Estimating Affine Multifactor Term Structure Models Using Closed-Form Likelihood Expansions

We develop and implement a technique for maximum likelihood estimation in closed-form of multivariate affine yield models of the term structure of interest rates. Affine yield models owe their popularity among both practitioners and academics to the fact that they allow for straightforward pricing of bonds and other interest rate derivatives. However, estimation still poses many challenging issues. Applying the method of A‹t-Sahalia (2001), we derive closed-form approximations to the likelihood functions for all nine of the Dai and Singleton (2000) canonical affine models corresponding to dimensions 1, 2 and 3 of the state vector. Monte Carlo simulations reveal that our technique produces extremely accurate approximations of the exact likelihood function.

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