Estimation Of Stochastic Volatility Research Articles

The non-linear impact of monetary policy on shifts in economic policy uncertainty: evidence from the United States of America

A stochastic volatility estimation of VIX index’s latent volatility is used for the United States of America, as a proxy for the adjustments in the levels of investors’ uncertainty related to current and future economic policies. The impact of monetary policy stance on such measure is examined in the framework of the distributed lag non-linear models (DLNM). We place this analysis in the literature stream emphasizing the various sources of heterogeneity concerning investors’ expectations. The main finding is that the monetary policy does impact non-linearly the adjustments in investors’ predictions. While a tighter monetary policy does generally contribute to an increase in VIX’s latent volatility, the shape of such effect varies across different GLM and GAM specifications of DLNM. This outcome remains robust, even if: (1) we control for the global price of Brent crude and consumers’ confidence; (2) we use, instead of the stochastic framework, a Markov-switching GARCH-based estimator; or (3) we replace the monetary policy instrument with monetary policy uncertainty. We argue that accounting for its nonlinear effects on financial markets is of critical importance for the design of a monetary policy pursuing global financial stability.

Modelling Inflation Dynamics and Global Oil Price Shocks in OAPEC Countries: TVP-VAR

This paper aims to examine the dynamic pass-through effect of oil price shocks on inflation in OAPEC countries using quarterly data ranging from 1990:Q1 to 2022:Q4. The incorporation of the TVP-VAR model along with the Markov Chain Monte Carlo method with stochastic volatility estimation offers a robust framework for capturing the time-varying nature of the relationship. Additionally, the analysis of the Impulse Response Function provides valuable insights into the short-term and long-term dynamics following oil price shocks. The results demonstrate a significant positive pass-through effect of oil prices on inflation in the sample member states, with heterogeneous magnitude and persistence. These variations are attributed to diversity in oil dependency, exchange rate regimes, monetary policy frameworks and the degree of openness to global markets. The study suggests the need for effective inflation management strategies and appropriate policy responses to oil price fluctuations. Furthermore, policymakers may consider adjusting exchange rates, interest rates, or trade policies to manage inflationary pressures effectively.

Approximate Bayesian Estimation of Stochastic Volatility in Mean Models Using Hidden Markov Models: Empirical Evidence from Emerging and Developed Markets

Approximate Bayesian Estimation of Stochastic Volatility in Mean Models Using Hidden Markov Models: Empirical Evidence from Emerging and Developed Markets

Modeling Univariate and Multivariate Stochastic Volatility in R with stochvol and factorstochvol

Stochastic volatility (SV) models are nonlinear state-space models that enjoy increasing popularity for fitting and predicting heteroskedastic time series. However, due to the large number of latent quantities, their efficient estimation is non-trivial and software that allows to easily fit SV models to data is rare. We aim to alleviate this issue by presenting novel implementations of four SV models delivered in two R packages. Several unique features are included and documented. As opposed to previous versions, stochvol is now capable of handling linear mean models, heavy-tailed SV, and SV with leverage. Moreover, we newly introduce factorstochvol which caters for multivariate SV. Both packages offer a user-friendly interface through the conventional R generics and a range of tailor-made methods. Computational efficiency is achieved via interfacing R to C++ and doing the heavy work in the latter. In the paper at hand, we provide a detailed discussion on Bayesian SV estimation and showcase the use of the new software through various examples.

Estimation of stochastic volatility and option prices

AbstractThis study suggests a method to estimate a stochastic volatility model incorporating both information on high/low prices and the leverage effect. The likelihood‐based inference of Markov Chain Monte Carlo is conducted to estimate parameters and volatility. Simulation reveals that our method improves estimation and pricing options. We also find that the information on high/low prices is more likely to contribute to the improvement than the leverage effect.

Bayesian semiparametric multivariate stochastic volatility with application

In this article, we establish a Cholesky-type multivariate stochastic volatility estimation framework, in which we let the innovation vector follow a Dirichlet process mixture (DPM), thus enabling us to model highly flexible return distributions. The Cholesky decomposition allows parallel univariate process modeling and creates potential for estimating high-dimensional specifications. We use Markov chain Monte Carlo methods for posterior simulation and predictive density computation. We apply our framework to a five-dimensional stock-return data set and analyze international stock-market co-movements among the largest stock markets. The empirical results show that our DPM modeling of the innovation vector yields substantial gains in out-of-sample density forecast accuracy when compared with the prevalent benchmark models.

