Maximum Likelihood Estimation in the Mixed Fractional Vasicek Model

Abstract

We investigate the asymptotic properties of maximum likelihood estimators of the drift parameters for fractional Vasicek model driven by a sub-fractional Brownian motion.

Asymptotic Growth of Sample Paths of Tempered Fractional Brownian Motions, with Statistical Applications to Vasicek-Type Models

“…Additionally, several researchers have delved into statistical inference within the Model (1), introducing different types of Gaussian noises. For instance, Prakasa Rao considered maximum likelihood estimation for sub-fractional [13] and mixed fractional [14] Vasicek models. In [15], the authors investigated least-squares estimation in the Vasicek model driven by a Gaussian process belonging to a wide class, including FBM, bifractional, and sub-fractional Brownian motions (see also [16] for the application of these results to other examples of noise).…”

Interest Rate Modelling in the Presence of Discontinuities and its Sensitivities

“…Wu and Liang (2018) studied the Vasicek model with mixed-exponential jumps and its applications in finance and insurance, by first obtaining the explicit form of Laplace transform of the model distribution through the aid of piecewise deterministic Markov process theory and the martingale theory. Rao (2021) discussed asymptotic properties of the maximum likelihood estimator of unknown parameters in a fractional Vasicek model driven by a fractional Brownian motion, while Guo (2021) evaluated the benefit of bias-correction method in enhancing the Vasicek model for market risk management. In the next section, we discuss the important mathematical tools needed for the success of the paper.…”

Parametric Estimation for Processes Driven by Infinite Dimensional Mixed Fractional Brownian Motion

“…The problem of estimation of parameters for processes driven by processes which are mixtures of independent Brownian and fractional Brownian motions started from the works of Cheridito (2001), Rudomino-Dusyatska (2003) and more recently in Prakasa Rao (2015a,b;2017a,b;2018a,b;, 2020, 2021a among others. Mixed fractional Brownian models were studied in Mishura (2008) and Prakasa Rao (2010) .…”