Forecasting volatility of crude oil futures using a GARCH–RNN hybrid approach

Volatility is an important element for various financial instruments owing to its ability to measure the risk and reward value of a given financial asset. Owing to its importance, forecasting volatility has become a critical task in financial forecasting. In this paper, we propose a suite of hybrid models for forecasting volatility of crude oil under different forecasting horizons. Specifically, we combine the parameters of generalized autoregressive conditional heteroscedasticity (GARCH) and Glosten–Jagannathan–Runkle (GJR)-GARCH with long short-term memory (LSTM) to create three new forecasting models named GARCH–LSTM, GJR-LSTM, and GARCH-GJRGARCH LSTM in order to forecast crude oil volatility of West Texas Intermediate on different forecasting horizons and compare their performance with the classical volatility forecasting models. Specifically, we compare the performances against existing methodologies of forecasting volatility such as GARCH and found that the proposed hybrid models improve upon the forecasting accuracy of Crude Oil: West Texas Intermediate under various forecasting horizons and perform better than GARCH and GJR-GARCH, with GG–LSTM performing the best of the three proposed models at 7-, 14-, and 21-day-ahead forecasts in terms of heteroscedasticity-adjusted mean square error and heteroscedasticity-adjusted mean absolute error, with significance testing conducted through the model confidence set showing that GG–LSTM is a strong contender for forecasting crude oil volatility under different forecasting regimes and rolling-window schemes. The contribution of the paper is that it enhances the forecasting ability of crude oil futures volatility, which is essential for trading, hedging, and purposes of arbitrage, and that the proposed model dwells upon existing literature and enhances the forecasting accuracy of crude oil volatility by fusing a neural network model with multiple econometric models.     

Backtesting extreme value theory models of expected shortfall

We use stock market data to analyze the quality of alternative models and procedures for forecasting expected shortfall (ES) at different significance levels. We compute ES forecasts from conditional models applied to the full distribution of returns as well as from models that focus on tail events using extreme value theory (EVT). We also apply the semiparametric filtered historical simulation (FHS) approach to ES forecasting to obtain 10-day ES forecasts. At the 10-day horizon we combine FHS with EVT. The performance of the different models is assessed using six different ES backtests recently proposed in the literature. Our results suggest that conditional EVT-based models produce more accurate 1-day and 10-day ES forecasts than do non-EVT based models. Under either approach, asymmetric probability distributions for return innovations tend to produce better forecasts. Incorporating EVT in parametric or semiparametric approaches also improves ES forecasting performance. These qualitative results are also valid for the recent crisis period, even though all models then underestimate the level of risk. FHS narrows the range of numerical forecasts obtained from alternative models, thereby reducing model risk. Combining EVT and FHS seems to be best approach for obtaining accurate ES forecasts.     

Forecasting bank loans loss-given-default

With the advent of the new Basel Capital Accord, banking organizations are invited to estimate credit risk capital requirements using an internal ratings based approach. In order to be compliant with this approach, institutions must estimate the loss-given-default, the fraction of the credit exposure that is lost if the borrower defaults. This study evaluates the ability of a parametric fractional response regression and a nonparametric regression tree model to forecast bank loan credit losses. The out-of-sample predictive ability of these models is evaluated at several recovery horizons after the default event. The out-of-time predictive ability is also estimated for a recovery horizon of 1 year. The performance of the models is benchmarked against recovery estimates given by historical averages. The results suggest that regression trees are an interesting alternative to parametric models in modeling and forecasting loss-given-default.     

The role of no-arbitrage on forecasting: Lessons from a parametric term structure model

Parametric term structure models have been successfully applied to numerous problems in fixed income markets, including pricing, hedging, managing risk, as well as to the study of monetary policy implications. In turn, dynamic term structure models, equipped with stronger economic structure, have been mainly adopted to price derivatives and explain empirical stylized facts. In this paper, we combine flavors of those two classes of models to test whether no-arbitrage affects forecasting. We construct cross-sectional (allowing arbitrages) and arbitrage-free versions of a parametric polynomial model to analyze how well they predict out-of-sample interest rates. Based on US Treasury yield data, we find that no-arbitrage restrictions significantly improve forecasts. Arbitrage-free versions achieve overall smaller biases and root mean square errors for most maturities and forecasting horizons. Furthermore, a decomposition of forecasts into forward-rates and holding return premia indicates that the superior performance of no-arbitrage versions is due to a better identification of bond risk premium.     

