Volatility forecasting: combinations of realized volatility measures and forecasting models

This article examines financial time series volatility forecasting performance. Different from other studies which either focus on combining individual realized measures or combining forecasting models, we consider both. Specifically, we construct nine important individual realized measures and consider combinations including the mean, the median and the geometric means as well as an optimal combination. We also apply a simple AR(1) model, an SV model with contemporaneous dependence, an HAR model and three linear combinations of these models. Using the robust forecasting evaluation measures including RMSE and QLIKE, our empirical evidence from both equity market indices and exchange rates suggests that combinations of both volatility measures and forecasting models improve the forecast performance significantly.     

Forecasting stock market volatility and information content of implied volatility index

This study investigates the incremental information content of implied volatility index relative to the GARCH family models in forecasting volatility of the three Asia-Pacific stock markets, namely India, Australia and Hong Kong. To examine the in-sample information content, the conditional variance equations of GARCH family models are augmented by incorporating implied volatility index as an explanatory variable. The return-based realized variance and the range-based realized variance constructed from 5-min data are used as proxy for latent volatility. To assess the out-of-sample forecast performance, we generate one-day-ahead rolling forecasts and employ the Mincer–Zarnowitz regression and encompassing regression. We find that the inclusion of implied volatility index in the conditional variance equation of GARCH family model reduces volatility persistence and improves model fitness. The significant and positive coefficient of implied volatility index in the augmented GARCH family models suggests that it contains relevant information in describing the volatility process. The study finds that volatility index is a biased forecast but possesses relevant information in explaining future realized volatility. The results of encompassing regression suggest that implied volatility index contains additional information relevant for forecasting stock market volatility beyond the information contained in the GARCH family model forecasts.     

Maturity and volatility effects on UK smiles

The smile effect is a result of an empirical observation of the options implied volatility with the same expiration date, across different exercise prices. However, its shape has been under discussion seeming to be dependent on the option underlying security. In this paper, and filling up a scarce empirical research on the topic, we used liquid equity options on 9 stocks traded on the London International Financial Futures and Options Exchange (LIFFE) between August 1990 and December 1991. We tested two different hypothesis for testing two different phenomena: (1) the increase of the smile as maturity approaches; (2) and the association between the smile and the volatility of the underlying stock. In order to estimate implied volatilities for unavailable exercise prices, we modelled the smile using cubic B-spline curves. We found empirical support for the smile intensification (the U-shape is more pronounced) as maturity approaches as well as when volatility rises. However, we found two major sources of disagreement with the literature on stochastic volatility models. First, as maturity approaches, out-of-the-money options implied volatility tends to be higher than the implied volatility of in-the-money options. Second, as the volatility of the underlying asset increases, the implied volatility of in-the-money options tends to be higher than implied volatility of out-of-the-money options.Received: September 2001, Accepted: September 2003, JEL Classification: G13Correspondence to: João L. C. DuqueWe thank Professor Dean A. Paxson (University of Manchester), António Sousa Câmara (University of Strathclyde), Ser-Huang Poon (University of Lancaster) and the attendees of the 26th EFA Annual Conference for helpful comments on previous versions of this paper. We also want to thank to two anonymous referees for their relevant comments and suggestions. Financial support granted by the Fundação para a Ciência e a Tecnologia (FCT) and the Programa Praxis XXI is gratefully acknowledged.     

Further empirical evidence on the forecasting of volatility with smooth transition exponential smoothing

Smooth transition exponential smoothing (STES) uses a logistic function of a user-specified transition variable as adaptive time varying smoothing parameter. This paper empirically addresses three aspects of the use of STES for volatility forecasting. Previous empirical results showed the method performing well in comparison with fixed parameter exponential smoothing and a variety of GARCH models. However, those results related only to forecasting weekly volatility. In this paper, we address the use of STES for forecasting daily volatility. A second issue that we evaluate is the robustness of STES in the presence of extreme outlying observations. The third aspect that we consider is the use of trading volume within a transition variable in the STES method. Our simulation results suggest that STES performs well in terms of robustness, when compared with standard methods and several alternative robust methods. Analysis using stock return data shows that STES has the potential to outperform standard and robust forms of fixed parameter exponential smoothing and GARCH models. The results suggest the use of the sign and size of past shocks as STES transition variables, and provide no clear support for the incorporation of trading volume in a transition variable.     

The information content of implied volatility in developed versus developing FX markets

This article predicts the daily movement of monthly foreign exchange (FX) rate volatility using a linear combination of a time-series model and implied volatilities from options. The focus is on analysing the FX volatilities in three developing economies (the Brazilian real (BRL), the Indian rupee (INR) and the Russian ruble (RUB)) against the US dollar (USD). The empirical exercise utilizes two time-series models, mixed data sampling (MIDAS) and GARCH. The analysis indicates that for both developed and developing economies the predictive power of MIDAS and that of GARCH is comparable. Further on in this article, we will ascertain whether the relationship between realized and implied volatility is fundamentally different in the case of developing economies from that among developed economies. Thus, we compare the pairs USD/BRL, USD/INR and USD/RUB against EURO/USD and USD/Japanese yen to determine the information content and predictive power of implied volatilities. Plots of the MIDAS coefficients show that the volatility is more persistent in developing economies than in developed economies.     

