Finance Association, vol. 44(1), pages 205-209, March.
    7. Stephen E. Satchell & Richard C. Stapleton & Marti G. Subrahmanyam, 1997. "The Pricing of Marked-to-Market Contingent Claims in a No-Arbitrage Economy," New York University, Leonard N. Stern School Finance Department Working Paper Seires 96-37, New York University, Leonard N. Stern School of Business-.
    8. Ho, Teng-Suan & Stapleton, Richard C & Subrahmanyam, Marti G, 1995. "Multivariate Binomial Approximations for Asset Prices with Nonstationary Variance and Covariance Characteristics," The Review of Financial Studies, Society for Financial Studies, vol. 8(4), pages 1125-1152.
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    Cited by:

    1. Cheng Cai & Tiziano De Angelis & Jan Palczewski, 2021. "The American put with finite-time maturity and stochastic interest rate," Papers 2104.08502, arXiv.org, revised Feb 2024.
    2. Minqiang Li, 2010. "A quasi-analytical interpolation method for pricing American options under general multi-dimensional diffusion processes," Review of Derivatives Research, Springer, vol. 13(2), pages 177-217, July.
    3. Cheng Cai & Tiziano De Angelis & Jan Palczewski, 2022. "The American put with finite‐time maturity and stochastic interest rate," Mathematical Finance, Wiley Blackwell, vol. 32(4), pages 1170-1213, October.

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