Exchange rate expectations and the pricing of Chinese cross-listed stocks

I show that the price discounts of Chinese cross-listed stocks (American Depositary Receipts (ADRs) and H-shares) to their underlying A-shares indicate the expected yuan/US dollar exchange rate. The forecasting models reveal that ADR and H-share discounts predict exchange rate changes more accurately than the random walk and forward exchange rates, particularly at long forecast horizons. Using panel estimations, I find that ADR and H-share investors form their exchange rate expectations according to standard exchange rate theories such as the Harrod-Balassa-Samuelson effect, the risk of competitive devaluations, relative purchasing power parity, uncovered interest rate parity, and the risk of currency crisis.     

How rating agencies achieve rating stability

Surveys on the use of agency credit ratings reveal that some investors believe that rating agencies are relatively slow in adjusting their ratings. A well-accepted explanation for this perception on the timeliness of ratings is the through-the-cycle methodology that agencies use. According to Moody’s, through-the-cycle ratings are stable because they are intended to measure default risk over long investment horizons, and because they are changed only when agencies are confident that observed changes in a company’s risk profile are likely to be permanent. To verify this explanation, we quantify the impact of the long-term default horizon and the prudent migration policy on rating stability from the perspective of an investor – with no desire for rating stability. This is done by benchmarking agency ratings with a financial ratio-based (credit-scoring) agency-rating prediction model and (credit-scoring) default-prediction models of various time horizons. We also examine rating-migration practices. The final result is a better quantitative understanding of the through-the-cycle methodology.By varying the time horizon in the estimation of default-prediction models, we search for a best match with the agency-rating prediction model. Consistent with the agencies’ stated objectives, we conclude that agency ratings are focused on the long term. In contrast to one-year default prediction models, agency ratings place less weight on short-term indicators of credit quality.We also demonstrate that the focus of agencies on long investment horizons explains only part of the relative stability of agency ratings. The other aspect of through-the-cycle methodology – agency-rating migration policy – is an even more important factor underlying the stability of agency ratings. We find that rating migrations are triggered when the difference between the actual agency rating and the model predicted rating exceeds a certain threshold level. When rating migrations are triggered, agencies adjust their ratings only partially, consistent with the known serial dependency of agency-rating migrations.     

Impact of financial market uncertainty and macroeconomic factors on stock–bond correlation in emerging markets

This paper examines the impact of global financial market uncertainty and domestic macroeconomic factors on stock–bond correlation in emerging markets. In particular, by applying the wavelet analysis approach, we are able to examine stock–bond correlations over different time horizons in ten emerging markets. We find that stock–bond correlation patterns vary significantly between the time horizons. In particular, the correlation in short horizon changes the sign rapidly showing sustainable negative episodes while the correlation in long horizon stays positive most of the time. The most important factor influencing stock–bond correlation in short horizon is the monetary policy stance, while the factors with the greatest long-term impact are inflation and stock market uncertainty. Finally, global stock market uncertainty plays a more significant role than global bond market uncertainty in explaining stock–bond correlations in emerging markets.     

Forecasting Intraday Volatility and Value-at-Risk with High-Frequency Data

In this paper, we develop modeling tools to forecast Value-at-Risk and volatility with investment horizons of less than one day. We quantify the market risk based on the study at a 30-min time horizon using modified GARCH models. The evaluation of intraday market risk can be useful to market participants (day traders and market makers) involved in frequent trading. As expected, the volatility features a significant intraday seasonality, which motivates us to include the intraday seasonal indexes in the GARCH models. We also incorporate realized variance (RV) and time-varying degrees of freedom in the GARCH models to capture more intraday information on the volatile market. The intrinsic tail risk index is introduced to assist with understanding the inherent risk level in each trading time interval. The proposed models are evaluated based on their forecasting performance of one-period-ahead volatility and Intraday Value-at-Risk (IVaR) with application to the 30 constituent stocks. We find that models with seasonal indexes generally outperform those without; RV can improve the out-of-sample forecasts of IVaR; student GARCH models with time-varying degrees of freedom perform best at 0.5 and 1 % IVaR, while normal GARCH models excel for 2.5 and 5 % IVaR. The results show that RV and seasonal indexes are useful to forecasting intraday volatility and Intraday VaR.     

Forecasting exchange rates out-of-sample with panel methods and real-time data

This paper evaluates out-of-sample exchange rate forecasting with Purchasing Power Parity (PPP) and Taylor rule fundamentals for 9 OECD countries vis-à-vis the U.S. dollar over the period from 1973:Q1 to 2009:Q1 at short and long horizons. In contrast with previous work, which reports “forecasts” using revised data, I construct a quarterly real-time dataset that incorporates only the information available to market participants when the forecasts were made. Using bootstrapped out-of-sample test statistics, the exchange rate model with Taylor rule fundamentals performs better at the one-quarter horizon and panel estimation is not able to improve its performance. The PPP model, however, forecasts better at the 16-quarter horizon and its performance increases in panel framework. The results are in accord with previous research on PPP and Taylor rule models.     

