Factor Stochastic Volatility Model Research Articles

Global uncertainty and potential shelters: gold, bitcoin, and currencies as weak and strong safe havens for main world stock markets

This article investigates five safe-haven asset responses from 2014 to 2022, including the unprecedented COVID-19 crisis, Russian invasion of Ukraine, and sharp US interest rate increases of 2015 and 2022. We apply the unique approach of the multivariate factor stochastic volatility (MSV) model, which is extremely efficient for financial market analysis and allows us to conduct dynamic factor analysis of safe-haven relationships that cannot be observed directly. The research sample consists of five prospective safe-haven assets—gold, bitcoin, the euro, the Japanese yen, and the Swiss franc—and five primary world stock market indices—the S&P 500, Financial Times Stock Exchange (FTSE) 100, DAX, STOXX Europe 600, and Nikkei 225. Our findings are useful for investors searching for the best safe-haven assets among gold, bitcoin, and currencies to hedge against financial turmoil in global stock markets. Our unique findings suggest that safe-haven effects work differently for gold and the yen; that is, the Japanese yen acts as the strongest safe haven across all stock indices. Bitcoin is not a strong safe-haven currency since it has zero days of negative correlations with the considered stock indices, but it is a weak safe-haven during times of financial distress. Consequently, we state that strong and weak safe-haven properties vary across time and place. The novelty of our study lies in the methodological complexity of the MSV model (used for the first time to find the best safe-haven asset properties), dynamic factor analysis, a long-term research sample covering the Russian invasion of Ukraine in 2022, and an international investor perspective focusing on the world’s leading stock markets. We extend earlier studies by analyzing the interrelations of the world’s leading stock market indices with five potential safe-haven assets during the long period of 2014–2022 and using a unique dynamic factor analysis to show the differentiated behaviors of the Japanese yen and gold. Additionally, the main innovative contribution is a new framework of weak and strong safe-haven asset classifications not previously applied in the literature.

Co-volatility dynamics in global cryptocurrency and conventional asset classes: a multivariate stochastic factor volatility approach

Purpose This study aims to investigate the co-volatility patterns between cryptocurrencies and conventional asset classes across global markets, encompassing 26 global indices ranging from equities, commodities, real estate, currencies and bonds. Design/methodology/approach It used a multivariate factor stochastic volatility model to capture the dynamic changes in covariance and volatility correlation, thus offering empirical insights into the co-volatility dynamics. Unlike conventional research on price or return transmission, this study directly models the time-varying covariance and volatility correlation. Findings The study uncovers pronounced co-volatility movements between cryptocurrencies and specific indices such as GSCI Energy, GSCI Commodity, Dow Jones 1 month forward and U.S. 10-year TIPS. Notably, these movements surpass those observed with precious metals, industrial metals and global equity indices across various regions. Interestingly, except for Japan, equity indices in the USA, Canada, Australia, France, Germany, India and China exhibit a co-volatility movement. These findings challenge the existing literature on cryptocurrencies and provide intriguing evidence regarding their co-volatility dynamics. Originality This study significantly contributes to applying asset pricing models in cryptocurrency markets by explicitly addressing price and volatility dynamics aspects. Using the stochastic volatility model, the research adding methodological contribution effectively captures cryptocurrency volatility's inherent fluctuations and time-varying nature. While previous literature has primarily focused on bitcoin and a few other cryptocurrencies, this study examines the stochastic volatility properties of a wide range of cryptocurrency indices. Furthermore, the study expands its scope by examining global asset markets, allowing for a comprehensive analysis considering the broader context in which cryptocurrencies operate. It bridges the gap between traditional asset pricing models and the unique characteristics of cryptocurrencies.

Do stochastic risks flow between industrial and precious metals, Islamic stocks, green bonds, green stocks, clean investments, major foreign exchange rates, and Bitcoin?

This study examines the interactions between Bitcoin (BTC) and other major financial markets (forex, equity and bond, and industrial and precious metals). This interaction is viewed from the spectrum of spillover analysis, hedging, and portfolio analyses. Due to the high volatility and volatility clustering nature of most financial series, particularly BTC, we rely on a Multivariate Factor Stochastic Volatility (mvFSV) Model of Kastner et al. (2017). In order to capture the influence of extreme market conditions, we use a quantile-based mvFSV Model. Among other things, results confirm the importance of quantile analysis as results are sensitive to market conditions. For instance, currencies and industrial and precious metals are net transmitters of shocks at lower and middle quantiles, while these assets change their status to the net receiver of shocks at the upper quantile. Results of the total connectedness show that there is a high degree of interconnectedness among the assets, as the total connectedness index ranges between 86% and 100%. Besides, Islamic equities perform such as the most currencies and conventional assets in terms of the transmission of shocks and diversification benefits. The hedging potentials of Bitcoin over other assets were also examined, and results confirm that the hedging effectiveness is commodity-specific. Policy implications of these results are discussed.

