Parameter estimation in CKLS model by continuous observations

Abstract

We consider a stochastic differential equation of the form drt=(a−brt)dt+σrtβdWt, where a, b and σ are positive constants, β∈(12,1). We study the estimation of an unknown drift parameter (a,b) by continuous observations of a sample path {rt,t∈[0,T]}. We prove the strong consistency and asymptotic normality of the maximum likelihood estimator. We propose another strongly consistent estimator, which generalizes an estimator proposed in Dehtiar et al. (2021) for β=12. The identification of the diffusion parameters σ and β is discussed as well.