Modeling and predicting the CBOE market volatility index

This paper performs a thorough statistical examination of the time-series properties of the market volatility index (VIX) from the Chicago Board Options Exchange (CBOE). The motivation lies on the widespread consensus that the VIX is a barometer to the overall market sentiment as to what concerns risk appetite. To assess the statistical behavior of the time series, we run a series of preliminary analyses whose results suggest there is some long-range dependence in the VIX index. This is consistent with the strong empirical evidence in the literature supporting long memory in both options-implied and realized volatilities. We thus resort to linear and nonlinear heterogeneous autoregressive (HAR) processes, including smooth transition and threshold HAR-type models, as well as to smooth transition autoregressive trees (START) for modeling and forecasting purposes. The in-sample results for the HAR-type indicate that they cope with the long-range dependence in the VIX time series as well as the more popular ARFIMA model. In addition, the highly nonlinear START specification also does a god job in controlling for the long memory. The out-of-sample analysis evince that the linear ARMA and ARFIMA models perform very well in the short run and very poorly in the long-run, whereas the START model entails by far the best results for the longer horizon despite of failing at shorter horizons. In contrast, the HAR-type models entail reasonable relative performances in most horizons. Finally, we also show how a simple forecast combination brings about great improvements in terms of predictive ability for most horizons.heterogeneous autoregression, implied volatility, smooth transition, VIX.

The Information Content of Treasury Bond Options Concerning Future Volatility and Price Jumps

We study the relation between realized and implied volatility in the bond market. Realized volatility is constructed from high-frequency (5-minute) returns on 30 year Treasury bond futures. Implied volatility is backed out from prices of associated bond options. Recent nonparametric statistical techniques are used to separate realized volatility into its continuous sample path and jump components, thus enhancing forecasting performance. We generalize the heterogeneous autoregressive (HAR) model to include implied volatility as an additional regressor, and to the separate forecasting of the realized components. We also introduce a new vector HAR (VecHAR) model for the resulting simultaneous system, controlling for possible endogeneity of implied volatility in the forecasting equations. We show that implied volatility is a biased and inefficient forecast in the bond market. However, implied volatility does contain incremental information about future volatility relative to both components of realized volatility, and even subsumes the information content of daily and weekly return based measures. Perhaps surprisingly, the jump component of realized bond return volatility is, to some extent, predictable, and bond options appear to be calibrated to incorporate information about future jumps in Treasury bond prices, and hence interest rates.Bipower variation, bond futures options, HAR, Heterogeneous Autoregressive Model, implied volatility, jumps, realized volatility, VecHAR, volatility forecasting

Smile from the Past: A general option pricing framework with multiple volatility and leverage components

In the current literature, the analytical tractability of discrete time option pricing models is guarantee only for rather specific type of models and pricing kernels. We propose a very general and fully analytical option pricing framework encompassing a wide class of discrete time models featuring multiple components structure in both volatility and leverage and a flexible pricing kernel with multiple risk premia. Although the proposed framework is general enough to include either GARCH-type volatility, Realized Volatility or a combination of the two, in this paper we focus on realized volatility option pricing models by extending the Heterogeneous Autoregressive Gamma (HARG) model of Corsi et al. (2012) to incorporate heterogeneous leverage structures with multiple components, while preserving closed-form solutions for option prices. Applying our analytically tractable asymmetric HARG model to a large sample of S&P 500 index options, we evidence its superior ability to price out-of-the-money options compared to existing benchmarks

Market volatility : can machine learning methods enhance volatility forecasting?