Time-Varying Uncertainty of the Federal Reserve's Output Gap Estimate

AbstractA factor stochastic volatility model estimates the common component to output gap estimates produced by the staff of the Federal Reserve, its time-varying volatility, and time-varying, horizon-specific forecast uncertainty. The output gap estimates are uncertain even well after the fact. Nevertheless, the common component is clearly procyclical, and positive innovations to the common component produce movements in macroeconomic variables consistent with an increase in aggregate demand. Heightened macroeconomic uncertainty, as measured by the common component's volatility, leads to persistently negative economic responses.

Flexible and Robust Particle Tempering for State Space Models

Density tempering (also called density annealing) is a sequential Monte Carlo approach to Bayesian inference for general state models which is an alternative to Markov chain Monte Carlo. When applied to state space models, it moves a collection of parameters and latent states (which are called particles) through a number of stages, with each stage having its own target distribution. The particles are initially generated from a distribution that is easy to sample from, e.g. the prior; the target at the final stage is the posterior distribution. Tempering is usually carried out either in batch mode, involving all the data at each stage, or sequentially with observations added at each stage, which is called data tempering. Efficient Markov moves for generating the parameters and states for each stage of particle based density tempering are proposed. This allows the proposed SMC methods to increase (scale up) the number of parameters and states that can be handled. Most current methods use a pseudo-marginal Markov move step with the states “integrated out”, and the parameters generated by a random walk proposal; although this strategy is general, it can be very inefficient when the states or parameters are high dimensional. By adding batch tempering at each stage, previous methods are extended to make data tempering more robust to outliers and structural changes for models with intractable likelihoods. The performance of the proposed methods is evaluated using univariate stochastic volatility models with outliers and structural breaks, and high dimensional factor stochastic volatility models having many parameters and many latent states.11This article has an online supplement that contains additional technical details and empirical results.

The intermediating role of the Chinese renminbi in Asian currency markets: Evidence from partial wavelet coherence

This study presents an innovative perspective on the dynamic interdependence of Asian currency markets, focusing particularly on the intermediating role of the Chinese renminbi (CNY) in introducing the co-movement between non-major Asian currencies. In this regard, the multivariate factor stochastic volatility (SV) model is estimated and continuous wavelet analysis is applied. The novelty of this study is that it employs wavelet coherence analysis to identify the localized time-varying co-movement of Asian currencies and their lead–lag relations specific to a particular scale and thus investment horizon. Furthermore, the CNY’s intermediating role in inducing co-movement between Asian currencies is examined by applying dynamic partial correlation analysis based on the multivariate factor SV model and partial wavelet coherence analysis, which evaluate the degree of the co-movement between Asian currencies after controlling for the common influence of the CNY. The results clearly indicate the prominent role of the CNY in facilitating region-wide connectedness of Asian currency markets.

Variational Bayes approximation of factor stochastic volatility models

Estimation and prediction in high dimensional multivariate factor stochastic volatility models is an important and active research area, because such models allow a parsimonious representation of multivariate stochastic volatility. Bayesian inference for factor stochastic volatility models is usually done by Markov chain Monte Carlo methods (often by particle Markov chain Monte Carlo methods), which are usually slow for high dimensional or long time series because of the large number of parameters and latent states involved. Our article makes two contributions. The first is to propose a fast and accurate variational Bayes methods to approximate the posterior distribution of the states and parameters in factor stochastic volatility models. The second is to extend this batch methodology to develop fast sequential variational updates for prediction as new observations arrive. The methods are applied to simulated and real datasets, and shown to produce good approximate inference and prediction compared to the latest particle Markov chain Monte Carlo approaches, but are much faster.

On the joint volatility dynamics in international dairy commodity markets*

The present study investigates the price (co)volatility of four dairy commodities—skim milk powder, whole milk powder, butter, and cheddar cheese—in three major dairy markets. It uses a multivariate factor stochastic volatility model for estimating the time‐varying covariance and correlation matrices by imposing a low‐dimensional latent dynamic factor structure. The empirical results support four factors representing the European Union and Oceania dairy sectors as well as the milk powder markets. Factor volatilities and marginal posterior volatilities of each dairy commodity increase after the 2006/07 global (food) crisis, which also coincides with the free trade agreements enacted from 2007 onward and EU and US liberalization policy changes. The model‐implied correlation matrices show increasing dependence during the second half of 2006, throughout the first half of 2007, as well as during 2008 and 2014, which can be attributed to various regional agricultural dairy policies. Furthermore, in‐sample value at risk measures (VaRs and CoVaRs) are provided for each dairy commodity under consideration.

