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Perturbation analysis of a nonlinear equation arising in the Schaefer-Schwartz model of interest rates

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  • Beata Stehlikova

Abstract

We deal with the interest rate model proposed by Schaefer and Schwartz, which models the long rate and the spread, defined as the difference between the short and the long rates. The approximate analytical formula for the bond prices suggested by the authors requires a computation of a certain constant, defined via a nonlinear equation and an integral of a solution to a system of ordinary differential equations. In this paper we use perturbation methods to compute this constant. Coefficients of its expansion are given in a closed form and can be constructed to arbitrary order. However, our numerical results show that a very good accuracy is achieved already after using a small number of terms.

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  • Beata Stehlikova, 2014. "Perturbation analysis of a nonlinear equation arising in the Schaefer-Schwartz model of interest rates," Papers 1410.6321, arXiv.org.
    • Handle: RePEc:arx:papers:1410.6321
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    References listed on IDEAS

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    1. Christiansen, Charlotte, 2013. "Predicting severe simultaneous recessions using yield spreads as leading indicators," Journal of International Money and Finance, Elsevier, vol. 32(C), pages 1032-1043.
    2. Babbs, Simon H. & Nowman, K. Ben, 1999. "Kalman Filtering of Generalized Vasicek Term Structure Models," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 34(1), pages 115-130, March.
    3. Ahrens, R., 2002. "Predicting recessions with interest rate spreads: a multicountry regime-switching analysis," Journal of International Money and Finance, Elsevier, vol. 21(4), pages 519-537, August.
    4. Christiansen, Charlotte, 2005. "Multivariate term structure models with level and heteroskedasticity effects," Journal of Banking & Finance, Elsevier, vol. 29(5), pages 1037-1057, May.
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