Parameter estimation in CKLS model by continuous observations

05/28/2021

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by   Yuliya Mishura, et al.

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We consider a stochastic differential equation of the form dr_t = (a - b r_t) dt + σ r_t^β dW_t, where a, b and σ are positive constants, β∈(1/2,1). We study the estimation of an unknown drift parameter (a,b) by continuous observations of a sample path {r_t, 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=1/2. The identification of the diffusion parameters σ and β is discussed as well.