Volatility forecasting and microstructure noise

It is common practice to use the sum of frequently sampled squared returns to estimate volatility, yielding the so-called realized volatility. Unfortunately, returns are contaminated by market microstructure noise. Several noise-corrected realized volatility measures have been proposed. We assess to what extent correction for microstructure noise improves forecasting future volatility using a MIxed DAta Sampling (MIDAS) regression framework. We study the population prediction properties of various realized volatility measures, assuming i.i.d$i.i.d$. microstructure noise. Next we study optimal sampling issues theoretically, when the objective is forecasting and microstructure noise contaminates realized volatility. We distinguish between conditional and unconditional optimal sampling schemes, and find that conditional optimal sampling seems to work reasonably well in practice.     

Improving the realized GARCH’s volatility forecast for Bitcoin with jump-robust estimators

This study employs the realized GARCH (RGARCH) model to estimate the volatility of Bitcoin returns and measure the benefits of various scaled realized measures in forecasting volatility. Empirical results show that considerable price jumps occurred in the Bitcoin market, suggesting that a jump-robust realized measure is crucial to estimate Bitcoin volatility. The RGARCH model, especially the one with tri-power variation, outperforms the standard GARCH model. Additionally, the RGARCH model with jump-robust realized measures can provide steady forecasting performance. This study is timely given that the CME may release a Bitcoin option product and our results are relevant to option pricing     

Forecasting realized volatility: a Bayesian model‐averaging approach

How to measure and model volatility is an important issue in finance. Recent research uses high‐frequency intraday data to construct ex post measures of daily volatility. This paper uses a Bayesian model‐averaging approach to forecast realized volatility. Candidate models include autoregressive and heterogeneous autoregressive specifications based on the logarithm of realized volatility, realized power variation, realized bipower variation, a jump and an asymmetric term. Applied to equity and exchange rate volatility over several forecast horizons, Bayesian model averaging provides very competitive density forecasts and modest improvements in point forecasts compared to benchmark models. We discuss the reasons for this, including the importance of using realized power variation as a predictor. Bayesian model averaging provides further improvements to density forecasts when we move away from linear models and average over specifications that allow for GARCH effects in the innovations to log‐volatility. Copyright © 2009 John Wiley & Sons, Ltd.     

Is there a risk–return trade‐off? Evidence from high‐frequency data

This paper examines the intertemporal relation between risk and return for the aggregate stock market using high‐frequency data. We use daily realized, GARCH, implied, and range‐based volatility estimators to determine the existence and significance of a risk–return trade‐off for several stock market indices. We find a positive and statistically significant relation between the conditional mean and conditional volatility of market returns at the daily level. This result is robust to alternative specifications of the volatility process, across different measures of market return and sample periods, and after controlling for macro‐economic variables associated with business cycle fluctuations. We also analyze the risk–return relationship over time using rolling regressions, and find that the strong positive relation persists throughout our sample period. The market risk measures adopted in the paper add power to the analysis by incorporating valuable information, either by taking advantage of high‐frequency intraday data (in the case of realized, GARCH, and range volatility) or by utilizing the market's expectation of future volatility (in the case of implied volatility index). Copyright © 2006 John Wiley & Sons, Ltd.     

On portfolio optimization: How and when do we benefit from high‐frequency data?

We examine how the use of high‐frequency data impacts the portfolio optimization decision. Prior research has documented that an estimate of realized volatility is more precise when based upon intraday returns rather than daily returns. Using the framework of a professional investment manager who wishes to track the S&P 500 with the 30 Dow Jones Industrial Average stocks, we find that the benefits of using high‐frequency data depend upon the rebalancing frequency and estimation horizon. If the portfolio is rebalanced monthly and the manager has access to at least the previous 12 months of data, daily data have the potential to perform as well as high‐frequency data. However, substantial improvements in the portfolio optimization decision from high‐frequency data are realized if the manager rebalances daily or has less than a 6‐month estimation window. These findings are robust to transaction costs. Copyright © 2009 John Wiley & Sons, Ltd.     