Calibration of implied volatility for the exchange rate for the Chinese Yuan from its derivatives

Revised implied volatility curves and surfaces for the Chinese Yuan (CNY) exchange rate are obtained from market quotations for CNY non-deliverable options by solving an inverse problem of foreign exchange option pricing, which is calculated using a regularization approach in an optimal control framework. To take account of the market expectation for the CNY exchange rate, a stochastic adjusted factor is applied that follows a Vasicek model with parameters fitted from market quotations for CNY non-deliverable forwards. A well-posed numerical scheme is implemented.     

Time-varying relationship of news sentiment,implied volatility and stock returns

I examine the relationship between aggregate news sentiment, S&P 500 index (SPX) returns, and changes in the implied volatility index (VIX). I find a significant negative contemporaneous relationship between changes in VIX and both news sentiment and stock returns. This relationship is asymmetric whereby changes in VIX are larger following negative news and/or stock market declines. Vector autoregression (VAR) analysis of the dynamics and cross-dependencies between variables reveals a strong positive relationship between previous and current period changes in implied volatility and stock returns, while current period and lagged news sentiment has a significant positive (negative) relationship with stock returns (changes in VIX). I develop a simple trading strategy whereby high (low) levels of implied volatility signal attractive opportunities to take short (long) positions in the underlying index, while extremely negative (positive) news sentiment signals opportunities to enter short (long) index positions. The investor fear gauge (VIX) appears to perform better than news sentiment measures in forecasting future returns.     

Do misalignments predict aggregated stock-market volatility?

This paper considers forecasting regressions of “realized volatility” on a misalignment measure. Results show that this misalignment measure is useful to predict in and out-of-sample stock-market volatility at monthly horizons. The analysis also suggests a threshold effect.     

Does Implied Volatility Pricing Follow the Tenets of Prospect Theory?

Abstract

Prospect theory and behavioral finance are gaining recognition as useful frameworks for the analysis of economic behaviors. Yet, behavioral finance is generally concerned with specific anomalies and individual behaviors and does not deal with market indices. To bridge this gap, the authors studied the changes in the value of implied volatility indices on several markets, relative to changes in the level of the corresponding equity indices with dividends reinvestment. We hypothesized that the relation should follow the psychological tenets of prospect theory. In accordance with this hypothesis, the authors found concavity in the gain area, convexity in the loss area, and evidence that market losses have more impact than gains on the pricing of implied volatility indices. These findings are observed in all the markets under consideration and are robust to the use of different functional forms. The parameters are in the range observed in previous laboratory studies but vary in different trading environments.     

A new factor to explain implied volatility smirk

In this article, we find empirical evidence of a new smirk factor, obtained from the jump structure of the risk neutral distribution of the underlying Lévy process. As an application we show how to price a barrier style contract.     

Value at risk forecasting for volatility index

Forecasts of values at risk (VaRs) are made for volatility indices such as the VIX for the US S&P 500 index, the VKOSPI for the KOSPI (Korea Stock Price Index) and the OVX (oil volatility index) for crude oil funds, which is the first in the literature. In the forecasts, dominant features of the volatility indices are addressed: long memory, conditional heteroscedasticity, asymmetry and fat-tails. An out-of-sample comparison of the VaR forecasts is made in terms of violation probabilities, showing better performance of the proposed method than several competing methods which consider the features differently from ours. The proposed method is composed of heterogeneous autoregressive model for the mean, GARCH model for the volatility and skew-t distribution for the error.     

Modelling the implied volatility surface based on Shanghai 50ETF options

We develop a dynamic factor model to forecast the implied volatility surface (IVS) of Shanghai Stock Exchange 50ETF options. Based on the assumption that dynamic change in IVS is mean-reverting and Markovian, we use a state space model to capture the dynamics of IVS, and set the latent factors to be the Ornstein–Uhlenbeck processes. We obtain the optimal estimations of parameters using the Kalman filter algorithm. Empirical results show that our model performs better than the traditional IVS model in terms of fitting ability and prediction performance.     

Modelling exchange rate volatility with random level shifts

Recent literature has shown that the volatility of exchange rate returns displays long memory features. It has also been shown that if a short memory process is contaminated by level shifts, the estimate of the long memory parameter tends to be upward biased. In this article, we directly estimate a random level shift model to the logarithm of the absolute returns of five exchange rates series, in order to assess whether random level shifts (RLSs) can explain this long memory property. Our results show that there are few level shifts for the five series, but once they are taken into account the long memory property of the series disappears. We also provide out-of-sample forecasting comparisons, which show that, in most cases, the RLS model outperforms popular models in forecasting volatility. We further support our results using a variety of robustness checks.     

