Forecasting daily variability of the S&P 100 stock index using historical,realised and implied volatility measurements

The increasing availability of financial market data at intraday frequencies has not only led to the development of improved volatility measurements but has also inspired research into their potential value as an information source for volatility forecasting. In this paper, we explore the forecasting value of historical volatility (extracted from daily return series), of implied volatility (extracted from option pricing data) and of realised volatility (computed as the sum of squared high frequency returns within a day). First, we consider unobserved components (UC-RV) and long memory models for realised volatility which is regarded as an accurate estimator of volatility. The predictive abilities of realised volatility models are compared with those of stochastic volatility (SV) models and generalised autoregressive conditional heteroskedasticity (GARCH) models for daily return series. These historical volatility models are extended to include realised and implied volatility measures as explanatory variables for volatility. The main focus is on forecasting the daily variability of the Standard & Poor's 100 (S&P 100) stock index series for which trading data (tick by tick) of almost 7 years is analysed. The forecast assessment is based on the hypothesis of whether a forecast model is outperformed by alternative models. In particular, we will use superior predictive ability tests to investigate the relative forecast performances of some models. Since volatilities are not observed, realised volatility is taken as a proxy for actual volatility and is used for computing the forecast error. A stationary bootstrap procedure is required for computing the test statistic and its p-value. The empirical results show convincingly that realised volatility models produce far more accurate volatility forecasts compared to models based on daily returns. Long memory models seem to provide the most accurate forecasts.     

Forecasting daily exchange rate volatility using intraday returns

This study investigates whether intraday returns contain important information for forecasting daily volatility. Whereas in the existing literature volatility models for daily returns are improved by including intraday information such as the daily high and low, volume, the number of trades, and intraday returns, here the volatility of intraday returns is explicitly modelled. Daily volatility forecasts are constructed from multiple volatility forecasts for intraday intervals. It is shown for the DEM/USD and the YEN/USD exchange rates that this results in superior forecasts for daily volatility.     

Volatility Forecasting in the Hang Seng Index using the GARCH Approach

The aim of this paper is to add to the literature on volatility forecasting using data from the Hong Kong stock market to determine if forecasts from GARCH based models can outperform simple historical averaging models. Overall, unlike previous studies we find that the GARCH models with non-Normal distributions show a robust volatility forecasting performance in comparison to the historical models. The results indicate that although not all models outperform simple historical averaging, the EGARCH based models, with non-normal conditional volatility, tend to produce more accurate out-of-sample forecasts using both standard measures of forecast accuracy and financial loss functions. In addition we test for asymmetric adjustment in the Hang Seng, finding strong evidence of asymmetries due to the domination of financial and property firms in this market.     

Forecasting exchange rate volatility: The superior performance of conditional combinations of time series and option implied forecasts

This paper provides empirical evidence that combinations of option implied and time series volatility forecasts that are conditional on current information are statistically superior to individual models, unconditional combinations, and hybrid forecasts. Superior forecasting performance is achieved by both, taking into account the conditional expected performance of each model given current information, and combining individual forecasts. The method used in this paper to produce conditional combinations extends the application of conditional predictive ability tests to select forecast combinations. The application is for volatility forecasts of the Mexican peso–US dollar exchange rate, where realized volatility calculated using intraday data is used as a proxy for the (latent) daily volatility.     

Combining long memory and level shifts in modelling and forecasting the volatility of asset returns

We propose a parametric state space model of asset return volatility with an accompanying estimation and forecasting framework that allows for ARFIMA dynamics, random level shifts and measurement errors. The Kalman filter is used to construct the state-augmented likelihood function and subsequently to generate forecasts, which are mean and path-corrected. We apply our model to eight daily volatility series constructed from both high-frequency and daily returns. Full sample parameter estimates reveal that random level shifts are present in all series. Genuine long memory is present in most high-frequency measures of volatility, whereas there is little remaining dynamics in the volatility measures constructed using daily returns. From extensive forecast evaluations, we find that our ARFIMA model with random level shifts consistently belongs to the 10% Model Confidence Set across a variety of forecast horizons, asset classes and volatility measures. The gains in forecast accuracy can be very pronounced, especially at longer horizons.     

