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A Maximum Likelihood Approach to Estimation of Heath-Jarrow-Morton Models

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Abstract

Research on the Heath-Jarrow-Morton (1992) term structure models so far has focused on the class having time-deterministic instantaneous forward rate volatility. In this case the forward rate is Markovian, even if the spot rate process is not. However, this Markovian feature can only be used under the historical measure, involving two unsatisfactory assumptions: one on market price risk, usually made for pure mathematical tractability, the other to use futures yields as a proxy for the instantaneous forward rate, which may result in estimation bias. This paper circumvents both of these assumptions. First, the bias is quantified and shown to be non-negligible. Then futures contracts are treated as derivative instruments written on forward rates to derive the full information maximum likelihood estimator for observable futures prices, using both time series and cross-sectional data, without the need to assume and estimate any functional forms for the market price of interest rate risk. The derivation involves the likelihood transformation method of Duan (1994). The method is then applied to the estimation of a humped forward rate volatility model for Eurodollar futures series traded on the Chicago Mercantile Exchange.

Suggested Citation

  • Ram Bhar & Carl Chiarella & Thuy Duong To, 2002. "A Maximum Likelihood Approach to Estimation of Heath-Jarrow-Morton Models," Research Paper Series 80, Quantitative Finance Research Centre, University of Technology, Sydney.
  • Handle: RePEc:uts:rpaper:80
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    File URL: http://www.qfrc.uts.edu.au/research/research_papers/rp80.pdf
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    1. 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.
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    6. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    7. Chapman, David A & Long, John B, Jr & Pearson, Neil D, 1999. "Using Proxies for the Short Rate: When Are Three Months Like an Instant?," Review of Financial Studies, Society for Financial Studies, vol. 12(4), pages 763-806.
    8. Hull, John & White, Alan, 1990. "Pricing Interest-Rate-Derivative Securities," Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 573-592.
    9. Jurgen A. Doornik & Henrik Hansen, 2008. "An Omnibus Test for Univariate and Multivariate Normality," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 70(s1), pages 927-939, December.
    10. 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.
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    12. Carl Chiarella & Oh Kang Kwon, 2001. "Forward rate dependent Markovian transformations of the Heath-Jarrow-Morton term structure model," Finance and Stochastics, Springer, vol. 5(2), pages 237-257.
    13. Brennan, Michael J. & Schwartz, Eduardo S., 1979. "A continuous time approach to the pricing of bonds," Journal of Banking & Finance, Elsevier, vol. 3(2), pages 133-155, July.
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    15. Ramaprasad Bhar & Carl Chiarella, 1997. "Interest rate futures: estimation of volatility parameters in an arbitrage-free framework," Applied Mathematical Finance, Taylor & Francis Journals, vol. 4(4), pages 181-199.
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    Cited by:

    1. Laurini, Márcio Poletti & Ohashi, Alberto, 2015. "A noisy principal component analysis for forward rate curves," European Journal of Operational Research, Elsevier, vol. 246(1), pages 140-153.
    2. Lee, Kiseop & Xu, Mingxin, 2007. "Parameter estimation from multinomial trees to jump diffusions with k means clustering," MPRA Paper 3307, University Library of Munich, Germany, revised 26 Apr 2007.

    More about this item

    Keywords

    term structure; heath-jarrow-morton; time-deterministic forward volatility; humped forward volatility model; full information maximum likelihood;

    JEL classification:

    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • E43 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Interest Rates: Determination, Term Structure, and Effects
    • 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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