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.     

Forecasting currency volatility: A comparison of implied volatilities and AR(FI)MA models

We compare forecasts of the realized volatility of the pound, mark and yen exchange rates against the dollar, calculated from intraday rates, over horizons ranging from one day to three months. Our forecasts are obtained from a short memory ARMA model, a long memory ARFIMA model, a GARCH model and option implied volatilities. We find intraday rates provide the most accurate forecasts for the one-day and one-week forecast horizons while implied volatilities are at least as accurate as the historical forecasts for the one-month and three-month horizons. The superior accuracy of the historical forecasts, relative to implied volatilities, comes from the use of high frequency returns, and not from a long memory specification. We find significant incremental information in historical forecasts, beyond the implied volatility information, for forecast horizons up to one week.     

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.     

The incremental volatility information in one million foreign exchange quotations

The volatility information found in high-frequency exchange rate quotations and in implied volatilities is compared by estimating ARCH models for DM/$ returns. Reuters quotations are used to calculate five-minute returns and hence hourly and daily estimates of realised volatility that can be included in equations for the conditional variances of hourly and daily returns. The ARCH results show that there is a significant amount of information in five-minute returns that is incremental to options information when estimating hourly variances. The same conclusion is obtained by an out-of-sample comparison of forecasts of hourly realised 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.     

VOLATILITY FORECASTS,TRADING VOLUME,AND THE ARCH VERSUS OPTION‐IMPLIED VOLATILITY TRADE‐OFF

We investigate empirically the role of trading volume (1) in predicting the relative informativeness of volatility forecasts produced by autoregressive conditional heteroskedasticity (ARCH) models versus the volatility forecasts derived from option prices, and (2) in improving volatility forecasts produced by ARCH and option models and combinations of models. Daily and monthly data are explored. We find that if trading volume was low during period t?1 relative to the recent past, ARCH is at least as important as options for forecasting future stock market volatility. Conversely, if volume was high during period t?1 relative to the recent past, option‐implied volatility is much more important than ARCH for forecasting future volatility. Considering relative trading volume as a proxy for changes in the set of information available to investors, our findings reveal an important switching role for trading volume between a volatility forecast that reflects relatively stale information (the historical ARCH estimate) and the option‐implied forward‐looking estimate.     

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.     

STAR and ANN models: forecasting performance on the Spanish “Ibex-35” stock index

This paper studies whether it is possible to exploit the nonlinear behaviour of daily returns on the Spanish Ibex-35 stock index returns to improve forecasts over short and long horizons. In this sense, we examine the out-of-sample forecast performance of smooth transition autoregression (STAR) models and artificial neural networks (ANNs). We use one-step (obtained by using recursive and nonrecursive regressions) and multi-step-ahead forecasting methods. The forecasts are evaluated with statistical and economic criteria. In terms of statistical criteria, we compared the out-of-sample forecasts using goodness of forecast measures and various testing approaches. The results indicate that ANNs consistently surpass the random walk model and, although the evidence for this is weaker, provide better forecasts than the linear AR model and the STAR models for some forecast horizons and forecasting methods. In terms of the economic criteria, we assess the relative forecast performance in a simple trading strategy including the impact of transaction costs on trading strategy profits. The results indicate a better fit for ANN models, in terms of the mean net return and Sharpe risk-adjusted ratio, by using one-step-ahead forecasts. These results show there is a good chance of obtaining a more accurate fit and forecast of the daily stock index returns by using one-step-ahead predictors and nonlinear models, but that these are inherently complex and present a difficult economic interpretation.     

State‐preference pricing and volatility indices

This study uses a state‐preference pricing approach to develop a state‐price volatility index (SVX), as a forecast for market future realised volatility. We show that SVX is a more efficient forecaster than CBOE VIX for 30‐day realised volatility of SPX returns, using both in‐the‐sample and out‐of‐the‐sample tests. This result is robust to different measures of realised market volatilities. We also show that SVX provides a better volatility forecast than other alternative measures, including the at‐the‐money implied volatilities and GARCH (1, 1) volatility. Our results provide a foundation for forecasting higher risk‐neutral moments using the same state prices.     

The information content of implied volatilities and model-free volatility expectations: Evidence from options written on individual stocks

We measure the volatility information content of stock options for individual firms using option prices for 149 US firms and the S&P 100 index. We use ARCH and regression models to compare volatility forecasts defined by historical stock returns, at-the-money implied volatilities and model-free volatility expectations for every firm. For 1-day-ahead estimation, a historical ARCH model outperforms both of the volatility estimates extracted from option prices for 36% of the firms, but the option forecasts are nearly always more informative for those firms that have the more actively traded options. When the prediction horizon extends until the expiry date of the options, the option forecasts are more informative than the historical volatility for 85% of the firms. However, at-the-money implied volatilities generally outperform the model-free volatility expectations.     

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.     

