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Fundamental Properties of Bond Prices in Models of the Short-Term Rate

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  • Antonio Mele

Abstract

This article develops restrictions that arbitrage-constrained bond prices impose on the short-term rate process in order to be consistent with given dynamic properties of the term structure of interest rates. The central focus is the relationship between bond prices and the short-term rate volatility. In both scalar and multidimensional diffusion settings, typical relationships between bond prices and volatility are generated by joint restrictions on the risk-neutralized drift functions of the state variables and convexity of bond prices with respect to the short-term rate. The theory is illustrated by several examples and is partially extended to accommodate the occurrence of jumps and default. Copyright 2003, Oxford University Press.

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  • Antonio Mele, 2003. "Fundamental Properties of Bond Prices in Models of the Short-Term Rate," The Review of Financial Studies, Society for Financial Studies, vol. 16(3), pages 679-716, July.
    • Handle: RePEc:oup:rfinst:v:16:y:2003:i:3:p:679-716
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    Cited by:

    1. Kristensen, Dennis & Mele, Antonio, 2011. "Adding and subtracting Black-Scholes: A new approach to approximating derivative prices in continuous-time models," Journal of Financial Economics, Elsevier, vol. 102(2), pages 390-415.
    2. Takami, Marcelo Yoshio & Tabak, Benjamin Miranda, 2008. "Interest rate option pricing and volatility forecasting: An application to Brazil," Chaos, Solitons & Fractals, Elsevier, vol. 38(3), pages 755-763.
    3. Sonin, Isaac M. & Whitmeyer, Mark, 2020. "Some nontrivial properties of a formula for compound interest," Finance Research Letters, Elsevier, vol. 33(C).
    4. Xavier Gabaix, 2007. "Linearity-Generating Processes: A Modelling Tool Yielding Closed Forms for Asset Prices," NBER Working Papers 13430, National Bureau of Economic Research, Inc.
    5. Mele, Antonio, 2007. "Asymmetric stock market volatility and the cyclical behavior of expected returns," Journal of Financial Economics, Elsevier, vol. 86(2), pages 446-478, November.
    6. Mele, Antonio & Obayashi, Yoshiki & Shalen, Catherine, 2015. "Rate fears gauges and the dynamics of fixed income and equity volatilities," Journal of Banking & Finance, Elsevier, vol. 52(C), pages 256-265.
    7. Lioui, Abraham, 2007. "The asset allocation puzzle is still a puzzle," Journal of Economic Dynamics and Control, Elsevier, vol. 31(4), pages 1185-1216, April.
    8. Ka-Fai Li & Cho-Hoi Hui & Tsz-Kin Chung, 2012. "Determinants and Dynamics of Price Disparity in Onshore and Offshore Renminbi Forward Exchange Rate Markets," Working Papers 242012, Hong Kong Institute for Monetary Research.
    9. Mele, Antonio, 2004. "General Properties of Rational Stock-Market Fluctuations," Economics Series 153, Institute for Advanced Studies.
    10. Altissimo, Filippo & Mele, Antonio, 2005. "Simulated nonparametric estimation of dynamic models with applications to finance," LSE Research Online Documents on Economics 24658, London School of Economics and Political Science, LSE Library.
    11. Altissimo, Filippo & Mele, Antonio, 2004. "Simulated nonparametric estimation of continuous time models of asset prices and returns," LSE Research Online Documents on Economics 24674, London School of Economics and Political Science, LSE Library.
    12. Isaac M. Sonin & Mark Whitmeyer, 2018. "Some Nontrivial Properties of a Formula for Compound Interest," Papers 1809.10566, arXiv.org.

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    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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