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Bond, futures and option evaluation in the quadratic interest rate model

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  • Farshid Jamshidian
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    Abstract

    This paper develops the quadratic interest-rate model of Beaglehole and Tenney in detail. For the quadratic model as well as the multifactor Cox-Ingersoll-Ross square-root model, explicit pricing formulae in terms of one-dimensional integrals of elementary functions are given for bond options, bond exchange options, caps, options on bond futures and forward contracts, and futures delivery options. For the quadratic model, certain forward and transport equations are found that explicitly determine the dynamics of the term structure in terms of initial yield and volatility curves. These option-pricing formulae are thus determined in term of the initial curves. Some shortcomings of the model are identified. New formulae for some distributions and their truncated moments are also derived.

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    Bibliographic Info

    Article provided by Taylor & Francis Journals in its journal Applied Mathematical Finance.

    Volume (Year): 3 (1996)
    Issue (Month): 2 ()
    Pages: 93-115

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    Handle: RePEc:taf:apmtfi:v:3:y:1996:i:2:p:93-115

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    Web page: http://www.tandfonline.com/RAMF20

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    Related research

    Keywords: principal value integral; noncentral chi-squared distribution; forward risk adjustment; forward and transport equations; yield curve calibration;

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    Cited by:
    1. 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.
    2. Hans-Peter Bermin, 2012. "Bonds and Options in Exponentially Affine Bond Models," Applied Mathematical Finance, Taylor & Francis Journals, vol. 19(6), pages 513-534, December.
    3. Ben-Ameur, Hatem & Breton, Michele & Karoui, Lotfi & L'Ecuyer, Pierre, 2007. "A dynamic programming approach for pricing options embedded in bonds," Journal of Economic Dynamics and Control, Elsevier, vol. 31(7), pages 2212-2233, July.
    4. Dijkstra, Theo K. & Yao, Yong, 2002. "Moment generating function approach to pricing interest rate and foreign exchange rate claims," Insurance: Mathematics and Economics, Elsevier, vol. 31(2), pages 163-178, October.
    5. Rogers, L. C. G. & Stummer, Wolfgang, 2000. "Consistent fitting of one-factor models to interest rate data," Insurance: Mathematics and Economics, Elsevier, vol. 27(1), pages 45-63, August.
    6. Peng Cheng & Olivier Scaillet, 2002. "Linear-Quadratic Jump-Diffusion Modeling with Application to Stochastic Volatility," FAME Research Paper Series rp67, International Center for Financial Asset Management and Engineering.
    7. Andrea Macrina, 2012. "Heat Kernel Framework for Asset Pricing in Finite Time," Papers 1211.0856, arXiv.org, revised Sep 2013.
    8. Rafael Mendoza-Arriaga & Vadim Linetsky, 2014. "Time-changed CIR default intensities with two-sided mean-reverting jumps," Papers 1403.5402, arXiv.org.

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