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Control of price acceptability under the univariate Vasicek model

Author

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  • S. Dang-Nguyen

    (Alef-Servizi Spa, Viale Regina Margherita, 169 00199 Roma, Italy2ECE Paris Graduate School of Engineering, 37 quai de Grenelle CS71520 75 725 Paris 15, France)

  • Y. Rakotondratsimba

    (Alef-Servizi Spa, Viale Regina Margherita, 169 00199 Roma, Italy2ECE Paris Graduate School of Engineering, 37 quai de Grenelle CS71520 75 725 Paris 15, France)

Abstract

The valuation of the probability of a financial contract to be lower or higher than a given price under the univariate Vasicek model is discussed in this paper. This price restriction can be justified by consistency reasons, since some prices may not be coherent on a financial point of view, e.g. they imply negative yields, or thought as unreachable by the asset manager. At first, assuming that the pricing functions is monotone, the price constraints are formulated in terms of a threshold on the value of the spot rate process. Since this process is Gaussian, these limits are reformulated in terms of a barrier of the Gaussian increments. Next, once the thresholds are identified, the probability to satisfy the price restriction after the generation of the spot rate at one future date can be computed. Then, assuming that the bounds on the spot rate are constant during a Monte-Carlo simulation, the probability of generating a path of this process that does not satisfy the constraint is valued using some results related to the hitting times. Lastly, the proposed approach is applied to various interest rates sensitive contracts and is illustrated by some numerical examples.

Suggested Citation

  • S. Dang-Nguyen & Y. Rakotondratsimba, 2016. "Control of price acceptability under the univariate Vasicek model," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 3(03), pages 1-40, September.
    • Handle: RePEc:wsi:ijfexx:v:03:y:2016:i:03:n:s2424786316500146
    DOI: 10.1142/S2424786316500146
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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. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    3. Gregory R. Duffee & Richard H. Stanton, 2012. "Estimation of Dynamic Term Structure Models," Quarterly Journal of Finance (QJF), World Scientific Publishing Co. Pte. Ltd., vol. 2(02), pages 1-51.
    4. Duffie, Darrell & Singleton, Kenneth J, 1999. "Modeling Term Structures of Defaultable Bonds," The Review of Financial Studies, Society for Financial Studies, vol. 12(4), pages 687-720.
    5. Viatcheslav Gorovoi & Vadim Linetsky, 2004. "Black's Model of Interest Rates as Options, Eigenfunction Expansions and Japanese Interest Rates," Mathematical Finance, Wiley Blackwell, vol. 14(1), pages 49-78, January.
    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. Mark Broadie & Paul Glasserman & Steven Kou, 1997. "A Continuity Correction for Discrete Barrier Options," Mathematical Finance, Wiley Blackwell, vol. 7(4), pages 325-349, October.
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