Quantile forecasts of daily exchange rate returns from forecasts of realized volatility

Quantile forecasts are central to risk management decisions because of the widespread use of Value-at-Risk. A quantile forecast is the product of two factors: the model used to forecast volatility, and the method of computing quantiles from the volatility forecasts. In this paper we calculate and evaluate quantile forecasts of the daily exchange rate returns of five currencies. The forecasting models that have been used in recent analyses of the predictability of daily realized volatility permit a comparison of the predictive power of different measures of intraday variation and intraday returns in forecasting exchange rate variability. The methods of computing quantile forecasts include making distributional assumptions for future daily returns as well as using the empirical distribution of predicted standardized returns with both rolling and recursive samples. Our main findings are that the Heterogenous Autoregressive model provides more accurate volatility and quantile forecasts for currencies which experience shifts in volatility, such as the Canadian dollar, and that the use of the empirical distribution to calculate quantiles can improve forecasts when there are shifts.     

Implied volatility index for the Norwegian equity market

We introduce and evaluate the NOVIX - an implied volatility index for the Norwegian equity index OBX. NOVIX is created according to the VIX methodology. We compare the NOVIX to the German VDAX-NEW and the U.S. VIX and find that NOVIX has similar properties as these two indices. We also evaluate the VIX, VDAX-NEW and NOVIX in terms of volatility forecasting. As a benchmark model we use a precise HAR model of Corsi (2009) based on high-frequency data. All three implied volatility indices significantly improve daily, weekly and monthly forecasts of volatility of their underlying equity indices. This improvement is largest for the VIX, followed by VDAX-NEW and NOVIX.     

Volatility forecasting: Intra-day versus inter-day models

Volatility prediction is the key variable in forecasting the prices of options, value-at-risk and, in general, the risk that investors face. By estimating not only inter-day volatility models that capture the main characteristics of asset returns, but also intra-day models, we were able to investigate their forecasting performance for three European equity indices. A consistent relation is shown between the examined models and the specific purpose of volatility forecasts. Although researchers cannot apply one model for all forecasting purposes, evidence in favor of models that are based on inter-day datasets when their criteria based on daily frequency, such as value-at-risk and forecasts of option prices, are provided.     

Volatility forecasting in the Chinese commodity futures market with intraday data

Given the unique institutional regulations in the Chinese commodity futures market as well as the characteristics of the data it generates, we utilize contracts with three months to delivery, the most liquid contract series, to systematically explore volatility forecasting for aluminum, copper, fuel oil, and sugar at the daily and three intraday sampling frequencies. We adopt popular volatility models in the literature and assess the forecasts obtained via these models against alternative proxies for the true volatility. Our results suggest that the long memory property is an essential feature in the commodity futures volatility dynamics and that the ARFIMA model consistently produces the best forecasts or forecasts not inferior to the best in statistical terms.     

Forecasting volatility of the U.S. oil market

We examine the information content of the CBOE Crude Oil Volatility Index (OVX) when forecasting realized volatility in the WTI futures market. Additionally, we study whether other market variables, such as volume, open interest, daily returns, bid-ask spread and the slope of the futures curve, contain predictive power beyond what is embedded in the implied volatility. In out-of-sample forecasting we find that econometric models based on realized volatility can be improved by including implied volatility and other variables. Our results show that including implied volatility significantly improves daily and weekly volatility forecasts; however, including other market variables significantly improves daily, weekly and monthly volatility forecasts.     

