Dynamic factor long memory volatility

In this paper, we develop a long memory orthogonal factor (LMOF) multivariate volatility model for forecasting the covariance matrix of financial asset returns. We evaluate the LMOF model using the volatility timing framework of Fleming et al. [J. Finance, 2001, 56, 329–352] and compare its performance with that of both a static investment strategy based on the unconditional covariance matrix and a range of dynamic investment strategies based on existing short memory and long memory multivariate conditional volatility models. We show that investors should be willing to pay to switch from the static strategy to a dynamic volatility timing strategy and that, among the dynamic strategies, the LMOF model consistently produces forecasts of the covariance matrix that are economically more useful than those produced by the other multivariate conditional volatility models, both short memory and long memory. Moreover, we show that combining long memory volatility with the factor structure yields better results than employing either long memory volatility or the factor structure alone. The factor structure also significantly reduces transaction costs, thus increasing the feasibility of dynamic volatility timing strategies in practice. Our results are robust to estimation error in expected returns, the choice of risk aversion coefficient, the estimation window length and sub-period analysis.     

Accurate Short-Term Yield Curve Forecasting using Functional Gradient Descent

We propose a multivariate nonparametric technique for generatingreliable short-term historical yield curve scenarios and confidenceintervals. The approach is based on a Functional Gradient Descent(FGD) estimation of the conditional mean vector and covariancematrix of a multivariate interest rate series. It is computationallyfeasible in large dimensions and it can account for nonlinearitiesin the dependence of interest rates at all available maturities.Based on FGD we apply filtered historical simulation to computereliable out-of-sample yield curve scenarios and confidenceintervals. We back-test our methodology on daily USD bond datafor forecasting horizons from 1 to 10 days. Based on severalstatistical performance measures we find significant evidenceof a higher predictive power of our method when compared toscenarios generating techniques based on (i) factor analysis,(ii) a multivariate CCC-GARCH model, or (iii) an exponentialsmoothing covariances estimator as in the RiskMetrics^TM approach.     

Finite sample accuracy and choice of sampling frequency in integrated volatility estimation

We consider the properties of three estimation methods for integrated volatility, i.e. realized volatility, Fourier, and wavelet estimation, when a typical sample of high-frequency data is observed. We employ several different generating mechanisms for the instantaneous volatility process, e.g. Ornstein–Uhlenbeck, long memory, and jump processes. The possibility of market microstructure contamination is also entertained using models with bid-ask bounce and price discreteness, in which case alternative estimators with theoretical justification under market microstructure noise are also examined. The estimation methods are compared in a simulation study which reveals a general robustness towards persistence or jumps in the latent stochastic volatility process. However, bid-ask bounce effects render realized volatility and especially the wavelet estimator less useful in practice, whereas the Fourier method remains useful and is superior to the other two estimators in that case. More strikingly, even compared to bias correction methods for microstructure noise, the Fourier method is superior with respect to RMSE while having only slightly higher bias. A brief empirical illustration with high-frequency GE data is also included.     

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.     

ABC of SV: Limited information likelihood inference in stochastic volatility jump-diffusion models

We develop novel methods for estimation and filtering of continuous-time models with stochastic volatility and jumps using so-called Approximate Bayesian Computation which build likelihoods based on limited information. The proposed estimators and filters are computationally attractive relative to standard likelihood-based versions since they rely on low-dimensional auxiliary statistics and so avoid computation of high-dimensional integrals. Despite their computational simplicity, we find that estimators and filters perform well in practice and lead to precise estimates of model parameters and latent variables. We show how the methods can incorporate intra-daily information to improve on the estimation and filtering. In particular, the availability of realized volatility measures help us in learning about parameters and latent states. The method is employed in the estimation of a flexible stochastic volatility model for the dynamics of the S&P 500 equity index. We find evidence of the presence of a dynamic jump rate and in favor of a structural break in parameters at the time of the recent financial crisis. We find evidence that possible measurement error in log price is small and has little effect on parameter estimates. Smoothing shows that, recently, volatility and the jump rate have returned to the low levels of 2004–2006.     

Non-parametric estimation of historical volatility

Evolving volatility is a dominant feature observed in most financial time series and a key parameter used in option pricing and many other financial risk analyses. A number of methods for non-parametric scale estimation are reviewed and assessed with regard to the stylized features of financial time series. A new non-parametric procedure for estimating historical volatility is proposed based on local maximum likelihood estimation for the t-distribution. The performance of this procedure is assessed using simulated and real price data and is found to be the best among estimators we consider. We propose that it replaces the moving variance historical volatility estimator.     

The logarithmic vector multiplicative error model: an application to high frequency NYSE stock data

We develop a general form logarithmic vector multiplicative error model (log-vMEM). The log-vMEM improves on existing models in two ways. First, it is a more general form model as it allows the error terms to be cross-dependent and relaxes weak exogeneity restrictions. Second, the log-vMEM specification guarantees that the conditional means are non-negative without any restrictions imposed on the parameters. We further propose a multivariate lognormal distribution and a joint maximum likelihood estimation strategy. The model is applied to high frequency data associated with a number of NYSE-listed stocks. The results reveal empirical support for full interdependence of trading duration, volume and volatility, with the log-vMEM providing a better fit to the data than a competing model. Moreover, we find that unexpected duration and volume dominate observed duration and volume in terms of information content, and that volatility and volatility shocks affect duration in different directions. These results are interpreted with reference to extant microstructure theory.     

