IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v401y2014icp182-200.html
   My bibliography  Save this article

Pricing of range accrual swap in the quantum finance Libor Market Model

Author

Listed:
  • Baaquie, Belal E.
  • Du, Xin
  • Tang, Pan
  • Cao, Yang

Abstract

We study the range accrual swap in the quantum finance formulation of the Libor Market Model (LMM). It is shown that the formulation can exactly price the path dependent instrument. An approximate price is obtained as an expansion in the volatility of Libor. The Monte Carlo simulation method is used to study the nonlinear domain of the model and determine the range of validity of the approximate formula. The price of accrual swap is analyzed by generating daily sample values by simulating a two dimension Gaussian quantum field.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:401:y:2014:i:c:p:182-200
    DOI: 10.1016/j.physa.2014.01.042
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437114000545
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2014.01.042?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    2. 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.
    3. Patrick Navatte & François Quittard‐Pinon, 1999. "The Valuation of Interest Rate Digital Options and Range Notes Revisited," European Financial Management, European Financial Management Association, vol. 5(3), pages 425-440, November.
    4. Jang, Bong-Gyu & Yoon, Ji Hee, 2010. "Analytic valuation formulas for range notes and an affine term structure model with jump risks," Journal of Banking & Finance, Elsevier, vol. 34(9), pages 2132-2145, September.
    5. João Pedro Vidal Nunes, 2004. "MultiFactor Valuation of Floating Range Notes," Mathematical Finance, Wiley Blackwell, vol. 14(1), pages 79-97, January.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Li, Shaoyu & Huang, Henry H. & Zhang, Teng, 2020. "Generalized affine transform on pricing quanto range accrual note," The North American Journal of Economics and Finance, Elsevier, vol. 54(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Chiarella, Carl & Da Fonseca, José & Grasselli, Martino, 2014. "Pricing range notes within Wishart affine models," Insurance: Mathematics and Economics, Elsevier, vol. 58(C), pages 193-203.
    2. Ting‐Pin Wu & Son‐Nan Chen, 2008. "Valuation of floating range notes in a LIBOR market model," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 28(7), pages 697-710, July.
    3. Ping Wu & Robert J. Elliott, 2016. "Valuation of CMS range notes in a multifactor LIBOR market model," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 3(01), pages 1-19, March.
    4. Jang, Bong-Gyu & Yoon, Ji Hee, 2010. "Analytic valuation formulas for range notes and an affine term structure model with jump risks," Journal of Banking & Finance, Elsevier, vol. 34(9), pages 2132-2145, September.
    5. 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.
    6. Ping Wu & Robert J. Elliott, 2017. "Valuation of certain CMS spreads," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 31(4), pages 445-467, November.
    7. Lee, Sangwook & Kim, Min Jae & Lee, Sun Young & Kim, Soo Yong & Ban, Joon Hwa, 2013. "The effect of the subprime crisis on the credit risk in global scale," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(9), pages 2060-2071.
    8. João Pedro Vidal Nunes & Pedro Miguel Silva Prazeres, 2014. "Pricing Swaptions Under Multifactor Gaussian Hjm Models," Mathematical Finance, Wiley Blackwell, vol. 24(4), pages 762-789, October.
    9. Ashtiani, Mehrdad & Azgomi, Mohammad Abdollahi, 2015. "A survey of quantum-like approaches to decision making and cognition," Mathematical Social Sciences, Elsevier, vol. 75(C), pages 49-80.
    10. 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.
    11. 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.
    12. Bong-Gyu Jang & Kum-Hwan Roh, 2009. "Valuing qualitative options with stochastic volatility," Quantitative Finance, Taylor & Francis Journals, vol. 9(7), pages 819-825.
    13. 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.
    14. Baaquie, Belal E. & Cao, Yang, 2014. "Option volatility and the acceleration Lagrangian," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 393(C), pages 337-363.
    15. 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.
    16. 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).
    17. João Pedro Vidal Nunes, 2004. "MultiFactor Valuation of Floating Range Notes," Mathematical Finance, Wiley Blackwell, vol. 14(1), pages 79-97, January.
    18. Bravo, Jorge M. & Nunes, João Pedro Vidal, 2021. "Pricing longevity derivatives via Fourier transforms," Insurance: Mathematics and Economics, Elsevier, vol. 96(C), pages 81-97.
    19. Haoran Zheng & Bo Dong, 2024. "Quantum Temporal Winds: Turbulence in Financial Markets," Mathematics, MDPI, vol. 12(10), pages 1-28, May.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:401:y:2014:i:c:p:182-200. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.