Joint ML estimation of all parameters in a discrete time random field HJM type interest rate model

TL;DR

This paper develops a statistical framework for estimating parameters in discrete-time Heath-Jarrow-Morton interest rate models driven by spatial autoregression fields, establishing consistency and asymptotic normality of maximum likelihood estimators.

Contribution

It provides the first rigorous proof of the consistency and asymptotic normality of ML estimators in these complex interest rate models with non-i.i.d. data.

Findings

ML estimators are strongly consistent.

Estimators are asymptotically normal.

Results apply to models with stochastic discounting factors.

Abstract

We consider discrete time Heath-Jarrow-Morton type interest rate models, where the interest rate curves are driven by a geometric spatial autoregression field. Strong consistency and asymptotic normality of the maximum likelihood estimators of the parameters are proved for stable no-arbitrage models containing a general stochastic discounting factor, where explicit form of the ML estimators is not available given a non-i.i.d. sample. The results form the basis of further statistical problems in such models.