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Estimating the Volatility Structure of an Arbitrage-Free Interest Rate Model Via the Futures Markets

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Author Info

  • Ram Bhar

    (School of Banking & Finance, University of New South Wales)

  • Carl Chiarella

    (School of Finance & Economics, University of Technology, Sydney)

  • Thuy-Duong To

    (School of Finance & Economics, University of Technology, Sydney)

Abstract

This paper considers a class of Heath-Jarrow-Morton (1992) term structure models, characterized by time deterministic volatilities for the instantaneous forward rate. The bias that arises from using observed futures yields as a proxy for the unobserved instantaneous forward rate is analyzed. The fact that futures contracts can be viewed as derivative instruments on the forward rate is used to determine the likelihood function for futures prices. The likelihood transformation method of Duan (1994) is then used to obtain the full information maximum likelihood estimator for the observable futures prices. The approach is applied to estimate the volatility structure implied by futures contracts traded on the Chicago Mercantile Exchange.

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File URL: http://128.118.178.162/eps/fin/papers/0409/0409003.pdf
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Bibliographic Info

Paper provided by EconWPA in its series Finance with number 0409003.

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Length: 39 pages
Date of creation: 01 Sep 2004
Date of revision:
Handle: RePEc:wpa:wuwpfi:0409003

Note: Type of Document - pdf; pages: 39
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Web page: http://128.118.178.162

Related research

Keywords: Term structure; Heath-Jarrow-Morton; Yield curve; Forward rate volatility function; Estimation bias; FIML; Likelihood transformation; Futures contracts;

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References

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  1. Robert R. Bliss & Peter Richken, 1996. "Empirical tests of two state-variable Heath-Jarrow models," Proceedings, Federal Reserve Bank of Cleveland, issue Aug, pages 452-481.
  2. Andrew W. Lo, 1986. "Maximum Likelihood Estimation of Generalized Ito Processes with Discretely Sampled Data," NBER Technical Working Papers 0059, National Bureau of Economic Research, Inc.
  3. Michael J. Brennan and Eduardo S. Schwartz., 1979. "A Continuous-Time Approach to the Pricing of Bonds," Research Program in Finance Working Papers 85, University of California at Berkeley.
  4. Ram Bhar & Carl Chiarella, 1995. "Transformation of Heath-Jarrow-Morton Models to Markovian Systems," Working Paper Series 53, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
  5. Moraleda, Juan M. & Vorst, Ton C. F., 1997. "Pricing American interest rate claims with humped volatility models," Journal of Banking & Finance, Elsevier, vol. 21(8), pages 1131-1157, August.
  6. Duan, Jin-Chuan & Simonato, Jean-Guy, 1999. " Estimating and Testing Exponential-Affine Term Structure Models by Kalman Filter," Review of Quantitative Finance and Accounting, Springer, vol. 13(2), pages 111-35, September.
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  8. Amin, Kaushik I. & Morton, Andrew J., 1994. "Implied volatility functions in arbitrage-free term structure models," Journal of Financial Economics, Elsevier, vol. 35(2), pages 141-180, April.
  9. Pearson, Neil D & Sun, Tong-Sheng, 1994. " Exploiting the Conditional Density in Estimating the Term Structure: An Application to the Cox, Ingersoll, and Ross Model," Journal of Finance, American Finance Association, vol. 49(4), pages 1279-1304, September.
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  11. To, Thuy Duong & Carl Chiarella, 2003. "The Jump Component of the Volatility Structure of Interest Rate Futures Markets: An International Comparison," Royal Economic Society Annual Conference 2003 205, Royal Economic Society.
  12. Bliss, Robert R & Ritchken, Peter, 1996. "Empirical Tests of Two State-Variable Heath-Jarrow-Morton Models," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 28(3), pages 452-76, August.
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  16. Carl Chiarella & Oh Kwon, 2003. "Finite Dimensional Affine Realisations of HJM Models in Terms of Forward Rates and Yields," Review of Derivatives Research, Springer, vol. 6(2), pages 129-155, May.
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  21. Brennan, Michael J. & Schwartz, Eduardo S., 1982. "An Equilibrium Model of Bond Pricing and a Test of Market Efficiency," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 17(03), pages 301-329, September.
  22. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "A Theory of the Term Structure of Interest Rates," Econometrica, Econometric Society, vol. 53(2), pages 385-407, March.
  23. Yacine Ait-Sahalia, 2002. "Maximum Likelihood Estimation of Discretely Sampled Diffusions: A Closed-form Approximation Approach," Econometrica, Econometric Society, vol. 70(1), pages 223-262, January.
  24. 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.
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Cited by:
  1. Thuy-Duong To, 2004. "A Note on the Bias of using Futures Rates as a Proxy for the Instantaneous Forward Rate," Research Paper Series 149, Quantitative Finance Research Centre, University of Technology, Sydney.

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