Forecasting value-at-risk and expected shortfall using fractionally integrated models of conditional volatility: International evidence

The present study compares the performance of the long memory FIGARCH model, with that of the short memory GARCH specification, in the forecasting of multi-period value-at-risk (VaR) and expected shortfall (ES) across 20 stock indices worldwide. The dataset is composed of daily data covering the period from 1989 to 2009. The research addresses the question of whether or not accounting for long memory in the conditional variance specification improves the accuracy of the VaR and ES forecasts produced, particularly for longer time horizons. Accounting for fractional integration in the conditional variance model does not appear to improve the accuracy of the VaR forecasts for the 1-day-ahead, 10-day-ahead and 20-day-ahead forecasting horizons relative to the short memory GARCH specification. Additionally, the results suggest that underestimation of the true VaR figure becomes less prevalent as the forecasting horizon increases. Furthermore, the GARCH model has a lower quadratic loss between actual returns and ES forecasts, for the majority of the indices considered for the 10-day and 20-day forecasting horizons. Therefore, a long memory volatility model compared to a short memory GARCH model does not appear to improve the VaR and ES forecasting accuracy, even for longer forecasting horizons. Finally, the rolling-sampled estimated FIGARCH parameters change less smoothly over time compared to the GARCH models. Hence, the parameters' time-variant characteristic cannot be entirely due to the news information arrival process of the market; a portion must be due to the FIGARCH modelling process itself.     

Investor Sentiment and Corporate Disclosure

This paper investigates how firms react strategically to investor sentiment via their disclosure policies in an attempt to influence the sentiment‐induced biases in expectations. Proxying for sentiment using the Michigan Consumer Confidence Index, we show that during low‐sentiment periods, managers increase forecasts to “walk up” current estimates of future earnings over long horizons. In contrast, during periods of high sentiment, managers reduce their long‐horizon forecasting activity. Further, while there is an association between sentiment and the biases in analysts' estimates of future earnings, management disclosures vary with sentiment even after controlling for analyst pessimism, indicating that managers attempt to communicate with investors at large, and not just analysts. Our study provides evidence that firms' long‐horizon disclosure choices reflect managers' desire to maintain optimistic earnings valuations.     

Long Memory and Forecasting in Euroyen Deposit Rates

We test for long memory in 3- and 6-month daily returns series on Eurocurrency deposits denominated in Japanese yen (Euroyen). The fractional differencing parameter is estimated using the spectral regression method. The conflicting evidence obtained from the application of tests against a unit root as well as tests against stationarity provides the motivation for testing for fractional roots. Significant evidence of positive long-range dependence is found in the Euroyen returns series. The estimated fractional models result in dramatic out-of-sample forecasting improvements over longer horizons compared to benchmark linear models, thus providing strong evidence against the martingale model.     

Using implied volatility jumps for realized volatility forecasting: Evidence from the Chinese market

This study examines the Chinese implied volatility index (iVIX) to determine whether jump information from the index is useful for volatility forecasting of the Shanghai Stock Exchange 50ETF. Specifically, we consider the jump sizes and intensities of the 50ETF and iVIX as well as cojumps. The findings show that both the jump size and intensity of the 50ETF can improve the forecasting accuracy of the 50ETF volatility. Moreover, we find that the jump size and intensity of the iVIX provide no significant predictive ability in any forecasting horizon. The cojump intensity of the 50ETF and iVIX is a powerful predictor for volatility forecasting of the 50ETF in all forecasting horizons, and the cojump size is helpful for forecasting in short forecasting horizon. In addition, for a one-day forecasting horizon, the iVIX jump size in the cojump is more predictive of future volatility than that of the 50ETF when simultaneous jumps occur. Our empirical results are robust and consistent. This work provides new insights into predicting asset volatility with greater accuracy.     

Short-run forecasting of the euro-dollar exchange rate with economic fundamentals

We propose a fundamentals-based econometric model for the weekly changes in the euro-dollar rate with the distinctive feature of mixing economic variables quoted at different frequencies. The model obtains good in-sample fit and, more importantly, encouraging out-of-sample forecasting results at horizons ranging from one-week to one month. Specifically, we obtain statistically significant improvements upon the hard-to-beat random-walk model using traditional statistical measures of forecasting error at all horizons. Moreover, our model obtains a great improvement when we use the direction of change metric, which has more economic relevance than other loss measures. With this measure, our model performs much better at all forecasting horizons than a naive model that predicts the exchange rate as an equal chance to go up or down, with statistically significant improvements.     

