Related papers: Local asymptotic properties for Cox-Ingersoll-Ross…
In this paper, we consider a one-dimensional jump-type Cox-Ingersoll-Ross process driven by a Brownian motion and a subordinator, whose growth rate is an unknown parameter. Considering the process observed continuously or discretely at high…
We investigate the long-time asymptotic behavior of various entropy measures associated with the Cox-Ingersoll-Ross (CIR) and squared Bessel processes. As the one-dimensional distributions of both processes follow noncentral chi-squared…
The present paper investigates Cox-Ingersoll-Ross (CIR) processes of dimension less than 1, with a focus on obtaining an equation of a new type including local times for the square root of the CIR process. We utilize the fact that…
We study the sticky Cox-Ingersoll-Ross (CIR) process in one dimension, a diffusion on $[0,\infty)$ with a sticky boundary condition at the origin, arising as the marginal process in a sparse Bayesian inference framework based on…
We consider a pure-jump stable Cox-Ingersoll-Ross ($\alpha$-stable CIR) process driven by a non-symmetric stable L{\'e}vy process with jump activity $\alpha$ $\in$ (1, 2) and we address the joint estimation of drift, scaling and jump…
This paper provides insight into the estimation and asymptotic behavior of parameters in interest rate models, focusing primarily on the Cox-Ingersoll-Ross (CIR) process and its extension -- the more general Chan-Karolyi-Longstaff-Sanders…
In this paper, we consider a stochastic model based on the Cox- Ingersoll- Ross model (CIR). The stochastic model is parameterized analytically by applying It\^o's calculus and the trend functions of the proposed process is calculated. The…
We study the estimation of a stable Cox-Ingersoll-Ross model, which is a special subcritical continuous-state branching process with immigration. The process is characterized in terms of some stochastic equations. The exponential ergodicity…
Cox-Ingersoll-Ross (CIR) processes are widely used in financial modeling such as in the Heston model for the approximative pricing of financial derivatives. Moreover, CIR processes are mathematically interesting due to the irregular square…
The drift sequential parameter estimation problems for the Cox-Ingersoll-Ross (CIR) processes under the limited duration of observation are studied. Truncated sequential estimation methods for both scalar and {two}-dimensional parameter…
We study the large deviations for Cox-Ingersoll-Ross (CIR) processes with small noise and state-dependent fast switching via associated Hamilton-Jacobi equations. As the separation of time scales, when the noise goes to $0$ and the rate of…
We study local asymptotic properties of likelihood ratios of certain Heston models. We distinguish three cases: subcritical, critical and supercritical models. For the drift parameters, local asymptotic normality is proved in the…
We study asymptotic properties of conditional least squares estimators for the drift parameters of two-factor affine diffusions based on continuous time observations. We distinguish three cases: subcritical, critical and supercritical. For…
We propose a change detection method for the famous Cox--Ingersoll--Ross model. This model is widely used in financial mathematics and therefore detecting a change in its parameters is of crucial importance. We develop one- and two-sided…
For a diffusion process $X(t)$ of drift $\mu(x)$ and of diffusion coefficient $D=1/2$, we study the joint distribution of the two local times $A(t)= \int_{0}^{t} d\tau \delta(X(\tau)) $ and $B(t)= \int_{0}^{t} d\tau \delta(X(\tau)-L) $ at…
We study sufficient conditions for a local asymptotic mixed normality property of statistical models. We develop a scheme with the $L^2$ regularity condition proposed by Jeganathan [\textit{Sankhya Ser. A} \textbf{44} (1982) 173--212] so…
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,…
We present new high order approximations schemes for the Cox-Ingersoll-Ross (CIR) process that are obtained by using a recent technique developed by Alfonsi and Bally (2021) for the approximation of semigroups. The idea consists in using a…
This paper studies two related stochastic processes driven by Brownian motion: the Cox-Ingersoll-Ross (CIR) process and the Bessel process. We investigate their shared and distinct properties, focusing on time-asymptotic growth rates,…
We consider a simple mean reverting diffusion process, with piecewise constant drift and diffusion coefficients, discontinuous at a fixed threshold. We discuss estimation of drift and diffusion parameters from discrete observations of the…