Time-varying Uncertainty of the Federal Reserve's Output Gap Estimate

A factor stochastic volatility model estimates the common component to estimates of the output gap produced by the staff of the Federal Reserve, its time-varying volatility, and time-varying, horizon-specific forecast uncertainty. Output gap estimates are very uncertain, even well after the fact, especially at business cycle turning points. However, the common component of the output gap estimates is clearly procyclical, and innovations to the common factor produce persistent positive effects on economic activity. Output gaps estimated by the Congressional Budget Office have very similar properties. Increased macroeconomic uncertainty, as measured by the common factor's volatility, leads to persistent negative responses in economic variables.

Bayesian inference for a single factor copula stochastic volatility model using Hamiltonian Monte Carlo

For modeling multivariate financial time series a single factor copula model with stochastic volatility margins is proposed. It generalizes single factor models based on the multivariate normal distribution by allowing for symmetric and asymmetric tail dependence. A joint Bayesian approach using Hamiltonian Monte Carlo (HMC) within Gibbs sampling is developed. Thus, the information loss caused by the two-step approach for margins and dependence is avoided. Further, the Bayesian approach is tractable in high dimensional parameter spaces in addition to uncertainty quantification through credible intervals. By introducing indicators for different copula families the copula families are selected automatically in the Bayesian framework. In a first simulation study the performance of HMC for the copula part is compared to a procedure based on adaptive rejection Metropolis sampling within Gibbs sampling. It is shown that HMC considerably outperforms this alternative approach in terms of effective sample size per minute. In a second simulation study satisfactory performance is seen for the full HMC within Gibbs procedure. The approach is illustrated for a portfolio of financial assets with respect to one-day ahead value at risk forecasts. Comparison to a two-step estimation procedure and to relevant benchmark models, such as a multivariate factor stochastic volatility model, shows superior performance of the proposed approach.

Leverage, Asymmetry, and Heavy Tails in the High-Dimensional Factor Stochastic Volatility Model

We develop a factor stochastic volatility model that incorporates leverage effects, return asymmetry, and heavy tails across all systematic and idiosyncratic model components. Our model leads to a flexible high-dimensional dependence structure that allows for time-varying correlations, tail dependence, and volatility response to both systematic and idiosyncratic return shocks. We develop an efficient Markov chain Monte Carlo algorithm for posterior estimation based on the particle Gibbs, ancestor sampling, particle efficient importance sampling methods, and interweaving strategy. To obtain parsimonious specifications in practice, we build computationally efficient model selection directly into our estimation algorithm. We validate the performance of our proposed estimation method via simulation studies with different model specifications. An empirical study for a sample of U.S. stocks shows that return asymmetry is a systematic phenomenon and our model outperforms other factor models for value-at-risk evaluation.

Hedging capabilities of Bitcoin for Asian currencies

AbstractThis study investigates whether Bitcoin (BTC) can provide a hedge against the fiat currencies in Asia over various investment horizons. We focus on Asia because it is one of the fastest‐growing regions worldwide, where cryptocurrencies are actively traded. A wavelet transform technique is combined with a multivariate factor stochastic volatility (SV) model to examine the dynamic correlation properties and risk reduction effectiveness of BTC in both the time and frequency domains. We use gold and oil as benchmarks and compared their results with those of BTC. The estimated correlations indicate that the Asian currencies tend to be negatively correlated with BTC; therefore, the latter could provide a hedge against the former over the medium (8–32 days) and long (32–64 days) terms. By contrast, Asian currencies tend to be positively correlated with oil and gold for the same horizons. We also analyze the downside risk reduction effectiveness of BTC for the portfolio of Asian currencies and find that BTC provides better risk reduction than oil and gold, particularly over the medium and long terms. This study makes significant contributions to the literature by demonstrating that the correlation properties and risk reduction effectiveness of BTC differ depending on the investment horizons. We believe our findings using the wavelet‐based SV model can help heterogeneous investors detect portfolio risks and thus, identify optimal hedging strategies over various investment horizons.

Correlations among cryptocurrencies: Evidence from multivariate factor stochastic volatility model

This paper is the first study to apply the multivariate factor stochastic volatility model (MFSVM) for analyzing the correlations among six cryptocurrencies. We use MFSVM with the Bayesian estimation procedure for the period from August 8, 2015, to January 1, 2020. According to the findings, there is a significant positive correlation between price volatility values of Bitcoin and Litecoin. Besides, the volatility values of Ethereum have a positive correlation with both Ripple and Stellar. There is also a positive correlation between the volatility values of Ripple and Dash. These findings are robust to consider different correlation networks. The evidence implies that Bitcoin is mainly related to Litecoin, but Ethereum is associated with other cryptocurrencies.

