Journal of Applied Mathematics
Volume 2004 (2004), Issue 4, Pages 293-309
doi:10.1155/S1110757X04306133

Maximum likelihood estimator of the volatility of forward rates driven by geometric spatial AR sheet

József Gáll,1 Gyula Pap,1 and Martien C. A. van Zuijlen2

1Faculty of Informatics, University of Debrecen, P.O. Box 12, Debrecen 4010, Hungary
2Department of Mathematics, University of Nijmegen, Toernooiveld 1, Nijmegen 6525 ED, The Netherlands

Received 29 June 2003; Revised 23 March 2004

Copyright © 2004 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Discrete-time forward interest rate curve models are studied, where the curves are driven by a random field. Under the assumption of no-arbitrage, the maximum likelihood estimator of the volatility parameter is given and its asymptotic behaviour is studied. First, the so-called martingale models are examined, but we will also deal with the general case, where we include the market price of risk in the discount factor.