A New Algorithm for Approximate Maximum Likelihood Estimation in Sub-fractional Chan-Karolyi-Longstaff-Sanders Model
Jaya P. N. Bishwal *
Department of Mathematics and Statistics, University of North Carolina at Charlotte, 376 Fretwell Bldg., 9201 University City Blvd. Charlotte, NC 28223, USA.
*Author to whom correspondence should be addressed.
Abstract
The paper introduces several approximate maximum likelihood estimators of the parameters of the sub-fractional Chan-Karolyi-Longstaff-Sanders (CKLS) interest rate model and obtains their rates of convergence. A new algorithm inspired by Newton-Cotes formula is presented to improve the accuracy of estimation. The estimators are useful for simulation of interest rates. The proposed new algorithm could be useful for other stochastic computation. It also proposes a generalization of the CKLS interest rate model with sub-fractional Brownian motion drivers which preserves medium range memory.
Keywords: It^o stochastic differential equation, sub-fractional Brownian motion, sub-fractional diffusion process, discrete observations, term structure of interest rates, approximate maximum likelihood estimators, Newton-Cotes distribution