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Pricing American options for interest rate caps and coupon bonds in quantum finance

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  • Baaquie, Belal E.
  • Liang, Cui

Abstract

American option for interest rate caps and coupon bonds are analyzed in the formalism of quantum finance. Calendar time and future time are discretized to yield a lattice field theory of interest rates that provides an efficient numerical algorithm for evaluating the price of American options. The algorithm is shown to hold over a wide range of strike prices and coupon rates. All the theoretical constraints that American options have to obey are shown to hold for the numerical prices of American interest rate caps and coupon bond options. Non-trivial correlation between the different interest rates are efficiently incorporated in the numerical algorithm. New inequalities are conjectured, based on the results of the numerical study, for American options on interest rate instruments.

Suggested Citation

  • Baaquie, Belal E. & Liang, Cui, 2007. "Pricing American options for interest rate caps and coupon bonds in quantum finance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 381(C), pages 285-316.
    • Handle: RePEc:eee:phsmap:v:381:y:2007:i:c:p:285-316
    DOI: 10.1016/j.physa.2007.02.054
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    References listed on IDEAS

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    1. Li, Anlong & Ritchken, Peter & Sankarasubramanian, L, 1995. "Lattice Models for Pricing American Interest Rate Claims," Journal of Finance, American Finance Association, vol. 50(2), pages 719-737, June.
    2. Montagna, Guido & Nicrosini, Oreste & Moreni, Nicola, 2002. "A path integral way to option pricing," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 310(3), pages 450-466.
    3. Belal E. Baaquie, 2005. "A Common Market Measure for Libor and Pricing Caps, Floors and Swaps in a Field Theory of Forward Interest Rates," Papers physics/0503126, arXiv.org.
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    6. Belal E. Baaquie, 2005. "A Common Market Measure For Libor And Pricing Caps, Floors And Swaps In A Field Theory Of Forward Interest Rates," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 8(08), pages 999-1018.
    7. G. Montagna & O. Nicrosini & N. Moreni, 2002. "A Path Integral Way to Option Pricing," Papers cond-mat/0202143, arXiv.org.
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    Cited by:

    1. Baaquie, Belal E. & Yu, Miao, 2017. "Option price and market instability," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 471(C), pages 512-535.
    2. Baaquie, Belal Ehsan, 2018. "Bonds with index-linked stochastic coupons in quantum finance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 499(C), pages 148-169.

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