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Stylised Properties of the Interest Rate Term Structure Under The Benchmark Approach

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Abstract

Market models which re ect stylised properties of the interest rate term structure are widely used for modelling and pricing interest rate derivatives. We consider a market model involving the short rate and a diversified global stock index. We illustrate the stylised properties of the interest rate term structure implied by a system of stochastic differential equations specifying the short rate and the discounted stock index under the benchmark approach. Comparison with empirical evidence demonstrates the explanatory power of a discounted stock index modelled by a squared Bessel process.

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  • Kevin Fergusson & Eckhard Platen, 2014. "Stylised Properties of the Interest Rate Term Structure Under The Benchmark Approach," Research Paper Series 351, Quantitative Finance Research Centre, University of Technology, Sydney.
    • Handle: RePEc:uts:rpaper:351
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    File URL: https://www.uts.edu.au/sites/default/files/qfr-archive-03/QFR-rp351.pdf
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    1. Jean-Philippe Bouchaud & Nicolas Sagna & Rama Cont & Nicole El-Karoui & Marc Potters, 1999. "Phenomenology of the interest rate curve," Applied Mathematical Finance, Taylor & Francis Journals, vol. 6(3), pages 209-232.
    2. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    3. Andrew Matacz & Jean-Philippe Bouchaud, 2000. "An Empirical Investigation Of The Forward Interest Rate Term Structure," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 3(04), pages 703-729.
    4. Ahn, Dong-Hyun & Gao, Bin, 1999. "A Parametric Nonlinear Model of Term Structure Dynamics," The Review of Financial Studies, Society for Financial Studies, vol. 12(4), pages 721-762.
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    1. Fergusson, Kevin, 2020. "Less-Expensive Valuation And Reserving Of Long-Dated Variable Annuities When Interest Rates And Mortality Rates Are Stochastic," ASTIN Bulletin, Cambridge University Press, vol. 50(2), pages 381-417, May.
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    3. Kevin John Fergusson, 2018. "Less-Expensive Pricing and Hedging of Extreme-Maturity Interest Rate Derivatives and Equity Index Options Under the Real-World Measure," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 3-2018.

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