Bayesian Inference of Stochastic Volatility Model by Hybrid Monte Carlo (original) (raw)

Empirical Analysis of Stochastic Volatility Model by Hybrid Monte Carlo Algorithm

Journal of Physics: Conference Series, 2013

The stochastic volatility model is one of volatility models which infer latent volatility of asset returns. The Bayesian inference of the stochastic volatility (SV) model is performed by the hybrid Monte Carlo (HMC) algorithm which is superior to other Markov Chain Monte Carlo methods in sampling volatility variables. We perform the HMC simulations of the SV model for two liquid stock returns traded on the Tokyo Stock Exchange and measure the volatilities of those stock returns. Then we calculate the accuracy of the volatility measurement using the realized volatility as a proxy of the true volatility and compare the SV model with the GARCH model which is one of other volatility models. Using the accuracy calculated with the realized volatility we find that empirically the SV model performs better than the GARCH model.

Financial Time Series Analysis of SV Model by Hybrid Monte Carlo

Lecture Notes in Computer Science, 2000

We apply the hybrid Monte Carlo (HMC) algorithm to the financial time sires analysis of the stochastic volatility (SV) model for the first time. The HMC algorithm is used for the Markov chain Monte Carlo (MCMC) update of volatility variables of the SV model in the Bayesian inference. We compute parameters of the SV model from the artificial financial data and compare the results from the HMC algorithm with those from the Metropolis algorithm. We find that the HMC decorrelates the volatility variables faster than the Metropolis algorithm. We also make an empirical analysis based on the Yen/Dollar exchange rates.

The Usage of Markov Chain Monte Carlo (MCMC) Methods in Time-varying Volatility Models

Journal of Risk & Control, 2023

Markov Chain Monte Carlo (MCMC) techniques, in the context of Bayesian inference, constitute a practical and effective tool to produce samples from an arbitrary distribution. These algorithms are applied to calculate parameter values of predictive models of the phenomenon of varying volatility in data time series. For this purpose, 3 such research models of time-varying volatility are simulated in STAN a probabilistic programming language for statistical inference. The accuracy of these models' predictive function is confirmed by applying in data time series with known prior values. Moreover, Stan models' performance is illustrated by the real stock prices of two shares in the stock market of New York. Finally, an Information Criterion of the results is applied to each model as well, to evaluate their predictive ability, comparing and selecting the most effective one.

Bayesian estimation of realized stochastic volatility model by Hybrid Monte Carlo algorithm

Journal of Physics: Conference Series, 2014

The hybrid Monte Carlo algorithm (HMCA) is applied for Bayesian parameter estimation of the realized stochastic volatility (RSV) model. Using the 2nd order minimum norm integrator (2MNI) for the molecular dynamics (MD) simulation in the HMCA, we find that the 2MNI is more efficient than the conventional leapfrog integrator. We also find that the autocorrelation time of the volatility variables sampled by the HMCA is very short. Thus it is concluded that the HMCA with the 2MNI is an efficient algorithm for parameter estimations of the RSV model.

A Markov Chain Quasi-Monte Carlo Method for Bayesian Estimation of Stochastic Volatility Model

SSRN Electronic Journal, 2000

In this paper, we propose a Markov Chain Quasi-Monte Carlo (MCQMC) approach for Bayesian estimation of a discrete-time stochastic volatility (SV) model first proposed by . The Bayesian approach pioneered by Jacquier et al. (1994) represents a feasible way to estimate SV models. Under the conventional Bayesian estimation method for SV models, pseudo-random numbers are usually used. Here we develop an algorithm to construct the Markov chain using a quasi-Monte Carlo sequence, or a low discrepancy sequence. We conjecture that the quasi-Monte Carlo sequence gives more precise estimates of the parameters in the SV model. We demonstrate the proposed method and justify our conjecture using both simulated and real financial returns data.

Comparing stochastic volatility models through Monte Carlo simulations

Computational Statistics & Data Analysis, 2006

Stochastic volatility models are important tools for studying the behavior of many financial markets. For this reason a number of versions have been introduced and studied in the recent literature. The goal is to review and compare some of these alternatives by using Bayesian procedures. The quantity used to assess the goodness-of-fit is the Bayes factor, whereas the ability to forecast the volatility has been tested through the computation of the one-step-ahead value-at-risk (VaR). Model estimation has been carried out through adaptive Markov chain Monte Carlo (MCMC) procedures. The marginal likelihood, necessary to compute the Bayes factor, has been computed through reduced runs of the same MCMC algorithm and through an auxiliary particle filter. The empirical analysis is based on the study of three international financial indexes.

Bayesian Analysis of Stochastic Volatility Models

2009

Time varying volatility is a characteristic of many financial series. An alternative to the popular ARCH framework is a Stochastic Volatility model which is harder to estimate than the ARCH family. In this paper we estimate and compare two classes of Stochastic Volatility models proposed in financial literature: the Log normal autoregressive model with some extensions and the Heston model. The basic univariate Stochastic Volatility model is extended to allow for the "leverage effect" via correlation between the volatility and the mean innovations and for fat tails in the mean equation innovation.A Bayesian Markov Chain Monte Carlo algorithm developed in Jacquier, Polson and Rossi 2004 is analyzed and applied to a large data base of the French financial market. Moreover, explicit expression for the parameter's estimators is found via Monte Carlo technique.

Estimation of stochastic volatility models via Monte Carlo maximum likelihood

Journal of Econometrics, 1998

This paper discusses the Monte Carlo maximum likelihood method of estimating stochastic volatility (SV) models. The basic SV model can be expressed as a linear state space model with log chi-square disturbances. The likelihood function can be approximated arbitrarily accurately by decomposing it into a Gaussian part, constructed by the Kalman filter, and a remainder function, whose expectation is evaluated by simulation. No modifications of this estimation procedure are required when the basic SV model is extended in a number of directions likely to arise in applied empirical research. This compares favorably with alternative approaches. The finite sample performance of the new estimator is shown to be comparable to the Monte Carlo Markov chain (MCMC) method.

Classical and Bayesian Analysis of Univariate and Multivariate Stochastic Volatility Models

Econometric Reviews, 2006

In this paper Efficient Importance Sampling (EIS) is used to perform a classical and Bayesian analysis of univariate and multivariate Stochastic Volatility (SV) models for financial return series. EIS provides a highly generic and very accurate procedure for the Monte Carlo (MC) evaluation of high-dimensional interdependent integrals. It can be used to carry out ML-estimation of SV models as well as simulation smoothing where the latent volatilities are sampled at once. Based on this EIS simulation smoother a Bayesian Markov Chain Monte Carlo (MCMC) posterior analysis of the parameters of SV models can be performed. JEL classification: C15, C22, C52

Estimation of realized stochastic volatility models using Hamiltonian Monte Carlo-Based methods

Computational Statistics, 2014

This study develops and compares performance of Hamiltonian Monte Carlo (HMC) and Riemann manifold Hamiltonian Monte Carlo (RMHMC) samplers with that of multi-move Metropolis-Hastings sampler to estimate stochastic volatility (SV) and realized SV (RSV) models with asymmetry effect. In terms of inefficiency factor, empirical results show that the RMHMC sampler give the best performance for estimating parameters, followed by multi-move Metropolis-Hastings sampler. In particular, it is also shown that RMHMC sampler offers a greater advantage in the mixing property of latent volatility chains and in the computational time than HMC sampler.