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

Ram Bhar, Carl Chiarella and Thuy Duong To
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Ram Bhar: School of Banking and Finance, University of New South Wales
Thuy Duong To: School of Banking and Finance, University of NSW

No 80, Research Paper Series from Quantitative Finance Research Centre, University of Technology, Sydney

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.

Keywords: term structure; heath-jarrow-morton; time-deterministic forward volatility; humped forward volatility model; full information maximum likelihood (search for similar items in EconPapers)
JEL-codes: C51 E43 G12 G13 (search for similar items in EconPapers)
Pages: 32 pages
Date: 2002-05-01
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Citations: View citations in EconPapers (7)

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