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

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  • 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
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    References listed on IDEAS

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    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. 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.
    3. 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..
    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.
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