Specifying a consistent joint maximum-likelihood (JMLE) approach to testing bond models

In this paper we extend the results derived in our earlier work to develop a methodology to employ the maximum-likelihood estimation technique for the pricing of interest rate instruments. In order to price bonds and their derivative assets, researchers must identify a preference parameter in addition to the dynamics for the interest rate process. There are two approaches to obtaining estimators for both preference and dynamics parameters: (1) a two-stage approach and (2) a single-stage joint maximum-likelihood (JMLE) approach. The first approach, while tractable, suffers from serious drawbacks, primarily those relating to the use of the estimates from the first stage in estimating parameters in the second stage. In this paper, we develop the theory necessary for joint maximum-likelihood (JMLE) over the set of bond prices and the interest rate. We operationalize the theory by assuming that the error processes for all coupon bonds are mutually independent and uniformly distributed with a mean of zero. This specification is at least partially justifiable by the observation that since market prices are quoted in 1/32 of a dollar, theoretical prices must always be rounded either up or down. JML estimators can be obtained from the joint log-likelihood function by the methods of sequential quadratic programming.