Parameter estimation in CKLS model by continuous observations

Abstract

We consider a stochastic differential equation of the form $dr_t = (a - b r_t) dt + \sigma r_t^\beta dW_t$, where $a$, $b$ and $\sigma$ are positive constants, $\beta\in(\frac12,1)$. We study the estimation of an unknown drift parameter $(a,b)$ by continuous observations of a sample path $\{r_t, t \in [0,T]\}$. 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 $\beta=\frac12$. The identification of the diffusion parameters $\sigma$ and $\beta$ is discussed as well.