Stock market reactions to upside and downside volatility of Bitcoin: A quantile analysis

We investigate how sensitive developed and emerging equity markets are to volatility dynamics of Bitcoin during tranquil, bear, and bull market regimes. Intraday price fluctuations of Bitcoin are represented by three measures of realized volatility, viz. total variance, upside semivariance, and downside semivariance. Our empirical analysis relies on a quantile regression framework, after orthogonalizing raw returns with respect to an array of relevant global factors and accounting for structural shifts in the series. The results suggest that developed-market returns are positively related to the realized variance proxy across various market conditions, while emerging-market returns are positively (negatively) correlated with realized variance during bear (normal and bull) market periods. The upside (downside) component of realized variance has a negative (positive) influence on returns of either market category, and the dependence structure is highly asymmetric across the return distribution. Additionally, we document that developed and emerging markets are more sensitive to downside volatility than to upside volatility when they enter tranquil or bull territory. Our results offer practical implications for policymakers and investors.     

The day of the week effect on stock market volatility

This study tests the presence of the day of the week effect on stock market volatility by using the S&P 500 market index during the period of January 1973 and October 1997. The findings shown that the day of the week effect is present in both volatility and return equations. While the highest and lowest returns are observed on Wednesday and Monday, the highest and the lowest volatility are observed on Friday and Wednesday, respectively. Further investigation of sub-periods reinforces our findings that the volatility pattern across the days of the week is statistically different.(JEL G10, G12, C22)     

Two are better than one: Volatility forecasting using multiplicative component GARCH-MIDAS models

We examine the properties and forecast performance of multiplicative volatility specifications that belong to the class of generalized autoregressive conditional heteroskedasticity–mixed-data sampling (GARCH-MIDAS) models suggested in Engle, Ghysels, and Sohn (Review of Economics and Statistics, 2013, 95, 776–797). In those models volatility is decomposed into a short-term GARCH component and a long-term component that is driven by an explanatory variable. We derive the kurtosis of returns, the autocorrelation function of squared returns, and the R² of a Mincer–Zarnowitz regression and evaluate the QMLE and forecast performance of these models in a Monte Carlo simulation. For S&P 500 data, we compare the forecast performance of GARCH-MIDAS models with a wide range of competitor models such as HAR (heterogeneous autoregression), realized GARCH, HEAVY (high-frequency-based volatility) and Markov-switching GARCH. Our results show that the GARCH-MIDAS based on housing starts as an explanatory variable significantly outperforms all competitor models at forecast horizons of 2 and 3 months ahead.     

Asset price volatility and banks

This paper examines the operation of Diamond–Dybvig banks when depositors have access to the asset market. Previous studies have shown that banks are redundant in this environment since it is impossible to prevent the strategic withdrawals. This paper shows that the strategic withdrawals can be prevented if the market risk, due to asset price volatility, is considered. Banks provide deterministic returns to the depositors since the aggregate withdrawals are predictable, and therefore, banks can choose the portfolio such that no asset liquidation is involved. However, an individual consumer with stochastic liquidity need is vulnerable to the price volatility if he holds the asset directly. Therefore, banks improve the consumers’ welfare by providing the insurance against not only the liquidity shock but also the market risk. Banks are not redundant.     

Forecasting volatility with time-varying leverage and volatility of volatility effects

Predicting volatility is of primary importance for business applications in risk management, asset allocation, and the pricing of derivative instruments. This paper proposes a measurement model that considers the possibly time-varying interaction of realized volatility and asset returns according to a bivariate model to capture its major characteristics: (i) the long-term memory of the volatility process, (ii) the heavy-tailedness of the distribution of returns, and (iii) the negative dependence of volatility and daily market returns. We assess the relevance of the effects of “the volatility of volatility” and time-varying “leverage” to the out-of-sample forecasting performance of the model, and evaluate the density of forecasts of market volatility. Empirical results show that our specification can outperform the benchmark HAR–GARCH model in terms of both point and density forecasts.     

Trading and non-trading period realized market volatility: Does it matter for forecasting the volatility of US stocks?