Coincident and leading indicators of the stock market

In this paper we have two goals: first, we want to represent monthly stock market fluctuations by constructing a non-linear coincident financial indicator. The indicator is constructed as an unobservable factor whose first moment and conditional volatility are driven by a two-state Markov variable. It can be interpreted as the investors' real-time belief about the state of financial conditions. Second, we want to explore an approach in which investors may use their perceptions of the state of the economy to form forecasts of financial market conditions and possibly of excess returns. To investigate this, we build leading indicators as forecasts of the estimated coincident financial index. The leading indicators yield better within and out-of-sample performance in forecasting, not only the state of the stock market but also of excess stock returns, as compared with the performance obtained using linear methods that have been proposed in the existing literature.     

A neural network enhanced volatility component model

Volatility prediction, a central issue in financial econometrics, attracts increasing attention in the data science literature as advances in computational methods enable us to develop models with great forecasting precision. In this paper, we draw upon both strands of the literature and develop a novel two-component volatility model. The realized volatility is decomposed by a nonparametric filter into long- and short-run components, which are modeled by an artificial neural network and an ARMA process, respectively. We use intraday data on four major exchange rates and a Chinese stock index to construct daily realized volatility and perform out-of-sample evaluation of volatility forecasts generated by our model and well-established alternatives. Empirical results show that our model outperforms alternative models across all statistical metrics and over different forecasting horizons. Furthermore, volatility forecasts from our model offer economic gain to a mean-variance utility investor with higher portfolio returns and Sharpe ratio.     

Forecasting stock market volatility: Further international evidence

Abstract

This paper evaluates the out-of-sample forecasting accuracy of eleven models for monthly volatility in fifteen stock markets. Volatility is defined as within-month standard deviation of continuously compounded daily returns on the stock market index of each country for the ten-year period 1988 to 1997. The first half of the sample is retained for the estimation of parameters while the second half is for the forecast period. The following models are employed: a random walk model, a historical mean model, moving average models, weighted moving average models, exponentially weighted moving average models, an exponential smoothing model, a regression model, an ARCH model, a GARCH model, a GJR-GARCH model, and an EGARCH model. First, standard (symmetric) loss functions are used to evaluate the performance of the competing models: mean absolute error, root mean squared error, and mean absolute percentage error. According to all of these standard loss functions, the exponential smoothing model provides superior forecasts of volatility. On the other hand, ARCH-based models generally prove to be the worst forecasting models. Asymmetric loss functions are employed to penalize under-/over-prediction. When under-predictions are penalized more heavily, ARCH-type models provide the best forecasts while the random walk is worst. However, when over-predictions of volatility are penalized more heavily, the exponential smoothing model performs best while the ARCH-type models are now universally found to be inferior forecasters.     

Dynamic hedging with futures: a copula-based GARCH model with high-frequency data

Modeling the joint distribution of spot and futures returns is crucial for establishing optimal hedging strategies. This paper proposes a new class of dynamic copula-GARCH models that exploits information from high-frequency data for hedge ratio estimation. The copula theory facilitates constructing a flexible distribution; the inclusion of realized volatility measures constructed from high-frequency data enables copula forecasts to swiftly adapt to changing markets. By using data concerning equity index returns, the estimation results show that the inclusion of realized measures of volatility and correlation greatly enhances the explanatory power in the modeling. Moreover, the out-of-sample forecasting results show that the hedged portfolios constructed from the proposed model are superior to those constructed from the prevailing models in reducing the (estimated) conditional hedged portfolio variance. Finally, the economic gains from exploiting high-frequency data for estimating the hedge ratios are examined. It is found that hedgers obtain additional benefits by including high-frequency data in their hedging decisions; more risk-averse hedgers generate greater benefits.     

Forecasting global stock market volatilities in an uncertain world

We investigate the predictive relationship between uncertainty and global stock market volatilities from a high-frequency perspective. We show that uncertainty contains information beyond fundamentals (volatility) and strongly affects stock market volatility. Using several crucial uncertainty measures (i.e., uncertainty and implied volatility indices), we prove that the CBOE volatility index (VIX) performs best in point (density) forecasting; the financial stress index (FSI) in directional forecasting. Furthermore, VIX's predictive power improved dramatically after the COVID-19 outbreak, and the VIX-based portfolio strategy enables mean-variance investors to achieve higher returns. There are two empirical properties of VIX: (i) it helps reduce significantly forecast variance rather than bias; and (ii) its forecasts encompass other uncertainty forecasts well. Overall, we highlight the importance of considering uncertainty when exploring the expected stock market volatility.     

