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Simulation of nonlinear interest rates in quantum finance: Libor Market Model

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  • Baaquie, Belal E.
  • Tang, Pan

Abstract

The simulation of the Libor Market Model (LMM) is extensively studied in the framework of quantum finance. The imperfectly correlated Libor rates are simulated based on a Gaussian quantum field and a recursion equation of nontrivial stochastic drift. The Libor options are studied using both the simulation method and the analytical formula. The caplet price of simulation is compared with Black’s caplet formula which can be exactly derived from the LMM. The invariance of caplet price for different forward bond numeraire is verified by using the simulation. The simulation results for coupon bond options and swaptions are compared with the approximate price, which are limited for the reason that the approximate price is derived using the small volatility expansion. The simulation method is shown to have great potential in the application of pricing interest rate instruments.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:391:y:2012:i:4:p:1287-1308
    DOI: 10.1016/j.physa.2011.08.021
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    References listed on IDEAS

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    1. Farshid Jamshidian, 1997. "LIBOR and swap market models and measures (*)," Finance and Stochastics, Springer, vol. 1(4), pages 293-330.
    2. Leif Andersen & Jesper Andreasen, 2000. "Volatility skews and extensions of the Libor market model," Applied Mathematical Finance, Taylor & Francis Journals, vol. 7(1), pages 1-32.
    3. Riccardo Rebonato & Mark Joshi, 2002. "A Joint Empirical And Theoretical Investigation Of The Modes Of Deformation Of Swaption Matrices: Implications For Model Choice," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 5(07), pages 667-694.
    4. Baaquie, Belal E., 2010. "Interest rates in quantum finance: Caps, swaptions and bond options," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(2), pages 296-314.
    5. Andrew Matacz & Jean-Philippe Bouchaud, 2000. "Explaining The Forward Interest Rate Term Structure," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 3(03), pages 381-389.
    6. Baaquie, Belal E. & Yang, Cao, 2009. "Empirical analysis of quantum finance interest rates models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(13), pages 2666-2681.
    7. Baaquie, Belal E. & Pan, Tang, 2011. "Simulation of coupon bond European and barrier options in quantum finance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(2), pages 263-289.
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    Citations

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    Cited by:

    1. Xiangyi Meng & Jian-Wei Zhang & Jingjing Xu & Hong Guo, 2014. "Quantum spatial-periodic harmonic model for daily price-limited stock markets," Papers 1405.4490, arXiv.org.
    2. Meng, Xiangyi & Zhang, Jian-Wei & Guo, Hong, 2016. "Quantum Brownian motion model for the stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 452(C), pages 281-288.
    3. Pan Tang & Belal E. Baaquie & Xin Du & Ying Zhang, 2016. "Linearized Hamiltonian of the LIBOR market model: analytical and empirical results," Applied Economics, Taylor & Francis Journals, vol. 48(10), pages 878-891, February.
    4. Baaquie, Belal E. & Du, Xin & Tang, Pan & Cao, Yang, 2014. "Pricing of range accrual swap in the quantum finance Libor Market Model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 401(C), pages 182-200.
    5. Bueno-Guerrero, Alberto & Moreno, Manuel & Navas, Javier F., 2020. "Valuation of caps and swaptions under a stochastic string model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 559(C).

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