On economic uncertainty,stock market predictability and nonlinear spillover effects

This paper uses a k-th order nonparametric Granger causality test to analyze whether firm-level, economic policy and macroeconomic uncertainty indicators predict movements in real stock returns and their volatility. Linear Granger causality tests show that whilst economic policy and macroeconomic uncertainty indices can predict stock returns, firm-level uncertainty measures possess no predictability. However, given the existence of structural breaks and inherent nonlinearities in the series, we employ a nonparametric causality methodology, as linear modeling leads to misspecifications thus the results cannot be considered reliable. The nonparametric test reveals that in fact no predictability can be observed for the various measures of uncertainty i.e., firm-level, macroeconomic and economic policy uncertainty, vis-à-vis real stock returns. In turn, a profound causal predictability is demonstrated for the volatility series, with the exception of firm-level uncertainty. Overall our results not only emphasize the role of economic and firm-level uncertainty measures in predicting the volatility of stock returns, but also presage against using linear models which are likely to suffer from misspecification in the presence of parameter instability and nonlinear spillover effects.     

Volatility activity: Specification and estimation

The paper examines volatility activity and its asymmetry and undertakes further specification analysis of volatility models based on it. We develop new nonparametric statistics using high-frequency option-based VIX data to test for asymmetry in volatility jumps. We also develop methods for estimating and evaluating, using price data alone, a general encompassing model for volatility dynamics where volatility activity is unrestricted. The nonparametric application to VIX data, along with model estimation for S&P index returns, suggests that volatility moves are best captured by an infinite variation pure-jump martingale with a symmetric jump compensator around zero. The latter provides a parsimonious generalization of the jump-diffusions commonly used for volatility modeling.     

Extreme-quantile tracking for financial time series

Time series of financial asset values exhibit well-known statistical features such as heavy tails and volatility clustering. We propose a nonparametric extension of the classical Peaks-Over-Threshold method from extreme value theory to fit the time varying volatility in situations where the stationarity assumption may be violated by erratic changes of regime, say. As a result, we provide a method for estimating conditional risk measures applicable to both stationary and nonstationary series. A backtesting study for the UBS share price over the subprime crisis exemplifies our approach.     

Stick-breaking autoregressive processes

This paper considers the problem of defining a time-dependent nonparametric prior for use in Bayesian nonparametric modelling of time series. A recursive construction allows the definition of priors whose marginals have a general stick-breaking form. The processes with Poisson-Dirichlet and Dirichlet process marginals are investigated in some detail. We develop a general conditional Markov Chain Monte Carlo (MCMC) method for inference in the wide subclass of these models where the parameters of the marginal stick-breaking process are nondecreasing sequences. We derive a generalised Pólya urn scheme type representation of the Dirichlet process construction, which allows us to develop a marginal MCMC method for this case. We apply the proposed methods to financial data to develop a semi-parametric stochastic volatility model with a time-varying nonparametric returns distribution. Finally, we present two examples concerning the analysis of regional GDP and its growth.     

Efficient estimation of a multivariate multiplicative volatility model

We propose a multivariate generalization of the multiplicative volatility model of Engle and Rangel (2008), which has a nonparametric long run component and a unit multivariate GARCH short run dynamic component. We suggest various kernel-based estimation procedures for the parametric and nonparametric components, and derive the asymptotic properties thereof. For the parametric part of the model, we obtain the semiparametric efficiency bound. Our method is applied to a bivariate stock index series. We find that the univariate model of Engle and Rangel (2008) appears to be violated in the data whereas our multivariate model is more consistent with the data.     

Nonparametric model validations for hidden Markov models with applications in financial econometrics

We address the nonparametric model validation problem for hidden Markov models with partially observable variables and hidden states. We achieve this goal by constructing a nonparametric simultaneous confidence envelope for transition density function of the observable variables and checking whether the parametric density estimate is contained within such an envelope. Our specification test procedure is motivated by a functional connection between the transition density of the observable variables and the Markov transition kernel of the hidden states. Our approach is applicable for continuous-time diffusion models, stochastic volatility models, nonlinear time series models, and models with market microstructure noise.     

Stock market volatility and the business cycle

This paper investigates the joint time series behavior of monthly stock returns and growth in industrial production. We find that stock returns are well characterized by year-long episodes of high volatility, separated by longer quiet periods. Real output growth, on the other hand, is subject to abrupt changes in the mean associated with economic recessions. We study a bivariate model in which these two changes are driven by related unobserved variables, and conclude that economic recessions are the primary factor that drives fluctuations in the volatility of stock returns. This framework proves useful both for forecasting stock volatility and for identifying and forecasting economic turning points.     

An application of nonparametric volatility estimators to option pricing

We discuss the impact of volatility estimates from high frequency data on derivative pricing. The principal purpose is to estimate the diffusion coefficient of an Itô process using a nonparametric Nadaraya–Watson kernel approach based on selective estimators of spot volatility proposed in the econometric literature, which are based on high frequency data. The accuracy of different spot volatility estimates is measured in terms of how accurately they can reproduce market option prices. To this aim, we fit a diffusion model to S&P 500 data, and successively, we use the calibrated model to price European call options written on the S&P 500 index. The estimation results are compared to well-known parametric alternatives available in the literature. Empirical results not only show that using intra-day data rather than daily provides better volatility estimates and hence smaller pricing errors, but also highlight that the choice of the spot volatility estimator has effective impact on pricing.     

