# Asymptotic properties of maximum-likelihood estimators for Heston models based on continuous time observations

@article{Barczy2013AsymptoticPO, title={Asymptotic properties of maximum-likelihood estimators for Heston models based on continuous time observations}, author={M. Barczy and G. Pap}, journal={Statistics}, year={2013}, volume={50}, pages={389 - 417} }

We study asymptotic properties of maximum-likelihood estimators for Heston models based on continuous time observations of the log-price process. We distinguish three cases: subcritical (also called ergodic), critical and supercritical. In the subcritical case, asymptotic normality is proved for all the parameters, while in the critical and supercritical cases, non-standard asymptotic behaviour is described.

#### 21 Citations

Maximum likelihood estimators for a jump-type Heston model

- Mathematics, Economics
- 2015

We study asymptotic properties of maximum likelihood estimators of drift parameters for a jump-type Heston model based on continuous time observations of the price process together with its jump… Expand

Asymptotic properties of maximum likelihood estimator for the growth rate of a stable CIR process based on continuous time observations

- Mathematics, Economics
- 2019

ABSTRACT We consider a stable Cox–Ingersoll–Ross process driven by a standard Wiener process and a spectrally positive strictly stable Lévy process, and we study asymptotic properties of the maximum… Expand

Parameter estimation for the subcritical Heston model based on discrete time observations

- Mathematics, Economics
- 2014

We study asymptotic properties of some (essentially conditional least squares) parameter estimators for the subcritical Heston model based on discrete time observations derived from conditional least… Expand

On conditional least squares estimation for affine diffusions based on continuous time observations

- Mathematics
- 2017

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:… Expand

Least-Squares Estimation for the Subcritical Heston Model Based on Continuous-Time Observations

- Mathematics, Economics
- 2015

We prove strong consistency and asymptotic normality of least-squares estimators for the subcritical Heston model based on continuous-time observations. We also present some numerical illustrations… Expand

Asymptotic properties of maximum likelihood estimator for the growth rate for a jump-type CIR process based on continuous time observations

- Mathematics, Economics
- 2016

We consider a jump-type Cox--Ingersoll--Ross (CIR) process driven by a standard Wiener process and a subordinator, and we study asymptotic properties of the maximum likelihood estimator (MLE) for its… Expand

Weighted least-squares estimation for the subcritical Heston process

- Journal of Applied Probability
- 2018

Abstract We simultaneously estimate the four parameters of a subcritical Heston process. We do not restrict ourselves to the case where the stochastic volatility process never reaches zero. In order… Expand

Weighted least-squares estimation for the subcritical Heston process

- Mathematics, Computer Science
- J. Appl. Probab.
- 2018

This work simultaneously estimate the four parameters of a subcritical Heston process and proposes to make use of a weighted least squares estimator, establishing strong consistency and asymptotic normality for this estimator. Expand

Local asymptotic properties for the growth rate of a jump-type CIR process

- Mathematics
- 2019

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 a unknown parameter. The L\'evy measure of the… Expand

Moderate deviations for parameters estimation in a geometrically ergodic Heston process

- Mathematics
- 2018

We establish a moderate deviation principle for the maximum likelihood estimator of the four parameters of a geometrically ergodic Heston process. We also obtain moderate deviations for the maximum… Expand

#### References

SHOWING 1-10 OF 57 REFERENCES

Parameter estimation for the subcritical Heston model based on discrete time observations

- Mathematics, Economics
- 2014

We study asymptotic properties of some (essentially conditional least squares) parameter estimators for the subcritical Heston model based on discrete time observations derived from conditional least… Expand

Local asymptotic quadraticity of statistical experiments connected with a Heston model

- Mathematics
- 2015

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… Expand

Asymptotic Behavior of the Maximum Likelihood Estimator for Ergodic and Nonergodic Square-Root Diffusions

- Mathematics
- 2013

This article deals with the problem of global parameter estimation in the Cox-Ingersoll-Ross (CIR) model (X t ) t≥0. This model is frequently used in finance for example, to model the evolution of… Expand

Parameter estimation for a subcritical affine two factor model

- Mathematics
- 2013

For an affine two factor model, we study the asymptotic properties of the maximum likelihood and least squares estimators of some appearing parameters in the so-called subcritical (ergodic) case… Expand

Asymptotic properties of estimators in a stable Cox–Ingersoll–Ross model

- Mathematics
- 2013

We study the estimation of a stable Cox–Ingersoll–Ross model, which is a special subcritical continuous-state branching process with immigration. The exponential ergodicity and strong mixing property… Expand

Parameter Estimation for the Square-Root Diffusions: Ergodic and Nonergodic Cases

- Mathematics
- 2012

This article deals with the problem of parameter estimation in the Cox-Ingersoll-Ross (CIR) model (X t ) t≥0. This model is frequently used in finance for example as a model for computing the… Expand

On parameter estimation for critical affine processes

- Mathematics, Economics
- 2012

First we provide a simple set of sufficient conditions for the weak convergence of scaled affine processes with state space $R_+ \times R^d$. We specialize our result to one-dimensional continuous… Expand

Parameter estimation in stochastic differential equations

- Mathematics
- 2007

Continuous Sampling.- Parametric Stochastic Differential Equations.- Rates of Weak Convergence of Estimators in Homogeneous Diffusions.- Large Deviations of Estimators in Homogeneous Diffusions.-… Expand

Maximum Likelihood and Gaussian Estimation of Continuous Time Models in Finance

- Mathematics
- 2007

This paper overviews maximum likelihood and Gaussian methods of estimating continuous time models used in finance. Since the exact likelihood can be constructed only in special cases, much attention… Expand

Estimation for Continuous Branching Processes

- Mathematics
- 1998

The maximum-likelihood estimator for the curved exponential family given by continuous branching processes with immigration is investigated. These processes originated from population biology but… Expand