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Options in and on interest rate futures contracts: results from martingale pricing theory

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  • U. Cherubini
  • M. Esposito

Abstract

In this paper we address the theoretical problem of evaluating the quality option embedded in interest rate futures contracts. We use the martingale properties of the prices of interest-rate contingent claims under different probability measures in order to derive solutions for the value of futures and options on futures, accounting for the quality option and assuming a square-root model for the short rate. The futures pricing formula boils down to a simple linear combination of the futures prices of the zero-coupon bonds which constitute the deliverable bonds. A European call option on such a futures can be rewritten as an option on a single futures in which the strike price is 'curved', i.e. it is a decreasing function of the short rate.

Suggested Citation

  • U. Cherubini & M. Esposito, 1995. "Options in and on interest rate futures contracts: results from martingale pricing theory," Applied Mathematical Finance, Taylor & Francis Journals, vol. 2(1), pages 1-16.
    • Handle: RePEc:taf:apmtfi:v:2:y:1995:i:1:p:1-16
    DOI: 10.1080/13504869500000001
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    References listed on IDEAS

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    1. Peter Ritchken & L. Sankarasubramanian, 1992. "Pricing the Quality Option In Treasury Bond Futures1," Mathematical Finance, Wiley Blackwell, vol. 2(3), pages 197-214, July.
    2. Harrison, J. Michael & Pliska, Stanley R., 1983. "A stochastic calculus model of continuous trading: Complete markets," Stochastic Processes and their Applications, Elsevier, vol. 15(3), pages 313-316, August.
    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. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    5. Harrison, J. Michael & Kreps, David M., 1979. "Martingales and arbitrage in multiperiod securities markets," Journal of Economic Theory, Elsevier, vol. 20(3), pages 381-408, June.
    6. Vasicek, Oldrich Alfonso, 1977. "Abstract: An Equilibrium Characterization of the Term Structure," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(4), pages 627-627, November.
    7. Harrison, J. Michael & Pliska, Stanley R., 1981. "Martingales and stochastic integrals in the theory of continuous trading," Stochastic Processes and their Applications, Elsevier, vol. 11(3), pages 215-260, August.
    8. Cox, John C. & Ingersoll, Jonathan Jr. & Ross, Stephen A., 1981. "The relation between forward prices and futures prices," Journal of Financial Economics, Elsevier, vol. 9(4), pages 321-346, December.
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    Cited by:

    1. Umberto Cherubini & Elisa Luciano, 2002. "Multivariate Option Pricing with Copulas," ICER Working Papers - Applied Mathematics Series 05-2002, ICER - International Centre for Economic Research.
    2. Balbás, Alejandro & Reichardt, Susana, 2006. "On the future contract quality option: a new look," DEE - Working Papers. Business Economics. WB wb063711, Universidad Carlos III de Madrid. Departamento de Economía de la Empresa.
    3. Alejandro Balbas & Susana Reichardt, 2010. "On the future contract quality option: a new look," Applied Financial Economics, Taylor & Francis Journals, vol. 20(15), pages 1217-1229.
    4. Duffie, Darrell, 2003. "Intertemporal asset pricing theory," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, edition 1, volume 1, chapter 11, pages 639-742, Elsevier.

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