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The Valuation of Interest Rate Digital Options and Range Notes Revisited

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  • Patrick Navatte
  • François Quittard‐Pinon

Abstract

The aim of this paper is to value interest rate structured products in a simpler and more intuitive way than Turnbull (1995). Considering some assumptions with respect to the evolution of the term structure of interest rates, the price of a European interest rate digital call option is given. Recall it is a contract designed to pay one dollar at maturity if a reference interest rate is above a prespecified level (the strike), and zero in all the others cases. Combining two options of this type enables us to value a European range digital option. Then using a one factor linear gaussian model and the new well‐known change of numeraire approach, a closed‐form formula is found to value range notes which pay at the end of each defined period, a sum equal to a prespecified interest rate times the number of days the reference interest rate lies inside a corridor.

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  • 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.
    • Handle: RePEc:bla:eufman:v:5:y:1999:i:3:p:425-440
    DOI: 10.1111/1468-036X.00103
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    Cited by:

    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. 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.
    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. João Pedro Vidal Nunes, 2004. "MultiFactor Valuation of Floating Range Notes," Mathematical Finance, Wiley Blackwell, vol. 14(1), pages 79-97, January.
    6. Bong-Gyu Jang & Kum-Hwan Roh, 2009. "Valuing qualitative options with stochastic volatility," Quantitative Finance, Taylor & Francis Journals, vol. 9(7), pages 819-825.
    7. 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.
    8. 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.

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