Bivariate FIGARCH and fractional cointegration

We consider the modelling of volatility on closely related markets. Univariate fractional volatility (FIGARCH) models are now standard, as are multivariate GARCH models. In this paper, we adopt a combination of the two methodologies. There is as yet little consensus on the methodology for testing for fractional cointegration. The contribution of this paper is to demonstrate the feasibility of estimating and testing cointegrated bivariate FIGARCH models. We apply these methods to volatility on the NYMEX and IPE crude oil markets. We find a common order of fractional integration for the two volatility processes and confirm that they are fractionally cointegrated. An estimated error correction FIGARCH model indicates that the preponderant adjustment is of the IPE towards NYMEX.     

Bivariate asymmetric GARCH models with heavy tails and dynamic conditional correlations

A bivariate generalized autoregressive conditional heteroskedastic model with dynamic conditional correlation and leverage effect (DCC-GJR-GARCH) for modelling financial time series data is considered. For robustness it is helpful to assume a multivariate Student-t distribution for the innovation terms. This paper proposes a new modified multivariate t-distribution which is a robustifying distribution and offers independent marginal Student-t distributions with different degrees of freedom, thereby highlighting the relationship among different assets. A Bayesian approach with adaptive Markov chain Monte Carlo methods is used for statistical inference. A simulation experiment illustrates good performance in estimation over reasonable sample sizes. In the empirical studies, the pairwise relationship between the Australian stock market and foreign exchange market, and between the US stock market and crude oil market are investigated, including out-of-sample volatility forecasts.     

Impact of volatility estimation method on theoretical option values

The volatility of an asset price measures how uncertain we are about future asset price movements. It is one of the factors affecting option price and the only input into the Black–Scholes model that cannot be directly observed. Thus, estimating volatility properly is vital. Two approaches to calculating volatility are historical and implied volatilities. Using index options listed on the Chicago Board of Options Exchange, this paper focuses on historical volatility. Since numerous methods of estimating volatility may provide different results, this paper assesses the impact of volatility estimation method on theoretical option values.     

Two-step estimation of the volatility functions in diffusion models with empirical applications

In this article, we develop a two-step estimation procedure for the volatility function in diffusion models. We firstly estimate the volatility series at sampling time points based on high-frequency data. Then, the volatility function estimator can be obtained by using the kernel smoothing method. The resulting estimators are presented based on high-frequency data, and are shown to be consistent and asymptotically normal. We also consider boundary issues and then propose two methods to handle them. The asymptotic normality of two boundary-corrected estimators is established under some suitable conditions. The proposed estimators are illustrated by Monte Carlo simulations and real data.     

GHICA — Risk analysis with GH distributions and independent components

Over recent years, a study on risk management has been prompted by the Basel committee for regular banking supervisory. There are however limitations of some widely-used risk management methods that either calculate risk measures under the Gaussian distributional assumption or involve numerical difficulty. The primary aim of this paper is to present a realistic and fast method, GHICA, which overcomes the limitations in multivariate risk analysis. The idea is to first retrieve independent components (ICs) out of the observed high-dimensional time series and then individually and adaptively fit the resulting ICs in the generalized hyperbolic (GH) distributional framework. For the volatility estimation of each IC, the local exponential smoothing technique is used to achieve the best possible accuracy of estimation. Finally, the fast Fourier transformation technique is used to approximate the density of the portfolio returns.The proposed GHICA method is applicable to covariance estimation as well. It is compared with the dynamic conditional correlation (DCC) method based on the simulated data with d = 50 GH distributed components. We further implement the GHICA method to calculate risk measures given 20-dimensional German DAX portfolios and a dynamic exchange rate portfolio. Several alternative methods are considered as well to compare the accuracy of calculation with the GHICA one.     

Intraday periodicity adjustments of transaction duration and their effects on high-frequency volatility estimation

We study two methods of adjusting for intraday periodicity of high-frequency financial data: the well-known Duration Adjustment (DA) method and the recently proposed Time Transformation (TT) method (Wu (2012)). We examine the effects of these adjustments on the estimation of intraday volatility using the Autoregressive Conditional Duration-Integrated Conditional Variance (ACD-ICV) method of Tse and Yang (2012). We find that daily volatility estimates are not sensitive to intraday periodicity adjustment. However, intraday volatility is found to have a weaker U-shaped volatility smile and a biased trough if intraday periodicity adjustment is not applied. In addition, adjustment taking account of trades with zero duration (multiple trades at the same time stamp) results in deeper intraday volatility smile.     

