Parameters estimation of a Threshold Chan-Karolyi-Longstaff-Sanders process from continuous and discrete observations

2025/04/14 by Sara Mazzonetto, Mazzonetto, Sara, Benoît Nieto +1 · 2 citations
Economics, Econometrics and Finance · Business, Management and Accounting · Decision Sciences · #Stochastic processes and financial applications #Supply Chain and Inventory Management #Probability and Risk Models

paper · pdf · doi:10.48550/arxiv.2504.10022

Abstract

We consider a continuous time process that is self-exciting and ergodic, called threshold Chan-Karolyi-Longstaff-Sanders (CKLS) process. This process is a generalization of various models in econometrics, such as Vasicek model, Cox-Ingersoll-Ross, and Black-Scholes, allowing for the presence of several thresholds which determine changes in the dynamics. We study the asymptotic behavior of maximum-likelihood and quasi-maximum-likelihood estimators of the drift parameters in the case of continuous time and discrete time observations. We show that for high frequency observations and infinite horizon the estimators satisfy the same asymptotic normality property as in the case of continuous time observations. We also discuss diffusion coefficient estimation. Finally, we apply our estimators to simulated and real data to motivate considering (multiple) thresholds.

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• From CKLS Process to CIR-type and OU-type Processes: Using a Twice-differentiable Mapping and Generalized Girsanov's Theorem
• Estimation of the elasticity for CKLS model from high-frequency observations

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