Stochastic volatility with leverage: Fast and efficient likelihood inference

By Yashuhiro Omori, Siddhartha Chib, N. Shephard, Jouchi Nakajima. 2007

486 citations recorded by the source corpus.

This paper is concerned with the Bayesian analysis of stochastic volatility (SV) models with leverage. Specifically, the paper shows how the often used Kim et al. [1998. Stochastic volatility: likelihood inference and comparison with ARCH models. Review of Economic Studies 65, 361–393] method that was developed for SV models without leverage can be extended to models with leverage. The approach relies on the novel idea of approximating the joint distribution of the outcome and volatility innovations by a suitably constructed ten-component mixture of bivariate normal distributions. The resulting posterior distribution is summarized by MCMC methods and the small approximation error in working with the mixture approximation is corrected by a reweighting procedure. The overall procedure is fast and highly efficient. We illustrate the ideas on daily returns of the Tokyo Stock Price Index. Finally, extensions of the method are described for superposition models (where the log-volatility is made up of a linear combination of heterogenous and independent autoregressions) and heavy-tailed error distributions (student and log-normal).

Subfields: Finance, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/c0d135632c109a65e46ba2a707360998a97904cf

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Citations in the corpus

Rare shocks, great recessions (2013, unknown): “THE DSGE MODEL The model considered is the one used in Smets and Wouters (2007), which is based on earlier work by Christiano et al.”
Inference for Lévy‐Driven Stochastic Volatility Models via Adaptive Sequential Monte Carlo (2011, methodology): “For priors on the leverage parameter for discrete-time SV models, see, for example Omori et al. (2007).”
Time-Varying Parameter VAR Model with Stochastic Volatility: An Overview of Methodology and Empirical Applications (2011, methodology): “Though we draw samples from the posterior distribution based on the approximated model, its approximation error is small enough to implement the original model, and can be corrected by reweighting steps, as discussed by Kim, Shephard, and Chib (1998), and Omori et al. (2007).”
Bayesian semiparametric stochastic volatility modeling (2010, background): “(2), ht ⊥ yt assumes away any leverage effects (see Jacquier et al., 2004; Yu, 2005; Omori et al., 2007).”
Common Drifting Volatility in Large Bayesian VARs (2012, unknown): “We should also note that we depart from these previous studies in using the improved 10-state mixture approximation of Omori et al. (2007) instead of KSC’s original 7-state approximation, and we incorporate the reordering of Primiceri’s steps suggested in Del Negro and Primiceri (2014).”
Bayesian analysis of time-varying parameter vector autoregressive model for the Japanese economy and monetary policy (2011, unknown): “The mixture sampler draws sample from the approximated posterior density and its approximation error is small enough to implement the overall model, as discussed by Omori et al. (2007).”
Mean field variational bayes for elaborate distributions (2011, methodology): “Auxiliary mixture sampling was introduced for a Bayesian analysis of stochastic volatility models by Shephard (1994) and has been applied in this context by, for example, Kim et al. (1998), Chib et al. (2002), and Omori et al. (2007).”
Core Inflation and Trend Inflation (2016, methodology): “fied to use the Omori et al. (2007) ten-component gaussian mixture approximation for the log chi-squared error. The MCMC iterations in Stock and Watson (2007) have been corrected for an error pointed out by Del Negro and Primiceri (2015) that applies generally to models with stochastic volatility.”
Bayesian Multivariate Time Series Methods for Empirical Macroeconomics (2010, unknown): “6 Omori et al. (2007) recommend an even more accurate approximation using a mixture of 10 Normal distributions.”
Alternative Asymmetric Stochastic Volatility Models (2009, unknown): “Recently, So et al. (2002) considered a threshold effects model in which the breaks in the constant and autoregressive parameter in the SV equation depend on the signs of the previous returns.”
Measuring Uncertainty and Its Impact on the Economy (2016, methodology): “Whereas volatility and uncertainty are contemporaneous with y t in our model, in ﬁnance applications such as Omori, et al. (2007), volatility is lagged.”
Multivariate stochastic volatility (2009, methodology): “This problem has been fully resolved by the creative use of Monte Carlo methods, primarily Bayesian Markov chain Monte Carlo (MCMC) methods (Jacquier et al. (1994), Kim et al. (1998), Chib et al. (2002) and Omori et al. (2007) ).”
On the effects of world stock market and oil price shocks on food prices: An empirical investigation based on TVP-VAR models with stochastic volatility (2014, methodology): “According to Primiceri (2005), Omori et al. (2007) and Jouchi (2011), the TVP-VAR model is constructed form the basic structural VAR model by allowing the parameters to change over time.”