Bayesian Inference of Stochastic Volatility Model by Hybrid Monte Carlo

TL;DR

This paper demonstrates that the hybrid Monte Carlo algorithm improves Bayesian inference for stochastic volatility models by reducing autocorrelation in sampled variables, with applications to artificial and real financial data.

Contribution

It introduces the use of HMC for Bayesian inference in SV models and compares its efficiency to the Metropolis algorithm, showing faster decorrelation.

Findings

HMC decorrelates volatility variables faster than Metropolis.

HMC applied to Nikkei 225 data reveals strong volatility persistence.

Estimated phi value close to 1 indicates persistent volatility shocks.

Abstract

The hybrid Monte Carlo (HMC) algorithm is applied for the Bayesian inference of the stochastic volatility (SV) model. We use the HMC algorithm for the Markov chain Monte Carlo updates of volatility variables of the SV model. First we compute parameters of the SV model by using the artificial financial data and compare the results from the HMC algorithm with those from the Metropolis algorithm. We find that the HMC algorithm decorrelates the volatility variables faster than the Metropolis algorithm. Second we make an empirical study for the time series of the Nikkei 225 stock index by the HMC algorithm. We find the similar correlation behavior for the sampled data to the results from the artificial financial data and obtain a $\phi$ value close to one ($\phi \approx 0.977$), which means that the time series has the strong persistency of the volatility shock.