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Bonds and Options in Exponentially Affine Bond Models

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  • Hans-Peter Bermin

Abstract

In this article we apply the Flesaker--Hughston approach to invert the yield curve and to price various options by letting the randomness in the economy be driven by a process closely related to the short rate, called the abstract short rate. This process is a pure deterministic translation of the short rate itself, and we use the deterministic shift to calibrate the models to the initial yield curve. We show that we can solve for the shift needed in closed form by transforming the problem to a new probability measure. Furthermore, when the abstract short rate follows a Cox--Ingersoll--Ross (CIR) process we compute bond option and swaption prices in closed form. We also propose a short-rate specification under the risk-neutral measure that allows the yield curve to be inverted and is consistent with the CIR dynamics for the abstract short rate, thus giving rise to closed form bond option and swaption prices.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:apmtfi:v:19:y:2012:i:6:p:513-534
    DOI: 10.1080/1350486X.2011.646505
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    References listed on IDEAS

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    1. Erik Schlogl & Lutz Schlogl, 2000. "A square root interest rate model fitting discrete initial term structure data," Applied Mathematical Finance, Taylor & Francis Journals, vol. 7(3), pages 183-209.
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    4. Hull, John & White, Alan, 1990. "Pricing Interest-Rate-Derivative Securities," The Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 573-592.
    5. Damiano Brigo & Fabio Mercurio, 2001. "A deterministic-shift extension of analytically-tractable and time-homogeneous short-rate models," Finance and Stochastics, Springer, vol. 5(3), pages 369-387.
    6. repec:bla:jfinan:v:44:y:1989:i:1:p:205-09 is not listed on IDEAS
    7. Farshid Jamshidian, 1996. "Bond, futures and option evaluation in the quadratic interest rate model," Applied Mathematical Finance, Taylor & Francis Journals, vol. 3(2), pages 93-115.
    8. 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.
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    Cited by:

    1. Hans-Peter Bermin & Gareth Williams, 2017. "On Cash Settled Irr-Swaptions And Markov Functional Modeling," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(02), pages 1-20, March.
    2. Mitra, Sovan & Date, Paresh & Mamon, Rogemar & Wang, I-Chieh, 2013. "Pricing and risk management of interest rate swaps," European Journal of Operational Research, Elsevier, vol. 228(1), pages 102-111.

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