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Simulation of coupon bond European and barrier options in quantum finance

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  • Baaquie, Belal E.
  • Pan, Tang
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    Abstract

    Coupon bond European and barrier options are studied in the framework of quantum finance. The prices of European and barrier options are analyzed by generating sample values of the forward interest rates f(t,x) using a two-dimensional Gaussian quantum field A(t,x). The strong correlations of forward interest rates are described by the stiff propagator of the quantum field A(t,x). Using the Cholesky decomposition, A(t,x) is expressed in terms of white noise. The simulation results for European coupon bond and barrier options are compared with approximate formulas, which are obtained as power series in the volatility of the forward interest rates. The simulation shows that the simulated price deviates from the approximate value for large volatilities. The numerical algorithm is flexible and can be used for pricing any kind of option. It is shown that the three-factor HJM model can be derived from the quantum finance formulation.

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    Bibliographic Info

    Article provided by Elsevier in its journal Physica A: Statistical Mechanics and its Applications.

    Volume (Year): 390 (2011)
    Issue (Month): 2 ()
    Pages: 263-289

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    Handle: RePEc:eee:phsmap:v:390:y:2011:i:2:p:263-289

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    Web page: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/

    Related research

    Keywords: Coupon bond option; Barrier option; Monte Carlo simulation; Quantum finance;

    References

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    1. Carl Chiarella & Hing Hung & Thuy-Duong To, 2005. "The Volatility Structure of the Fixed Income Market under the HJM Framework: A Nonlinear Filtering Approach," Research Paper Series 151, Quantitative Finance Research Centre, University of Technology, Sydney.
    2. Inui, Koji & Kijima, Masaaki, 1998. "A Markovian Framework in Multi-Factor Heath-Jarrow-Morton Models," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 33(03), pages 423-440, September.
    3. Heath, David & Jarrow, Robert & Morton, Andrew, 1992. "Bond Pricing and the Term Structure of Interest Rates: A New Methodology for Contingent Claims Valuation," Econometrica, Econometric Society, vol. 60(1), pages 77-105, January.
    4. de Jong, Frank & Santa-Clara, Pedro, 1999. "The Dynamics of the Forward Interest Rate Curve: A Formulation with State Variables," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 34(01), pages 131-157, March.
    5. Carl Chiarella & Oh-Kang Kwon, 1999. "Forward Rate Dependent Markovian Transformations of the Heath-Jarrow-Morton Term Structure Model," Research Paper Series 5, Quantitative Finance Research Centre, University of Technology, Sydney.
    6. Knez, Peter J & Litterman, Robert & Scheinkman, Jose Alexandre, 1994. " Explorations into Factors Explaining Money Market Returns," Journal of Finance, American Finance Association, vol. 49(5), pages 1861-82, December.
    7. Carl Chiarella & Oh Kwon, 2003. "Finite Dimensional Affine Realisations of HJM Models in Terms of Forward Rates and Yields," Review of Derivatives Research, Springer, vol. 6(2), pages 129-155, May.
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    Cited by:
    1. Baaquie, Belal E. & Tang, Pan, 2012. "Simulation of nonlinear interest rates in quantum finance: Libor Market Model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(4), pages 1287-1308.

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