The impact of co-jumps in the oil sector

We study the dynamics of the oil sector using a new multivariate stochastic volatility model with a structure of common factors subjected to jumps in mean and conditional variance. This model contributes to the literature allowing the estimation of spillover effects between assets in a multivariate framework through joint jumps (co-jumps), identifying the permanent and transitory effects through a structure defined by Bernoulli processes. The jump structure introduced in the article can be interpreted as a regime-switching model with an endogenous number of states, avoiding the difficulties associated with models with a fixed number of regimes. We apply the model to oil prices and stock prices of integrated oil companies. The jump structure allows dating the relevant events in the oil sector in the period 2000–2019. The period analyzed encompasses important events in the oil market such as the price escalation in 2008 and the falling prices in 2014. We also apply the model to estimate risk management measures and portfolio allocation and perform a comparison with other multivariate models of conditional volatility, showing the good properties of the model in these applications.     

Forward-looking portfolio selection with multivariate non-Gaussian models

In this study, we suggest a portfolio selection framework based on time series of stock log-returns, option-implied information, and multivariate non-Gaussian processes. We empirically assess a multivariate extension of the normal tempered stable (NTS) model and of the generalized hyperbolic (GH) one by implementing an estimation method that simultaneously calibrates the multivariate time series of log-returns and, for each margin, the univariate observed one-month implied volatility smile. To extract option-implied information, the connection between the historical measure P and the risk-neutral measure Q, needed to price options, is provided by the multivariate Esscher transform. The method is applied to fit a 50-dimensional series of stock returns, to evaluate widely known portfolio risk measures and to perform a forward-looking portfolio selection analysis. The proposed models are able to produce asymmetries, heavy tails, both linear and non-linear dependence and, to calibrate them, there is no need for liquid multivariate derivative quotes.     

Time-varying Beta Risk for Australian Industry Portfolios: An Exploratory Analysis

The central focus of this paper is to provide an initial exploratory examination of ex post time-varying beta estimation, modeling and asset pricing tests. In particular, these issues are investigated using a sample of monthly data on Australian industry portfolios over the nineteen-year period 1974 to 1992. While primarily illustrative in nature, the industry betas are modeled, estimated and tested with reasonable success in terms of regimes related to periods of regulation/deregulation/imputation; the level of market returns; and a measure of volatility on the risk-free rate of interest. However, univariate and multivariate tests reported in the paper provided mixed evidence concerning the applicability of a time-varying beta CAPM, that incorporates these variables.     

Volatility dynamics for the S&P 500: Further evidence from non-affine,multi-factor jump diffusions

We apply Markov chain Monte Carlo methods to time series data on S&P 500 index returns, and to its option prices via a term structure of VIX indices, to estimate 18 different affine and non-affine stochastic volatility models with one or two variance factors, and where jumps are allowed in both the price and the instantaneous volatility. The in-sample fit to the VIX term structure shows that the second (stochastic long-term volatility) factor is required to fit the VIX term structure. Out-of-sample tests on the fit to individual option prices, as well as in-sample tests, show that the inclusion of jumps is less important than allowing for non-affine dynamics. The estimation and testing periods together cover more than 21 years of daily data.     

Do measures of systemic risk predict U.S. corporate bond default rates?

Using univariate and multivariate Mixed Data Sampling (MIDAS) and LASSO estimation methodologies, we explore whether the U.S. annual average corporate bond default rate can be predicted by 12 monthly systemic risk measures proposed in the literature. We find that nearly all of the systemic risk indicators have predictive power for the default rate. Granger causality tests based on multivariate mixed frequency VAR models further support this conclusion. On the basis of MIDAS models, we illustrate that five of these indicators are able to forecast out-of-sample the 2009 corporate default crisis. Using a LASSO multivariate model, it is further shown that the systemic risk indicators can forecast out-of-sample both the 2009 default rate and the default rates during the buildup before the crisis and in the aftermath of the crisis. Institution-specific and volatility systemic risk measures are the most relevant for modeling U.S. corporate bond default rates, with the Conditional VaR measure of Adrian and Brunnermeier (2016) exhibiting the best performance.     

Understanding Delta-Hedged Option Returns in Stochastic Volatility Environments

In this paper, we provide a novel representation of delta-hedged option returns in a stochastic volatility environment. The representation of delta-hedged option returns provided in this paper consists of two terms: volatility risk premium and parameter estimation risk. In an empirical analysis, we examine delta-hedged option returns based on the result of a historical simulation with the USD-JPY currency option market data from October 2003 to June 2010. We find that the delta-hedged option returns for OTM put options are strongly affected by parameter estimation risk as well as the volatility risk premium, especially in the post-Lehman shock period.     

Volatility transmission in global financial markets

This paper considers the transmission of volatility in global foreign exchange, equity and bond markets. Using a multivariate GARCH framework which includes measures of realised volatility as explanatory variables, significant volatility and news spillovers are found to occur on the same trading day between Japan, Europe, and the United States. All markets exhibit significant degrees of asymmetry in terms of the transmission of volatility associated with good and bad news. There are also strong links between diffusive volatilities in all three markets, whereas jump activity is only important within the equity markets. The results of this paper deepen our understanding of how news and volatility are propagated through global financial markets.