IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v374y2007i1p331-348.html

Empirical investigation of a field theory formula and Black's formula for the price of an interest-rate caplet

Author

Listed:
  • Baaquie, Belal E.
  • Liang, Cui

Abstract

The industry standard for pricing an interest-rate caplet is Black's formula. Another distinct price of the same caplet can be derived using a quantum field theory model of the forward interest rates. An empirical study is carried out to compare the two caplet pricing formulae. Historical volatility and correlation of forward interest rates are used to generate the field theory caplet price; another approach is to fit a parametric formula for the effective volatility using market caplet price. The study shows that the field theory model generates the price of a caplet and cap fairly accurately. Black's formula for a caplet is compared with field theory pricing formula. It is seen that the field theory formula for caplet price has many advantages over Black's formula.

Suggested Citation

  • Baaquie, Belal E. & Liang, Cui, 2007. "Empirical investigation of a field theory formula and Black's formula for the price of an interest-rate caplet," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 374(1), pages 331-348.
    • Handle: RePEc:eee:phsmap:v:374:y:2007:i:1:p:331-348
    DOI: 10.1016/j.physa.2006.07.024
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437106007953
    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.2006.07.024?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

    for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. David Heath & Robert Jarrow & Andrew Morton, 2008. "Bond Pricing And The Term Structure Of Interest Rates: A New Methodology For Contingent Claims Valuation," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 13, pages 277-305, World Scientific Publishing Co. Pte. Ltd..
    3. Belal E. Baaquie & Marakani Srikant & Mitch C. Warachka, 2003. "A Quantum Field Theory Term Structure Model Applied to Hedging," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 6(05), pages 443-467.
    4. 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.
    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.
    Full references (including those not matched with items on IDEAS)

    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. Baaquie, Belal E. & Liang, Cui & Warachka, Mitch C., 2007. "Hedging LIBOR derivatives in a field theory model of interest rates," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 374(2), pages 730-748.
    2. 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.
    3. 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.
    4. 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.
    5. Nicolò Cangiotti, 2024. "Feynman Diagrams beyond Physics: From Biology to Economy," Mathematics, MDPI, vol. 12(9), pages 1-17, April.
    6. Camilla LandÊn, 2000. "Bond pricing in a hidden Markov model of the short rate," Finance and Stochastics, Springer, vol. 4(4), pages 371-389.
    7. Matsumura, Marco & Moreira, Ajax & Vicente, José, 2011. "Forecasting the yield curve with linear factor models," International Review of Financial Analysis, Elsevier, vol. 20(5), pages 237-243.
    8. Lioui, Abraham, 1998. "Erratum to "Currency risk hedging: Futures vs. forward" [J. Banking and Finance 22 (1) (1998) 61-81]1," Journal of Banking & Finance, Elsevier, vol. 22(5), pages 611-612, May.
    9. Lin, Bing-Huei, 1999. "Fitting the term structure of interest rates for Taiwanese government bonds," Journal of Multinational Financial Management, Elsevier, vol. 9(3-4), pages 331-352, November.
    10. Robert R. Bliss & Ehud I. Ronn, 1997. "Callable U.S. Treasury bonds: optimal calls, anomalies, and implied volatilities," FRB Atlanta Working Paper 97-1, Federal Reserve Bank of Atlanta.
    11. Tucker, A. L. & Wei, J. Z., 1998. "Valuation of LIBOR-Contingent FX options," Journal of International Money and Finance, Elsevier, vol. 17(2), pages 249-277, April.
    12. Chiarella, Carl & Kang, Boda & Nikitopoulos, Christina Sklibosios & Tô, Thuy-Duong, 2013. "Humps in the volatility structure of the crude oil futures market: New evidence," Energy Economics, Elsevier, vol. 40(C), pages 989-1000.
    13. Will Hicks, 2020. "Pseudo-Hermiticity, Martingale Processes and Non-Arbitrage Pricing," Papers 2009.00360, arXiv.org, revised Apr 2021.
    14. Eckhard Platen, 2005. "An Alternative Interest Rate Term Structure Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 8(06), pages 717-735.
    15. Kimmel, Robert L., 2004. "Modeling the term structure of interest rates: A new approach," Journal of Financial Economics, Elsevier, vol. 72(1), pages 143-183, April.
    16. Roberto Baviera, 2017. "Back-of-the-envelope swaptions in a very parsimonious multicurve interest rate model," Papers 1712.06466, arXiv.org.
    17. Issler, João Victor, 1995. "Estimating the term structure of volatility and fixed income derivative pricing," FGV EPGE Economics Working Papers (Ensaios Economicos da EPGE) 272, EPGE Brazilian School of Economics and Finance - FGV EPGE (Brazil).
    18. Gapeev, Pavel V., 2004. "On arbitrage and Markovian short rates in fractional bond markets," Statistics & Probability Letters, Elsevier, vol. 70(3), pages 211-222, December.
    19. Chen An & Mahayni Antje B., 2008. "Endowment Assurance Products: Effectiveness of Risk-Minimizing Strategies under Model Risk," Asia-Pacific Journal of Risk and Insurance, De Gruyter, vol. 2(2), pages 1-29, March.
    20. Bujar Huskaj & Marcus Nossman, 2013. "A Term Structure Model for VIX Futures," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 33(5), pages 421-442, May.

    More about this item

    Keywords

    ;
    ;
    ;

    Statistics

    Access and download statistics

    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:374:y:2007:i:1:p:331-348. 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.