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Asymptotics Of Bond Yields And Volatilities For Extended Vasicek Models Under The Real-World Measure

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  • K. FERGUSSON

    (University of Melbourne, Centre for Actuarial Studies, Victoria 3010, Australia)

Abstract

Vasicek's short rate model is a mean reverting model of the short rate which permits closed-form pricing formulae of zero coupon bonds and options on zero coupon bonds. This paper supplies proofs which are valid for any single factor mean reverting Gaussian short rate model having time-inhomogeneous parameters. The formulae are for the expected present value of payoffs under the real-world probability measure, known as actuarial pricing. Importantly, we give formulae for asymptotic levels of bond yields and volatilities for extended Vasicek models when suitable conditions are imposed on the model parameters.

Suggested Citation

  • K. Fergusson, 2017. "Asymptotics Of Bond Yields And Volatilities For Extended Vasicek Models Under The Real-World Measure," Annals of Financial Economics (AFE), World Scientific Publishing Co. Pte. Ltd., vol. 12(01), pages 1-33, March.
    • Handle: RePEc:wsi:afexxx:v:12:y:2017:i:01:n:s2010495217500051
    DOI: 10.1142/S2010495217500051
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    References listed on IDEAS

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    1. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 5, pages 129-164, World Scientific Publishing Co. Pte. Ltd..
    2. Eckhard Platen, 2006. "A Benchmark Approach To Finance," Mathematical Finance, Wiley Blackwell, vol. 16(1), pages 131-151, January.
    3. Ho, Thomas S Y & Lee, Sang-bin, 1986. "Term Structure Movements and Pricing Interest Rate Contingent Claims," Journal of Finance, American Finance Association, vol. 41(5), pages 1011-1029, December.
    4. Platen, Eckhard, 2001. "A benchmark model for financial markets," SFB 373 Discussion Papers 2001,52, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    5. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    6. 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.
    7. Eckhard Platen & David Taylor, 2016. "Loading Pricing of Catastrophe Bonds and Other Long-Dated, Insurance-Type Contracts," Papers 1610.09875, arXiv.org.
    8. repec:bla:jfinan:v:44:y:1989:i:1:p:205-09 is not listed on IDEAS
    9. Eckhard Platen, 1999. "A short term interest rate model," Finance and Stochastics, Springer, vol. 3(2), pages 215-225.
    10. K. Fergusson & E. Platen, 2015. "Application Of Maximum Likelihood Estimation To Stochastic Short Rate Models," Annals of Financial Economics (AFE), World Scientific Publishing Co. Pte. Ltd., vol. 10(02), pages 1-26, December.
    11. 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. Kladívko, Kamil & Rusý, Tomáš, 2023. "Maximum likelihood estimation of the Hull–White model," Journal of Empirical Finance, Elsevier, vol. 70(C), pages 227-247.

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