We study the potential merits of using trading and non-trading period market volatilities to model and forecast the stock volatility over the next one to 22 days. We demonstrate the role of overnight volatility information by estimating heterogeneous autoregressive (HAR) model specifications with and without a trading period market risk factor using ten years of high-frequency data for the 431 constituents of the S&P 500 index. The stocks’ own overnight squared returns perform poorly across stocks and forecast horizons, as well as in the asset allocation exercise. In contrast, we find overwhelming evidence that the market-level volatility, proxied by S&P Mini futures, matters significantly for improving the model fit and volatility forecasting accuracy. The greatest model fit and forecast improvements are found for short-term forecast horizons of up to five trading days, and for the non-trading period market-level volatility. The documented increase in forecast accuracy is found to be associated with the stocks’ sensitivity to the market risk factor. Finally, we show that both the trading and non-trading period market realized volatilities are relevant in an asset allocation context, as they increase the average returns, Sharpe ratios and certainty equivalent returns of a mean–variance investor.     

REALIZED BETA GARCH: A MULTIVARIATE GARCH MODEL WITH REALIZED MEASURES OF VOLATILITY

We introduce a multivariate generalized autoregressive conditional heteroskedasticity (GARCH) model that incorporates realized measures of variances and covariances. Realized measures extract information about the current levels of volatilities and correlations from high‐frequency data, which is particularly useful for modeling financial returns during periods of rapid changes in the underlying covariance structure. When applied to market returns in conjunction with returns on an individual asset, the model yields a dynamic model specification of the conditional regression coefficient that is known as the beta. We apply the model to a large set of assets and find the conditional betas to be far more variable than usually found with rolling‐window regressions based exclusively on daily returns. In the empirical part of the paper, we examine the cross‐sectional as well as the time variation of the conditional beta series during the financial crises. Copyright © 2014 John Wiley & Sons, Ltd.     

Dynamic estimation of volatility risk premia and investor risk aversion from option-implied and realized volatilities

This paper proposes a method for constructing a volatility risk premium, or investor risk aversion, index. The method is intuitive and simple to implement, relying on the sample moments of the recently popularized model-free realized and option-implied volatility measures. A small-scale Monte Carlo experiment confirms that the procedure works well in practice. Implementing the procedure with actual S&P500 option-implied volatilities and high-frequency five-minute-based realized volatilities indicates significant temporal dependencies in the estimated stochastic volatility risk premium, which we in turn relate to a set of macro-finance state variables. We also find that the extracted volatility risk premium helps predict future stock market returns.     

Stochastic volatility models: conditional normality versus heavy‐tailed distributions

Most of the empirical applications of the stochastic volatility (SV) model are based on the assumption that the conditional distribution of returns, given the latent volatility process, is normal. In this paper, the SV model based on a conditional normal distribution is compared with SV specifications using conditional heavy‐tailed distributions, especially Student's t‐distribution and the generalized error distribution. To estimate the SV specifications, a simulated maximum likelihood approach is applied. The results based on daily data on exchange rates and stock returns reveal that the SV model with a conditional normal distribution does not adequately account for the two following empirical facts simultaneously: the leptokurtic distribution of the returns and the low but slowly decaying autocorrelation functions of the squared returns. It is shown that these empirical facts are more adequately captured by an SV model with a conditional heavy‐tailed distribution. It also turns out that the choice of the conditional distribution has systematic effects on the parameter estimates of the volatility process. Copyright © 2000 John Wiley & Sons, Ltd.     

The VIX,the variance premium and stock market volatility

We decompose the squared VIX index, derived from US S&P500 options prices, into the conditional variance of stock returns and the equity variance premium. We evaluate a plethora of state-of-the-art volatility forecasting models to produce an accurate measure of the conditional variance. We then examine the predictive power of the VIX and its two components for stock market returns, economic activity and financial instability. The variance premium predicts stock returns while the conditional stock market variance predicts economic activity and has a relatively higher predictive power for financial instability than does the variance premium.     

RARE SHOCKS,GREAT RECESSIONS

We estimate a DSGE (dynamic stochastic general equilibrium) model where rare large shocks can occur, by replacing the commonly used Gaussian assumption with a Student's t‐distribution. Results from the Smets and Wouters (American Economic Review 2007; 97 : 586–606) model estimated on the usual set of macroeconomic time series over the 1964–2011 period indicate that (i) the Student's t specification is strongly favored by the data even when we allow for low‐frequency variation in the volatility of the shocks, and (ii)) the estimated degrees of freedom are quite low for several shocks that drive US business cycles, implying an important role for rare large shocks. This result holds even if we exclude the Great Recession period from the sample. We also show that inference about low‐frequency changes in volatility—and, in particular, inference about the magnitude of Great Moderation—is different once we allow for fat tails. Copyright © 2014 John Wiley & Sons, Ltd.     