A multi-horizon comparison of density forecasts for the S&P 500 using index returns and option prices

We compare density forecasts of the S&P 500 index from 1991 to 2004, obtained from option prices and daily and 5-min index returns. Risk-neutral densities are given by using option prices to estimate diffusion and jump-diffusion processes which incorporate stochastic volatility. Three transformations are then used to obtain real-world densities. These densities are compared with historical densities defined by ARCH models. For horizons of two and four weeks the best forecasts are obtained from risk-transformations of the risk-neutral densities, while the historical forecasts are superior for the one-day horizon; our ranking criterion is the out-of-sample likelihood of observed index levels. Mixtures of the real-world and historical densities have higher likelihoods than both components for short forecast horizons.     

Does implied volatility provide any information beyond that captured in model-based volatility forecasts?

This paper contributes to our understanding of the informational content of implied volatility. Here we examine whether the S&P 500 implied volatility index (VIX) contains any information relevant to future volatility beyond that available from model based volatility forecasts. It is argued that this approach differs from the traditional forecast encompassing approach used in earlier studies. The findings indicate that the VIX index does not contain any such additional information relevant for forecasting volatility.     

Forecasting implied volatility in foreign exchange markets: a functional time series approach

We utilise novel functional time series (FTS) techniques to characterise and forecast implied volatility in foreign exchange markets. In particular, we examine the daily implied volatility curves of FX options, namely; Euro/United States Dollar, Euro/British Pound, and Euro/Japanese Yen. The FTS model is shown to produce both realistic and plausible implied volatility shapes that closely match empirical data during the volatile 2006–2013 period. Furthermore, the FTS model significantly outperforms implied volatility forecasts produced by traditionally employed parametric models. The evaluation is performed under both in-sample and out-of-sample testing frameworks with our findings shown to be robust across various currencies, moneyness segments, contract maturities, forecasting horizons, and out-of-sample window lengths. The economic significance of the results is highlighted through the implementation of a simple trading strategy.     

Forecasting hedge fund volatility: a Markov regime-switching approach

The article addresses forecasting volatility of hedge fund (HF) returns by using a non-linear Markov-Switching GARCH (MS-GARCH) framework. The in- and out-of-sample, multi-step ahead volatility forecasting performance of GARCH(1,1) and MS-GARCH(1,1) models is compared when applied to 12 global HF indices over the period of January 1990 to October 2010. The results identify different regimes with periods of high and low volatility for most HF indices. In-sample estimation results reveal a superior performance of the MS-GARCH model. The findings show that regime switching is related to structural changes in the market factor for most strategies. Out-of-sample forecasting shows that the MS-GARCH formulation provides more accurate volatility forecasts for most forecast horizons and for most HF strategies. Inclusion of MS dynamics in the GARCH specification highly improves the volatility forecasts for those strategies that are particularly sensitive to general macroeconomic conditions, such as Distressed Restructuring and Merger Arbitrage.     

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.     

The information content of risk-neutral skewness for volatility forecasting

The paper investigates whether risk-neutral skewness has incremental explanatory power for future volatility in the S&P 500 index. While most of previous studies have investigated the usefulness of historical volatility and implied volatility for volatility forecasting, we study the information content of risk-neutral skewness in volatility forecasting model. In particular, we concentrate on Heterogeneous Autoregressive model of Realized Volatility and Implied Volatility (HAR-RV-IV). We find that risk-neutral skewness contains additional information for future volatility, relative to past realized volatilities and implied volatility. Out-of-sample analyses confirm that risk-neutral skewness improves significantly the accuracy of volatility forecasts for future volatility.     

Financial crisis,Value-at-Risk forecasts and the puzzle of dependency modeling

Forecasting Value-at-Risk (VaR) for financial portfolios is a crucial task in applied financial risk management. In this paper, we compare VaR forecasts based on different models for return interdependencies: volatility spillover (Engle & Kroner, 1995), dynamic conditional correlations (Engle, 2002, 2009) and (elliptical) copulas (Embrechts et al., 2002). Moreover, competing models for marginal return distributions are applied. In particular, we apply extreme value theory (EVT) models to GARCH-filtered residuals to capture excess returns.Drawing on a sample of daily data covering both calm and turbulent market phases, we analyze portfolios consisting of German Stocks, national indices and FX-rates. VaR forecasts are evaluated using statistical backtesting and Basel II criteria. The extensive empirical application favors the elliptical copula approach combined with extreme value theory (EVT) models for individual returns. 99% VaR forecasts from the EVT-GARCH-copula model clearly outperform estimates from alternative models accounting for dynamic conditional correlations and volatility spillover for all asset classes in times of financial crisis.     

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.     

The jump component of S&P 500 volatility and the VIX index

Much research has investigated the differences between option implied volatilities and econometric model-based forecasts. Implied volatility is a market determined forecast, in contrast to model-based forecasts that employ some degree of smoothing of past volatility to generate forecasts. Implied volatility has the potential to reflect information that a model-based forecast could not. This paper considers two issues relating to the informational content of the S&P 500 VIX implied volatility index. First, whether it subsumes information on how historical jump activity contributed to the price volatility, followed by whether the VIX reflects any incremental information pertaining to future jump activity relative to model-based forecasts. It is found that the VIX index both subsumes information relating to past jump contributions to total volatility and reflects incremental information pertaining to future jump activity. This issue has not been examined previously and expands our understanding of how option markets form their volatility forecasts.