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.
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Paper provided by Quantitative Finance Research Centre, University of Technology, Sydney in its series Research Paper Series with number
80.
Find related papers by JEL classification: C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation E43 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Determination of Interest Rates; Term Structure of Interest Rates G12 - Financial Economics - - General Financial Markets - - - Asset Pricing G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
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