Time-varying Uncertainty of the Federal Reserve’s Output Gap Estimate

What is the output gap and when do we know it? A factor stochastic volatility model estimates the common component to forecasts of the output gap produced by the staff of the Federal Reserve, its time-varying volatility, and time-varying, horizon-specific forecast uncertainty. The common factor to these forecasts is highly procyclical, and unexpected increases to the common factor are associated with persistent responses in other macroeconomic variables. However, output gap estimates are very uncertain, even well after the fact. Output gap uncertainty increases around business cycle turning points. Lastly, increased macroeconomic uncertainty, as measured by the output gap's time-varying volatility, produces pronounced negative responses to other macroeconomic variables.

Skew selection for factor stochastic volatility models

ABSTRACTThis paper proposes factor stochastic volatility models with skew error distributions. The generalized hyperbolic skew t-distribution is employed for common-factor processes and idiosyncratic shocks. Using a Bayesian sparsity modeling strategy for the skewness parameter provides a parsimonious skew structure for possibly high-dimensional stochastic volatility models. Analyses of daily stock returns are provided. Empirical results show that the skewness is important for common-factor processes but less for idiosyncratic shocks. The sparse skew structure improves prediction and portfolio performance.

Option Pricing under the Jump Diffusion and Multifactor Stochastic Processes

In financial markets, there exists long-observed feature of the implied volatility surface such as volatility smile and skew. Stochastic volatility models are commonly used to model this financial phenomenon more accurately compared with the conventional Black-Scholes pricing models. However, one factor stochastic volatility model is not good enough to capture the term structure phenomenon of volatility smirk. In our paper, we extend the Heston model to be a hybrid option pricing model driven by multiscale stochastic volatility and jump diffusion process. In our model the correlation effects have been taken into consideration. For the reason that the combination of multiscale volatility processes and jump diffusion process results in a high dimensional differential equation (PIDE), an efficient finite element method is proposed and the integral term arising from the jump term is absorbed to simplify the problem. The numerical results show an efficient explanation for volatility smirks when we incorporate jumps into both the stock process and the volatility process.

Quantization meets Fourier: a new technology for pricing options

In this paper we introduce a novel pricing methodology for a broad class of models for which the characteristic function of the log-asset price can be efficiently computed. The method is based on a new quantization procedure, crucially exploiting for the first time the Fourier transform of the asset process, which fully characterizes the distribution of the log-asset. As opposed to previous quantizations based on Euler (or more sophisticated) discretization schemes, our method reveals to be fast and accurate, to the point that it is possible to calibrate the models on real data. Moreover, our approach allows to price options in multi factor stochastic volatility models including jumps. As a motivating example, we calibrate a Tempered Stable model on market data. This represents the first application of quantization to a pure jump process.

Macroeconomic Uncertainty Through the Lens of Professional Forecasters

ABSTRACTWe analyze the evolution of macroeconomic uncertainty in the United States, based on the forecast errors of consensus survey forecasts of various economic indicators. Comprehensive information contained in the survey forecasts enables us to capture a real-time measure of uncertainty surrounding subjective forecasts in a simple framework. We jointly model and estimate macroeconomic (common) and indicator-specific uncertainties of four indicators, using a factor stochastic volatility model. Our macroeconomic uncertainty estimates have three major spikes has three major spikes aligned with the 1973–1975, 1980, and 2007–2009 recessions, while other recessions were characterized by increases in indicator-specific uncertainties. We also show that the selection of data vintages affects the estimates and relative size of jumps in estimated uncertainty series. Finally, our macroeconomic uncertainty has a persistent negative impact on real economic activity, rather than producing “wait-and-see” dynamics.

Efficient Bayesian Inference for Multivariate Factor Stochastic Volatility Models

ABSTRACTWe discuss efficient Bayesian estimation of dynamic covariance matrices in multivariate time series through a factor stochastic volatility model. In particular, we propose two interweaving strategies to substantially accelerate convergence and mixing of standard MCMC approaches. Similar to marginal data augmentation techniques, the proposed acceleration procedures exploit nonidentifiability issues which frequently arise in factor models. Our new interweaving strategies are easy to implement and come at almost no extra computational cost; nevertheless, they can boost estimation efficiency by several orders of magnitude as is shown in extensive simulation studies. To conclude, the application of our algorithm to a 26-dimensional exchange rate dataset illustrates the superior performance of the new approach for real-world data. Supplementary materials for this article are available online.

Pricing of defaultable options with multiscale generalized Heston’s stochastic volatility

The possibility of default risk of an option writer becomes a more important issue in over-the-counter option market when systemic risk increases. It is desirable for the option price to reflect the default risk. On the other hand, it is known that a single scale, single factor stochastic volatility model such as the well-known Heston model would not price correctly in- and out-of-the money options. So, this paper studies the pricing of defaultable options under a multiscale generalized Heston’s stochastic volatility model introduced by Fouque and Lorig (2011) to resolve these issues. We derive an explicit solution formula for the defaultable option price and investigate the characteristics of the resultant price in comparison to the price under the original Heston model.