The stochastic volatility in mean model and automation: Evidence from TSE

This paper investigates the behavior of volatility in Canadian equity markets before and after automation. We employ a stochastic volatility in mean (SVM) model that incorporates the unobserved volatility as an explanatory variable in the mean equation. The volatility persistent estimates all increase post-automation, with the scaling parameter increasing as well. The parameter estimates which measure both the ex ante relationship between returns and volatility and the volatility feedback effect are found to be negative for all series, and to increase post-automation. Our results fall in line with those of (French, K.R., Schwert, G.W., & Stanbaugh, R.F. (1987). Expected stock returns and volatility. Journal of Financial Economics, 19, 3–29) who find similar relationship between unexpected volatility dynamics and returns and confirm the hypothesis that rational risk-averse investors require higher expected returns when unanticipated increase in future volatility are highly persistent. Finally, our findings are consistent since higher values of persistence are combined with larger negative values for the in-mean parameter.     

Parametric Value-at-Risk analysis: Evidence from stock indices

We evaluate the performance of several volatility models in estimating one-day-ahead Value-at-Risk (VaR) of seven stock market indices using a number of distributional assumptions. Because all returns series exhibit volatility clustering and long range memory, we examine GARCH-type models including fractionary integrated models under normal, Student-t and skewed Student-t distributions. Consistent with the idea that the accuracy of VaR estimates is sensitive to the adequacy of the volatility model used, we find that AR (1)-FIAPARCH (1,d,1) model, under a skewed Student-t distribution, outperforms all the models that we have considered including widely used ones such as GARCH (1,1) or HYGARCH (1,d,1). The superior performance of the skewed Student-t FIAPARCH model holds for all stock market indices, and for both long and short trading positions. Our findings can be explained by the fact that the skewed Student-t FIAPARCH model can jointly accounts for the salient features of financial time series: fat tails, asymmetry, volatility clustering and long memory. In the same vein, because it fails to account for most of these stylized facts, the RiskMetrics model provides the least accurate VaR estimation. Our results corroborate the calls for the use of more realistic assumptions in financial modeling.     

Realized volatility forecasting and market microstructure noise

We extend the analytical results for reduced form realized volatility based forecasting in ABM (2004) to allow for market microstructure frictions in the observed high-frequency returns. Our results build on the eigenfunction representation of the general stochastic volatility class of models developed byMeddahi (2001). In addition to traditional realized volatility measures and the role of the underlying sampling frequencies, we also explore the forecasting performance of several alternative volatility measures designed to mitigate the impact of the microstructure noise. Our analysis is facilitated by a simple unified quadratic form representation for all these estimators. Our results suggest that the detrimental impact of the noise on forecast accuracy can be substantial. Moreover, the linear forecasts based on a simple-to-implement ‘average’ (or ‘subsampled’) estimator obtained by averaging standard sparsely sampled realized volatility measures generally perform on par with the best alternative robust measures.     

Using CARRX models to study factors affecting the volatilities of Asian equity markets

The range of daily asset prices is often used as a measure of volatility. Using a CARRX (conditional autoregressive range with exogenous variables) model, and the parsimony principle, the paper investigates the factors affecting the volatilities of Asian equity markets. Since the beginning of the new Century, emerging Asian markets such as Taiwan and Shanghai have been undergoing various stages of financial globalization. The volatility of the equity market may not be explained solely by its own dynamics. In this paper, we examine volatility using the following factors: (i) lagged returns; (ii) lagged absolute returns; (iii) own trading volume; (iv) U.S. factors; (v) European factors; and (vi) regional (Asian) factors. Points (i) and (iii) are by and large significant, while (ii) is not. Controlling for (i), (ii) and (iii), we find evidence that the volatility of European markets has spillovers on to both the Taiwan and Tokyo markets, mild evidence that the volatility of the U.S. market has spillovers on to the Hong Kong market, but there are no spillovers from the European or U.S. markets on to the Shanghai market.