International market links and volatility transmission

This paper gauges volatility transmission between stock markets by testing conditional independence of their volatility measures. In particular, we check whether the conditional density of the volatility changes if we further condition on the volatility of another market. We employ nonparametric methods to estimate the conditional densities and model-free realized measures of volatility, allowing for both microstructure noise and jumps. We establish the asymptotic normality of the test statistic as well as the first-order validity of the bootstrap analog. Finally, we uncover significant volatility spillovers between the stock markets in China, Japan, UK and US.     

Evolving United States stock market volatility: The role of conventional and unconventional monetary policies

Despite the econometric advances of the last 30 years, the effects of monetary policy stance during the boom and busts of the stock market are not clearly defined. In this paper, we use a structural heterogeneous vector autoregressive (SHVAR) model with identified structural breaks to analyse the impact of both conventional and unconventional monetary policies on U.S. stock market volatility. We find that contractionary monetary policy enhances stock market volatility, but the importance of monetary policy shocks in explaining volatility evolves across different regimes and is relative to supply shocks (and shocks to volatility itself). In comparison to business cycle fluctuations, monetary policy shocks explain a greater fraction of the variance of stock market volatility at shorter horizons, as in medium to longer horizons. Our basic findings of a positive impact of monetary policy on equity market volatility (being relatively stronger during calmer stock market periods) are also corroborated by analyses conducted at the daily frequency based on an augmented heterogeneous autoregressive model of realised volatility (HAR-RV) and a multivariate k-th order nonparametric causality-in-quantiles framework. Our results have important implications both for investors and policymakers.     

Oil price uncertainty and movements in the US government bond risk premia

In this paper, we analyze the predictability of the movements of bond premia of US Treasury due to oil price uncertainty over the monthly period 1953:06 to 2016:12. For our purpose, we use a higher order nonparametric causality-in-quantiles framework, which in turn, allows us to test for predictability over the entire conditional distribution of not only bond returns, but also its volatility, by controlling for misspecification due to uncaptured nonlinearity and structural breaks, which we show to exist in our data. We find that oil uncertainty not only predicts (increases) US bond returns, but also its volatility, with the effect on the latter being stronger. In addition, oil uncertainty tends to have a stronger impact on the shortest and longest maturities (2- and 5-year), and relatively weaker impact on bonds with medium-term (3- and 4-year) maturities. Our results are robust to alternative measures of oil market uncertainty and bond market volatility.     

A discrete-time model for daily S & P500 returns and realized variations: Jumps and leverage effects

We develop an empirically highly accurate discrete-time daily stochastic volatility model that explicitly distinguishes between the jump and continuous-time components of price movements using nonparametric realized variation and Bipower variation measures constructed from high-frequency intraday data. The model setup allows us to directly assess the structural inter-dependencies among the shocks to returns and the two different volatility components. The model estimates suggest that the leverage effect, or asymmetry between returns and volatility, works primarily through the continuous volatility component. The excellent fit of the model makes it an ideal candidate for an easy-to-implement auxiliary model in the context of indirect estimation of empirically more realistic continuous-time jump diffusion and Lévy-driven stochastic volatility models, effectively incorporating the interdaily dependencies inherent in the high-frequency intraday data.     

Geopolitical risks and stock market dynamics of the BRICS

This paper examines the effect of geopolitical uncertainty on return and volatility dynamics in the BRICS stock markets via nonparametric causality-in-quantiles tests. The effect of geopolitical risks (GPRs) is found to be heterogeneous across the BRICS stock markets, suggesting that news regarding geopolitical tensions do not affect return dynamics in these markets in a uniform way. GPRs are generally found to impact stock market volatility measures rather than returns, and often at return quantiles below the median, indicating the role of GPRs as a driver of bad volatility in these markets. While Russia bears the greatest risk exposure to GPRs in terms of both return and volatility, India is found to be the most resilient BRICS nation in the group. Noting that geopolitical shocks and in particular terrorist incidents are largely unanticipated, our findings underscore the importance of a strong financial sector that can help return the market to stability and an open economy that allows local investors to diversify country-specific risks in their portfolios.     

Time-varying leverage effects

Vast empirical evidence points to the existence of a negative correlation, named ”leverage effect”, between shocks to variance and shocks to returns. We provide a nonparametric theory of leverage estimation in the context of a continuous-time stochastic volatility model with jumps in returns, jumps in variance, or both. Leverage is defined as a flexible function of the state of the firm, as summarized by the spot variance level. We show that its point-wise functional estimates have asymptotic properties (in terms of rates of convergence, limiting biases, and limiting variances) which crucially depend on the likelihood of the individual jumps and co-jumps as well as on the features of the jump size distributions. Empirically, we find economically important time-variation in leverage with more negative values associated with higher variance levels.     