FORECASTING VOLATILITY FOR PORTFOLIO SELECTION

The volatility of an asset is a primary input to the portfolio selection problem. Information about volatility is available from two sources, namely the share market and the option market. This paper examines the forecasting performance, over a three month investment horizon, of time series forecasts (from the share market) and option based implied volatilities. Three time series models, including GARCH, are used and twenty four implied volatility estimation models are employed. Using a data set of twelve UK companies, it is demonstrated that implied volatilities produce better individual forecasts than time series. However, more remarkably, forecasts combining implied volatilies and time series estimates significantly outperform both component forecasts.     

An evaluation of volatility forecasting techniques

The existing literature contains conflicting evidence regarding the relative quality of stock market volatility forecasts. Evidence can be found supporting the superiority of relatively complex models (including ARCH class models), while there is also evidence supporting the superiority of more simple alternatives. These inconsistencies are of particular concern because of the use of, and reliance on, volatility forecasts in key economic decision-making and analysis, and in asset/option pricing. This paper employs daily Australian data to examine this issue. The results suggest that the ARCH class of models and a simple regression model provide superior forecasts of volatility. However, the various model rankings are shown to be sensitive to the error statistic used to assess the accuracy of the forecasts. Nevertheless, a clear message is that volatility forecasting is a notoriously difficult task.     

Forecasting EUR–USD implied volatility: The case of intraday data

This study models and forecasts the evolution of intraday implied volatility on an underlying EUR–USD exchange rate for a number of maturities. To our knowledge we are the first to employ high frequency data in this context. This allows the construction of forecasting models that can attempt to exploit intraday seasonalities such as overnight effects. Results show that implied volatility is predictable at shorter horizons, within a given day and across the term structure. Moreover, at the conventional daily frequency, intraday seasonality effects can be used to augment the forecasting power of models. The type of inefficiency revealed suggests potentially profitable trading models.     

Improving Volatility Forecasts Using Market‐Elicited Ambiguity Aversion Information

Distinguishing between risk and uncertainty, this paper proposes a volatility forecasting framework that incorporates asymmetric ambiguity shocks in the (exponential) generalized autoregressive conditional heteroskedasticity‐in‐mean conditional volatility process. Spanning 25 years of daily data and considering the differential role of investors' ambiguity attitudes in the gain and loss domains, our models capture a rich set of information and provide more accurate volatility forecasts both in‐sample and out‐of‐sample when compared to ambiguity‐free or risk‐based counterparts. Ambiguity‐based volatility‐timing trading strategies confirm the economic significance of our proposed framework and indicate that an annualized excess return of 3.2% over the benchmark could be earned from 1995 to 2014.     

Forecasting oil price realized volatility using information channels from other asset classes

Motivated from Ross (1989) who maintains that asset volatilities are synonymous to the information flow, we claim that cross-market volatility transmission effects are synonymous to cross-market information flows or “information channels” from one market to another. Based on this assertion we assess whether cross-market volatility flows contain important information that can improve the accuracy of oil price realized volatility forecasting. We concentrate on realized volatilities derived from the intra-day prices of the Brent crude oil and four different asset classes (Stocks, Forex, Commodities and Macro), which represent the different “information channels” by which oil price volatility is impacted from. We employ a HAR framework and estimate forecasts for 1-day to 66-days ahead. Our findings provide strong evidence that the use of the different “information channels” enhances the predictive accuracy of oil price realized volatility at all forecasting horizons. Numerous forecasting evaluation tests and alternative model specifications confirm the robustness of our results.