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

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.