A multi-country test of the Fisher model for stock returns

This article provides a test of the Fisher model, linking expected stock returns and inflation, based on international data. Since the Fisher model is ‘universal’ and calls for a slope of 1 in any country, we improve the testing power by conducting a joint test over eight countries. The pooling of data for several countries seems to reduce the small-sample bias. We test the Fisher model, using an instrumental variable approach, for holding-period horizons ranging from 1–12 months. The Fisher model is not rejected at any horizon: however, the magnitude of the slope coefficient lends stronger support at long horizons. This study using multi-country panel data provides evidence corroborating the finding of Boudoukh and Richardson (1993) that the Fisher model holds at long horizons (5 years), using 180 years of US data.     

Asymmetry of information flow between volatilities across time scales

Conventional time series analysis, focusing exclusively on a time series at a given scale, lacks the ability to explain the nature of the data-generating process. A process equation that successfully explains daily price changes, for example, is unable to characterize the nature of hourly price changes. On the other hand, statistical properties of monthly price changes are often not fully covered by a model based on daily price changes. In this paper, we simultaneously model regimes of volatilities at multiple time scales through wavelet-domain hidden Markov models. We establish an important stylized property of volatility across different time scales. We call this property asymmetric vertical dependence. It is asymmetric in the sense that a low volatility state (regime) at a long time horizon is most likely followed by low volatility states at shorter time horizons. On the other hand, a high volatility state at long time horizons does not necessarily imply a high volatility state at shorter time horizons. Our analysis provides evidence that volatility is a mixture of high and low volatility regimes, resulting in a distribution that is non-Gaussian. This result has important implications regarding the scaling behavior of volatility, and, consequently, the calculation of risk at different time scales.     

FRACTIONAL DIFFERENCING MODELING AND FORECASTING OF EUROCURRENCY DEPOSIT RATES

Using the spectral regression method, we test for long-term stochastic memory in three- and six-month daily returns series of Eurocurrency deposits denominated in major currencies. Significant evidence of positive long-term dependence is found in several Eurocurrency returns series. Compared with benchmark linear models, the estimated fractional models result in dramatic out-of-sample forecasting improvements over longer horizons for the Eurocurrency deposits denominated in German marks, Swiss francs, and Japanese yen.     

Option-Implied Risk Aversion Estimates

Using a utility function to adjust the risk‐neutral PDF embedded in cross sections of options, we obtain measures of the risk aversion implied in option prices. Using FTSE 100 and S&P 500 options, and both power and exponential‐utility functions, we estimate the representative agent's relative risk aversion (RRA) at different horizons. The estimated coefficients of RRA are all reasonable. The RRA estimates are remarkably consistent across utility functions and across markets for given horizons. The degree of RRA declines broadly with the forecast horizon and is lower during periods of high market volatility.     

Moments of multivariate regime switching with application to risk-return trade-off

We use a Fourier transform to derive multivariate conditional and unconditional moments of multi-horizon returns under a regime-switching model. These moments are applied to examine the relevance of risk horizon and regimes for buy-and-hold investors. We analyze the impact of time-varying expected returns and risk (variance and covariance) on portfolio allocations' “term structure”—portfolio allocations as a function of the investment horizon. Using monthly observations on S&P composite index and 10-year Government Bond, we find that the term structure of the optimal allocations depends on market conditions measured by the probability of being in bull state. At short horizons and when this probability is low, buy-and-hold investors decrease their holdings of risky assets. We also find that the conditional optimal portfolio performs quite well at short and intermediate horizons and less at long horizons.     

Riding the yield curve: a spanning analysis

The average return on long-term bonds exceeds the return on short-term bills by a large amount over short investment horizons. A riding-the-yield-curve investment strategy takes advantage of the higher returns on longer term bonds. This strategy involves the purchase of bonds with maturities longer than the investment horizon and the sale of these bonds, before they mature, at the end of the investment horizon. Most of the literature that evaluates this strategy compares only ex post average returns or Sharpe ratios. In this paper, we use spanning tests to provide formal statistical evidence on the benefits of investing in long bonds when the investment horizon is short. The results for both the United States and Canada indicate that an investor with a short horizon is better off investing in short-term debt instruments than long-term bonds.