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The Valuation of American Options with Stochastic Interest Rates: A Generalization of the Geske-Johnson Technique

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  • Ho, T S
  • Stapleton, Richard C
  • Subrahmanyam, Marti G

Abstract

The Geske-Johnson approach provides an efficient and intuitively appealing technique for the valuation and hedging of American-style contingent claims. Here, the authors generalize their approach to a stochastic interest rate economy. The method is implemented using options exercisable on one of a finite number of dates. The authors illustrate how the value of an American-style option increases with interest rate volatility. The magnitude of this effect depends on the extent to which the option is in the money, the volatilities of the underlying asset and the interest rates, as well as the correlation between them. Copyright 1997 by American Finance Association.

Suggested Citation

  • Ho, T S & Stapleton, Richard C & Subrahmanyam, Marti G, 1997. "The Valuation of American Options with Stochastic Interest Rates: A Generalization of the Geske-Johnson Technique," Journal of Finance, American Finance Association, vol. 52(2), pages 827-840, June.
    • Handle: RePEc:bla:jfinan:v:52:y:1997:i:2:p:827-40
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    Cited by:

    1. Jr-Wei Huang & Sharon S. Yang & Chuang-Chang Chang, 2021. "Modeling Housing Price Dynamics and their Impact on the Cost of no-Negative-Equity-Guarantees for Equity Releasing Products," The Journal of Real Estate Finance and Economics, Springer, vol. 63(2), pages 249-279, August.
    2. Luca Barzanti & Corrado Corradi & Martina Nardon, 2006. "On the efficient application of the repeated Richardson extrapolation technique to option pricing," Working Papers 147, Department of Applied Mathematics, Università Ca' Foscari Venezia.
    3. Chang, Chuang-Chang & Tsay, Min-Hung & Lin, Jun-Biao, 2018. "A generalized Brennan–Rubinstein approach for valuing options with stochastic interest rates," The Quarterly Review of Economics and Finance, Elsevier, vol. 67(C), pages 92-99.
    4. Sol Kim, 2021. "Portfolio of Volatility Smiles versus Volatility Surface: Implications for pricing and hedging options," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 41(7), pages 1154-1176, July.
    5. 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.
    6. João Nunes, 2011. "American options and callable bonds under stochastic interest rates and endogenous bankruptcy," Review of Derivatives Research, Springer, vol. 14(3), pages 283-332, October.
    7. Ho, T. S. & Stapleton, Richard C. & Subrahmanyam, Marti G., 1997. "The valuation of American options on bonds1," Journal of Banking & Finance, Elsevier, vol. 21(11-12), pages 1487-1513, December.
    8. Medvedev, Alexey & Scaillet, Olivier, 2010. "Pricing American options under stochastic volatility and stochastic interest rates," Journal of Financial Economics, Elsevier, vol. 98(1), pages 145-159, October.
    9. B. Gao J. Huang, "undated". "The Valuation of American Barrier Options Using the Decomposition Technique," New York University, Leonard N. Stern School Finance Department Working Paper Seires 99-002, New York University, Leonard N. Stern School of Business-.
    10. Bert Menkveld & Ton Vorst, 1998. "A Pricing Model for American Options with Stochastic Interest Rates," Tinbergen Institute Discussion Papers 98-028/2, Tinbergen Institute.
    11. Manuel Moreno & Javier Navas, 2003. "On the Robustness of Least-Squares Monte Carlo (LSM) for Pricing American Derivatives," Review of Derivatives Research, Springer, vol. 6(2), pages 107-128, May.
    12. Chiarella, Carl & Ziogas, Andrew, 2005. "Evaluation of American strangles," Journal of Economic Dynamics and Control, Elsevier, vol. 29(1-2), pages 31-62, January.
    13. Ballestra, Luca Vincenzo & D’Innocenzo, Enzo & Guizzardi, Andrea, 2024. "A new bivariate approach for modeling the interaction between stock volatility and interest rate: An application to S&P500 returns and options," European Journal of Operational Research, Elsevier, vol. 314(3), pages 1185-1194.
    14. Stephen E. Satchell & Richard C. Stapleton & Marti G. Subrahmanyam, 1997. "The Pricing of Marked†to†Market Contingent Claims in a No†Arbitrage Economy," Australian Journal of Management, Australian School of Business, vol. 22(1), pages 1-20, June.
    15. Lung-Fu Chang & Mao-Wei Hung, 2006. "Valuation of vulnerable American options with correlated credit risk," Review of Derivatives Research, Springer, vol. 9(2), pages 137-165, September.
    16. Blessing Taruvinga & Boda Kang & Christina Sklibosios Nikitopoulos, 2018. "Pricing American Options with Jumps in Asset and Volatility," Research Paper Series 394, Quantitative Finance Research Centre, University of Technology, Sydney.
    17. Chang, Chuang-Chang, 2001. "Efficient procedures for the valuation and hedging of American currency options with stochastic interest rates," Journal of Multinational Financial Management, Elsevier, vol. 11(3), pages 241-268, July.
    18. Gao, Bin & Huang, Jing-zhi & Subrahmanyam, Marti, 2000. "The valuation of American barrier options using the decomposition technique," Journal of Economic Dynamics and Control, Elsevier, vol. 24(11-12), pages 1783-1827, October.
    19. 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.
    20. Jérôme Detemple & Weidong Tian, 2002. "The Valuation of American Options for a Class of Diffusion Processes," Management Science, INFORMS, vol. 48(7), pages 917-937, July.
    21. Lindset, Snorre & Lund, Arne-Christian, 2007. "A Monte Carlo approach for the American put under stochastic interest rates," Journal of Economic Dynamics and Control, Elsevier, vol. 31(4), pages 1081-1105, April.
    22. Lim, Terence & Lo, Andrew W. & Merton, Robert C. & Scholes, Myron S., 2006. "The Derivatives Sourcebook," Foundations and Trends(R) in Finance, now publishers, vol. 1(5–6), pages 365-572, April.

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