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Strong consistency of parameter estimators and simulations in a forward interest rate model

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Strong consistency of parameter estimators and simulations in a forward interest rate model

Erika F¨ ul¨ op

Abstract. We study the strong consistency of an autoregression parameter of a discrete time Heath-Jarrow-Morton type forward interest rate model, where the interest rate curves are driven by a geometric spatial autoregression field. In this paper the size of the subsamples corresponding to different time points is fixed: the observations of the forward rates are given for the same time to maturity values at each time point.

We show the consistency in the stable case and in an unstable case and give empirical results based on simulations as well.

Keywords. HJM forward interest rate models, geometric spatial autoregression field, strong consistency of ML estimators, simulations with R

AMS subject classification (2000): 62F12, 91B84, 65C60

This research has been supported by the European Union and Hungary, and co-financed by the European Social Fund within the confines of accentuated project ”Nemzeti Kiv´al´os´ag Program – Hazai hallgat´oi, illetve kutat´oi szem´elyi t´amogat´ast biztos´ıt´o rendszer kidolgoz´asa ´es m˝uk¨odtet´ese konvergencia program” under Grant No. T ´AMOP 4.2.4.A/2-11-1-2012-0001.

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