Nonparametric Estimation of Volatility and Its Parametric Analogs

This paper suggests a nonparametric method for stochastic volatility estimation and its comparison with other widespread econometric algorithms. A major advantage of this approach is that the volatility can be estimated even in the case of its completely unknown probability distribution. As demonstrated below, the new method has better characteristics against the popular parametric algorithms based on the GARCH model and Kalman filter.

Bayesian estimation of Gegenbauer long memory processes with stochastic volatility: methods and applications

Abstract This paper discusses a time series model which has generalized long memory in the mean process with stochastic volatility errors and develops a new Bayesian posterior simulator that couples advanced posterior maximisation techniques, as well as traditional latent stochastic volatility estimation procedures. Details are provided on the estimation process, data simulation, and out of sample performance measures. We conduct several rigorous simulation studies and verify our results for in and out of sample behaviour. We further compare the goodness of fit of the generalized process to the standard long memory model by considering two empirical studies on the US Consumer Price Index (CPI) and the US equity risk premium (ERP).

Estimation of stochastic volatility by using Ornstein–Uhlenbeck type models

In this study, we develop a technique for estimating the stochastic volatility (SV) of a financial time series by using Ornstein–Uhlenbeck type models. Using the daily closing prices from developed and emergent stock markets, we conclude that the incorporation of stochastic volatility into the time varying parameter estimation significantly improves the forecasting performance via Maximum Likelihood Estimation. Furthermore, our estimation algorithm is feasible with large data sets and have good convergence properties.

GMC/GEL estimation of stochastic volatility models

ABSTRACTIn this article we discuss the estimation of stochastic volatility (SV) using generalized empirical likelihood/minimum contrast methods based on moment conditionsmodels. We show via Monte Carlo simulations that the proposed methods have superior or equivalent performance to the other alternative methods, and, additionally, they offer robustness properties in the presence of heavy-tailed distributions and outliers.

Estimation of Stochastic Volatility with a Compensated Poisson Jump Using Quadratic Variation

The degree of variation of trading prices with respect to time is volatility-measured by the standard deviation of returns. We present the estimation of stochastic volatility from the stochastic differential equation for evenly spaced data. We indicate that, the price process is driven by a semi-martingale and the data are evenly spaced. The results of Malliavin and Mancino [1] are extended by adding a compensated poisson jump that uses a quadratic variation to calculate volatility. The volatility is computed from a daily data without assuming its functional form. Our result is well suited for financial market applications and in particular the analysis of high frequency data for the computation of volatility.

Multivariate Stochastic Volatility Estimation with Sparse Grid Integration

Multivariate stochastic volatility (MSV) models are nonlinear state space models that require either linear approximations or computationally demanding methods for handling the high dimensional integrals arising in the estimation problems of the latent volatilities and model parameters. Markov Chain Monte Carlo (MCMC) methods, which are based on Monte Carlo simulations using special sampling schemes, are by far the most studied method with several extensions and versions in previous stochastic volatility estimation studies. Exact nonlinear filters and particularly numerical integration based methods, such as the method proposed in this paper, were neglected and not studied as extensively as MCMC methods especially in the multivariate settings of stochastic volatility models. Filtering, smoothing, prediction and parameter estimation algorithms based on the sparse grid integration method are developed and proposed for a general MSV model. The proposed algorithms for estimation are compared with an implementation of MCMC based algorithms in a simulation study followed by an illustration of the proposed algorithms on empirical data of foreign exchange rate returns of US dollars and Euro. Results showed that the proposed algorithms based on the sparse grid integration method can be promising alternatives to the MCMC based algorithms especially in practical applications with their appealing characteristics.

Moment-based estimation of stochastic volatility

This paper makes use of the distributional information contained in high-frequency data to test for the specification of the functional form of the volatility process within the class of stochastic volatility models.Itō’s calculus is implemented in order to obtain the first and second conditional moment of the driving stochastic differential equation for the volatility process. These analytical expressions are augmented by their lag and lag squared and are used to form the corresponding GMM estimator.The base case stochastic volatility model is extended to allow for the leverage effect and jumps in returns. Empirical estimation confirms the presence of fast mean reversion in volatility and jumps in returns for the 5-min S&P 500 stock market index. Further estimation results also seem to indicate the presence of jumps in the volatility process that are correlated to the jumps in returns.