No-arbitrage semi-martingale restrictions for continuous-time volatility models subject to leverage effects,jumps and i.i.d. noise: Theory and testable distributional implications

We develop a sequential procedure to test the adequacy of jump-diffusion models for return distributions. We rely on intraday data and nonparametric volatility measures, along with a new jump detection technique and appropriate conditional moment tests, for assessing the import of jumps and leverage effects. A novel robust-to-jumps approach is utilized to alleviate microstructure frictions for realized volatility estimation. Size and power of the procedure are explored through Monte Carlo methods. Our empirical findings support the jump-diffusive representation for S&P500 futures returns but reveal it is critical to account for leverage effects and jumps to maintain the underlying semi-martingale assumption.     

Short-term spot rate models with nonparametric deterministic drift

Most studies assume stationarity when testing continuous-time interest-rate models. However, consistent with Bierens [Bierens, H. (1997). Testing the unit root with drift hypothesis against nonlinear trend stationary, with an application to the US price level and interest rate. Journal of Econometrics, 81, 29–64; Bierens, H. (2000). Nonparametric nonlinear co-trending analysis, with an application to interest and inflation in the United States. Journal of Business and Economics Statistics, 18, 323–337], our nonparametric test results support nonlinear trend stationarity. To accommodate nonstationarity, we detrend the interest-rate series and re-examine a variety of continuous-time models. The goodness-of-fit improves significantly for those models with drift-induced mean reversion and worsens for those with high volatility elasticity. The inclusion of a nonparametric trend component in the drift significantly reduces the level effect on the interest-rate volatility. These results suggest that the misspecification of the constant elasticity model should be attributed to the nonlinear trend component of the short-term interest-rate process.     

Testing for multivariate volatility functions using minimum volume sets and inverse regression

We propose two new types of nonparametric tests for investigating multivariate regression functions. The tests are based on cumulative sums coupled with either minimum volume sets or inverse regression ideas; involving no multivariate nonparametric regression estimation. The methods proposed facilitate the investigation for different features such as if a multivariate regression function is (i) constant, (ii) of a bathtub shape, and (iii) in a given parametric form. The inference based on those tests may be further enhanced through associated diagnostic plots. Although the potential use of those ideas is much wider, we focus on the inference for multivariate volatility functions in this paper, i.e. we test for (i) heteroscedasticity, (ii) the so-called ‘smiling effect’, and (iii) some parametric volatility models. The asymptotic behavior of the proposed tests is investigated, and practical feasibility is shown via simulation studies. We further illustrate our methods with real financial data.     

Options and earnings announcements: an empirical study for the European Options Exchange

In this paper we give an introduction in option pricing theory and explicitly specify the Black-Scholes model. Although market participants use this and similar models to price options, they violate one of the fundamental assumptions of the model. They do not set a constant value for the volatility of the underlying asset over time, but change the volatility even during a day. By means of event study methodology we investigate the volatility of the underlying asset and the volatility implicit in option prices around earnings announcements by firms. We find that the volatility in option prices increases before the announcement date and drops sharply afterwards. The volatility of the underlying stocks is higher only at the announcement dates and we do not observe a higher volatility around these dates. Hence, the constant volatility of the underlying asset, which is one of the assumptions in the Black-Scholes model, does not hold. However, the market seems to correctly anticipate the change in volatility, by correcting option prices.     

Time series properties of ARCH processes with persistent covariates

We investigate the time series properties of a volatility model, whose conditional variance is specified as in ARCH with an additional persistent covariate. The included covariate is assumed to be an integrated or nearly integrated process, with its effect on volatility given by a wide class of nonlinear volatility functions. In the paper, such a model is shown to generate many important characteristics that are commonly observed in financial time series. In particular, the model yields persistence in volatility, and also well predicts leptokurtosis. This is true for any type of volatility functions considered in the paper, as long as the covariate is integrated or nearly integrated. Stationary covariates cannot produce important characteristics observed in many financial time series. We present two empirical applications of the model, which show that the default premium (the yield spread between Baa and Aaa corporate bonds) affects stock return volatility and the interest rate differential between two countries accounts for exchange rate return volatility. The forecast evaluation shows that the model generally outperforms GARCH and FIGARCH at relatively lower frequencies.     

Testing for unit roots in time series models with non-stationary volatility

Many of the key macro-economic and financial variables in developed economies are characterized by permanent volatility shifts. It is known that conventional unit root tests are potentially unreliable in the presence of such behaviour, depending on a particular function (the variance profile) of the underlying volatility process. Somewhat surprisingly then, very little work has been undertaken to develop unit root tests which are robust to the presence of permanent volatility shifts. In this paper we fill this gap in the literature by proposing tests which are valid in the presence of a quite general class of permanent variance changes which includes single and multiple (abrupt and smooth-transition) volatility change processes as special cases. Our solution uses numerical methods to simulate the asymptotic null distribution of the statistics based on a consistent estimate of the variance profile which we also develop. The practitioner is not required to specify a parametric model for volatility. An empirical illustration using producer price inflation series from the Stock–Watson database is reported.