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Interest Rate Futures: Estimation of Volatility Parameters in an Arbitrage-Free Framework

Hedging interest rate exposures using interest rate futures contracts requires some knowledge of the volatility function of the interest rates. Use of historical data as well as interest rate options like caps and swapoptions to estimate this volatility function, have been proposed in the literature. In this paper the interest rate futures price is modelled within an arbitrage-free framework for a volatility function which includes a stochastic variable, the instantaneous spot interest rate. The resulting system is expressed in a state space form which is solved using extended Kalman filter. The technique is applied to short-term interest rate futures contracts trading on the Sydney Futures Exchange as well as on the Tokyo International Financial Futures Exchange. The residual diagnostics indicate suitability of the model and the bootstrap resampling technique is used to obtain small sample properties of the parameters of the volatility function.

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File URL: http://www.finance.uts.edu.au/research/wpapers/wp55.pdf
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Paper provided by Finance Discipline Group, UTS Business School, University of Technology, Sydney in its series Working Paper Series with number 55.

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Length: 26 pages
Date of creation: 01 Dec 1995
Date of revision:
Publication status: Published as: Bhar, R. and Chiarella, C., 1997, "Interest rate futures: Estimation of volatility parameters in an arbitrage-free framework", Applied Mathematical Finance, 4(4), pp. 181-199.
Handle: RePEc:uts:wpaper:55
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  1. Heath, David & Jarrow, Robert & Morton, Andrew, 1992. "Bond Pricing and the Term Structure of Interest Rates: A New Methodology for Contingent Claims Valuation," Econometrica, Econometric Society, vol. 60(1), pages 77-105, January.
  2. Carl Chiarella & Nadima El-Hassan, 1997. "Evaluation of Derivative Security Prices in the Heath-Jarrow-Morton Framework as Path Integrals Using Fast Fourier Transform Techniques," Working Paper Series 72, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
  3. Robert Jarrow & Stuart Turnbull, 1994. "Delta, gamma and bucket hedging of interest rate derivatives," Applied Mathematical Finance, Taylor & Francis Journals, vol. 1(1), pages 21-48.
  4. Chan, K C, et al, 1992. " An Empirical Comparison of Alternative Models of the Short-Term Interest Rate," Journal of Finance, American Finance Association, vol. 47(3), pages 1209-27, July.
  5. Peter Ritchken & L. Sankarasubramanian, 1995. "Volatility Structures Of Forward Rates And The Dynamics Of The Term Structure," Mathematical Finance, Wiley Blackwell, vol. 5(1), pages 55-72.
  6. Andrew Carverhill, 1994. "When Is The Short Rate Markovian?," Mathematical Finance, Wiley Blackwell, vol. 4(4), pages 305-312.
  7. Hull, John & White, Alan, 1990. "Pricing Interest-Rate-Derivative Securities," Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 573-92.
  8. repec:cup:cbooks:9780521321969 is not listed on IDEAS
  9. Brenner, Robin J. & Harjes, Richard H. & Kroner, Kenneth F., 1996. "Another Look at Models of the Short-Term Interest Rate," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 31(01), pages 85-107, March.
  10. R. Bhar & C. Chiarella, 1997. "Transformation of Heath?Jarrow?Morton models to Markovian systems," The European Journal of Finance, Taylor & Francis Journals, vol. 3(1), pages 1-26.
  11. Bhar, R. & Hunt, D.F., 1993. "Predicting the Short Term Forward Interest Rate Structure Using a Parsimonious Model," Papers e9307, Western Sydney - School of Business And Technology.
  12. Cox, John C. & Ingersoll, Jonathan Jr. & Ross, Stephen A., 1981. "The relation between forward prices and futures prices," Journal of Financial Economics, Elsevier, vol. 9(4), pages 321-346, December.
  13. Carl Chiarella & Nadima El-Hassan, 1996. "A Preference Free Partial Differential Equation for the Term Structure of Interest Rates," Working Paper Series 63, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
  14. Ram Bhar & Carl Chiarella, 1995. "The Estimation of the Heath-Jarrow-Morton Model by Use of Kalman Filtering Techniques," Working Paper Series 54, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
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