State estimation of nonlinear stochastic systems using a novel meta-heuristic particle filter

This paper proposes a new version of the particle filtering (PF) algorithm based on the invasive weed optimization (IWO) method. The sub-optimality of the sampling step in the PF algorithm is prone to estimation errors. In order to avert such approximation errors, this paper suggests applying the IWO algorithm by translating the sampling step into a nonlinear optimization problem. By introducing an appropriate fitness function, the optimization problem is properly treated. The validity of the proposed method is evaluated against three distinct examples: the stochastic volatility estimation problem in finance, the severely nonlinear waste water sludge treatment plant, and the benchmark target tracking on re-entry problem. By simulation analysis and evaluation, it is verified that applying the suggested IWO enhanced PF algorithm (PFIWO) would contribute to significant estimation performance improvements.

Nonparametric particle filtering and smoothing with quasi-Monte Carlo sampling

Sequential Monte Carlo methods (also known as particle filters and smoothers) are used for filtering and smoothing in general state-space models. These methods are based on importance sampling. In practice, it is often difficult to find a suitable proposal which allows effective importance sampling. This article develops an original particle filter and an original particle smoother which employ nonparametric importance sampling. The basic idea is to use a nonparametric estimate of the marginally optimal proposal. The proposed algorithms provide a better approximation of the filtering and smoothing distributions than standard methods. The methods’ advantage is most distinct in severely nonlinear situations. In contrast to most existing methods, they allow the use of quasi-Monte Carlo (QMC) sampling. In addition, they do not suffer from weight degeneration rendering a resampling step unnecessary. For the estimation of model parameters, an efficient on-line maximum-likelihood (ML) estimation technique is proposed which is also based on nonparametric approximations. All suggested algorithms have almost linear complexity for low-dimensional state-spaces. This is an advantage over standard smoothing and ML procedures. Particularly, all existing sequential Monte Carlo methods that incorporate QMC sampling have quadratic complexity. As an application, stochastic volatility estimation for high-frequency financial data is considered, which is of great importance in practice. The computer code is partly available as supplemental material.

Multi‐variate stochastic volatility modelling using Wishart autoregressive processes

A new multi‐variate stochastic volatility estimation procedure for financial time series is proposed. A Wishart autoregressive process is considered for the volatility precision covariance matrix, for the estimation of which a two step procedure is adopted. The first step is the conditional inference on the autoregressive parameters and the second step is the unconditional inference, based on a Newton‐Raphson iterative algorithm. The proposed methodology, which is mostly Bayesian, is suitable for medium dimensional data and it bridges the gap between closed‐form estimation and simulation‐based estimation algorithms. An example, consisting of foreign exchange rates data, illustrates the proposed methodology.

Bayesian State‐Space Estimation of Stochastic Volatility for Storable Commodities

Bayesian State‐Space Estimation of Stochastic Volatility for Storable Commodities

Estimation of stochastic volatility with LRD

Understanding the behaviour of market prices is not simple. Stock market prices tend to have complicated distributions with strong skewness and fat tails. One important step in forecasting tomorrow’s price is to estimate the volatility, i.e. how much tomorrow’s price is expected to differ from today’s price. In this paper the volatility is assumed to be a lognormal random process and in addition, it may display long-range dependence (LRD). The aim is to obtain the estimates of the mean, standard deviation and LRD parameter of the volatility process of the S&P 500.

Efficient estimation of stochastic volatility using noisy observations: a multi-scale approach

With the availability of high-frequency financial data, nonparametric estimation of the volatility of an asset return process becomes feasible. A major problem is how to estimate the volatility consistently and efficiently, when the observed asset returns contain error or noise, for example, in the form of microstructure noise. The issue of consistency has been addressed in the recent literature. However, the resulting estimator is not efficient. In work by Zhang, Myland and Aït-Sahalia, the best estimator converges to the true volatility only at the rate of n-1/6. In this paper, we propose an estimator, the multi-scale realized volatility (MSRV), which converges to the true volatility at the rate of n-1/4, which is the best attainable. We show a central limit theorem for the MSRV estimator, which permits intervals to be set for the true integrated volatility on the basis of the MSRV.

A rational probability density approach to stochastic volatility estimation

In the area of financial time series the Black-Scholes model is often used. However, it is well-known that although the volatility is assumed to be constant in the Black-Scholes model, in practice it is varying in time. This has led to the investigation of more general models in which the volatility is allowed to vary. In one class of such models the dynamic behavior of volatility is described by some stochastic process. A problem with such models is that it is generally very difficult to solve the volatility estimation problem for such models: the calculation of the conditional density of the volatility at some point in time, given the observations up till that point in time, is usually a difficult task for which there are no closed form expressions. In the present paper a class of models of the same type is presented, which however has the advantage that for these models the volatility estimation problem can be solved exactly. In our models all disturbances have a rational probability density function on the real line.