Does measurement error matter in volatility forecasting? Empirical evidence from the Chinese stock market

Based on methods developed by Bollerslev et al. (2016), we explicitly accounted for the heteroskedasticity in the measurement errors and for the high volatility of Chinese stock prices; we proposed a new model, the LogHARQ model, as a way to appropriately forecast the realized volatility of the Chinese stock market. Out-of-sample findings suggest that the LogHARQ model performs better than existing logarithmic and linear forecast models, particularly when the realized quarticity is large. The better performance is also confirmed by the utility based economic value test through volatility timing.     

Uncertainty and crude oil market volatility: new evidence

ABSTRACT

The main goal of this paper is to investigate the predictability of five economic uncertainty indices for oil price volatility in a changing world. We employ the standard predictive regression framework, several model combination approaches, as well as two prevailing model shrinkage methods to evaluate the performances of the uncertainty indices. The empirical results based on simple autoregression models including only one index suggest that global economic policy uncertainty (GEPU) and US equity market volatility (EMV) indices have significant predictive power for crude oil market volatility. In addition, the model combination approaches adopted in this paper can improve slightly the performances of individual autoregressive models. Lastly, the two model shrinkage methods, namely Elastin net and Lasso, outperform other individual AR-type model and combination models in most forecasting cases. Other empirical results based on alternative forecasting methods, estimation window sizes, high/low volatility and economic expansion/recession time periods further make sure the robustness of our major conclusions. The findings in this paper also have several important economic implications for oil investors.     

Forecasting realized volatility of crude oil futures with equity market uncertainty

This paper examines whether the equity market uncertainty (EMU) index contains incremental information for forecasting the realized volatility of crude oil futures. We use 5-min high-frequency transaction data for WTI crude oil futures and develop six heterogeneous autoregressive (HAR) models based on classical HAR-type models. The empirical results suggest that EMU contains more incremental information than the economic policy uncertainty (EPU) for forecasting the realized volatility of crude oil futures. More importantly, we argue that EMU is a non negligible additional predictive variable that can significantly improve the 1-day ahead predictive accuracy of all six HAR-type models, and improve the 1-week ahead forecasting performance of the HAR-RV, HAR-RV-J, HAR-RSV, HAR-RV-SJ models. These findings highlight a strong short-term and a weak mid-term predictive ability of EMU in the crude oil futures market.     

Fear connectedness among asset classes

This study investigates the interconnection between five implied volatility indices representative of different financial markets during the period 1 August 2008–29 December 2017. To this end, we first perform a static and dynamic analysis to measure the total volatility connectedness in the entire period (the system-wide approach) using a framework recently proposed by Diebold and Yilmaz. Second, we make use of a dynamic analysis to evaluate both the net directional connectedness for each market and all net pairwise directional connectedness. Our results suggest that a 38.99%, of the total variance of the forecast errors is explained by shocks across markets, indicating that the remainder 61.01% of the variation is due to idiosyncratic shocks. Furthermore, we find that volatility connectedness varies over time, with a surge during periods of increasing economic and financial instability. Finally, we also document frequently switch between a net volatility transmitter and a net volatility receiver role in the five markets under study.     

Forecasting the oil futures price volatility: A new approach

This study provides a new perspective of modelling and forecasting realized range-based volatility (RRV) for crude oil futures. We are the first to improve the Heterogeneous Autoregressive model of Realized Range-based Volatility (HAR-RRV) model by considering the significant jump components, signed returns and volatility of realized range-based volatility. The empirical results show that the volatility of volatility significantly exists in the oil futures market. Moreover, our new proposed models with significant jump components, signed returns and volatility of volatility can gain higher forecast accuracy than HAR-RRV-type models. The results are robust to different forecasting windows and forecasting horizons. Our new findings are strategically important for investors making better decisions.     

The Black–Scholes model as a determinant of the implied volatility smile: A simulation study

The paper represents an initial effort to shed light on the determinants of the implied volatility smile in financial (derivative) markets. It fully details the implications of the institutionalization of the Black–Scholes model in an uncertain world populated by individuals who are bounded by the amount of calculation or accounting which is technically possible. Combining model simulations, empirical analysis, and mathematical derivations, the paper proposes that the determinants of the volatility smile might be related to the behavior of traders. In pricing options, they use the widely accepted Black–Scholes formula with a measure of stock volatility that they derive from their subjective beliefs. Moreover, heterogeneity of traders’ beliefs and the way traders update their expectations have nontrivial effects, both on equilibrium prices and on the emergence of the implied volatility smile.     

Volatility forecasting: long memory,regime switching and heteroscedasticity

In this article, we account for the first time for long memory, regime switching and the conditional time-varying volatility of volatility (heteroscedasticity) to model and forecast market volatility using the heterogeneous autoregressive model of realized volatility (HAR-RV) and its extensions. We present several interesting and notable findings. First, existing models exhibit significant nonlinearity and clustering, which provide empirical evidence on the benefit of introducing regime switching and heteroscedasticity. Second, out-of-sample results indicate that combining regime switching and heteroscedasticity can substantially improve predictive power from a statistical viewpoint. More specifically, our proposed models generally exhibit higher forecasting accuracy. Third, these results are widely consistent across a variety of robustness tests such as different forecasting windows, forecasting models, realized measures, and stock markets. Consequently, this study sheds new light on forecasting future volatility.