This dissertation aims to test whether the use of machine learning (ML) techniques can improve volatility forecasting accuracy. More specifically, if it can beat the best econometric model, the Heterogeneous Autoregressive model of Realized Volatility (HAR-RV). Using S&P 500 Index data from May-2007 to August-2022, the superiority of the HAR-RV was tested and attested against competing econometric models EWMA and GARCH(1,1). Next, the performance of the ML Artificial Neural Network algorithms Long Short-Term Memory (LSTM) and Gated Recurrent Unit (GRU) are compared to the performance of the econometric models. Five different variable sets are tested for the ML models. It is found that while both ML models are able to beat the EWMA and GARCH(1,1) models by a significant margin, the HAR-RV model still outperforms LSTM and GRU. Moreover, an analysis is conduced on the models’ predictions on the period corresponding to the Covid-19 crisis. The results did not show any evidence suggesting that ML methods have a particular advantage at predicting during high volatility events. Finally, a plausible cause that could undermine the remarkable qualities of the ML methods in the aim of volatility forecasting is discussed. It is found that the rigorous set of conditions needed to be met for the proper setup of ML models are very difficult to be met using financial data, which hinders the aptitude of ML for this purpose.Esta tese visa testar se o uso de técnicas de Machine Learning (ML) pode melhorar a precisão da previsão da volatilidade. Mais especificamente, se estes algoritmos conseguem superar o melhor modelo econométrico, o Heterogeneous Autoregressive model of Realized Volatility (HAR-RV). Usando dados do Índice S&P 500 de Maio-2007 a Agosto-2022, a superioridade do HAR-RV perante os modelos econométricos concorrentes EWMA e GARCH(1,1), foi testada e confirmada. Em seguida, o desempenho dos algoritmos ML de redes neurais artificiais de Long Short-Term Memory (LSTM) e Gated Recurrent Unit (GRU) são comparados com o desempenho dos modelos econométricos tradicionais. Cinco conjuntos diferentes de variáveis são testados para os modelos ML. Verifica-se que enquanto ambos os modelos ML são capazes de superar os modelos EWMA e GARCH(1,1) por uma margem significante, o modelo HARRV ainda tem um desempenho superior ao LSTM e ao GRU. É ainda feita uma análise das previsões dos modelos durante o período correspondente à crise do Covid-19. Os resultados não mostram qualquer evidência que sugira que os métodos ML têm uma particular vantagem durante eventos de alta volatilidade. Finalmente, é discutida uma possível causa que poderá debilitar as sofisticadas qualidades dos métodos ML para a finalidade de previsão de volatilidade. Verifica-se que o conjunto rigoroso de condições necessárias para a correcta configuração dos modelos ML é muito difícil de se cumprir utilizando series temporais de volatilidade de mercado, o que prejudica a aptidão dos modelos ML para esta finalidade

Asymmetry and Long Memory in Volatility Modelling

A wide variety of conditional and stochastic variance models has been used to estimate latent volatility (or risk). In this paper, we propose a new long memory asymmetric volatility model which captures more flexible asymmetric patterns as compared with several existing models. We extend the new specification to realized volatility by taking account of measurement errors, and use the Efficient Importance Sampling technique to estimate the model. As an empirical example, we apply the new model to the realized volatility of S&P500 to show that the new specification of asymmetry significantly improves the goodness of fit, and that the out-of-sample forecasts and Value-at-Risk (VaR) thresholds are satisfactory. Overall, the results of the out-of-sample forecasts show the adequacy of the new asymmetric and long memory volatility model for the period including the global financial crisis.Asymmetric volatility, Long memory, Realized volatility, Measurement errors, Efficient importance sampling.

A Multiple Indicators Model for Volatility Using Intra-Daily Data

Many ways exist to measure and model financial asset volatility. In principle, as the frequency of the data increases, the quality of forecasts should improve. Yet, there is no consensus about a true' or best' measure of volatility. In this paper we propose to jointly consider absolute daily returns, daily high-low range and daily realized volatility to develop a forecasting model based on their conditional dynamics. As all are non-negative series, we develop a multiplicative error model that is consistent and asymptotically normal under a wide range of specifications for the error density function. The estimation results show significant interactions between the indicators. We also show that one-month-ahead forecasts match well (both in and out of sample) the market-based volatility measure provided by an average of implied volatilities of index options as measured by VIX.

Asymmetry and Long Memory in Volatility Modelling

A wide variety of conditional and stochastic variance models has been used to estimate latent volatility (or risk). In this paper, we propose a new long memory asymmetric volatility model which captures more flexible asymmetric patterns as compared with existing models. We extend the new specification to realized volatility by taking account of measurement errors, and use the Efficient Importance Sampling technique to estimate the model. As an empirical example, we apply the new model to the realized volatility of Standard and Poor’s 500 Composite Index to show that the new specification of asymmetry significantly improves the goodness of fit, and that the out-of-sample forecasts and Value-at-Risk (VaR) thresholds are satisfactory. Overall, the results of the out-of-sample forecasts show the adequacy of the new asymmetric and long memory volatility model for the period including the global financial crisis.Asymmetric volatility; long memory; realized volatility; measurement errors; efficient importance sampling

Realized volatility: a review

This paper reviews the exciting and rapidly expanding literature on realized volatility. After presenting a general univariate framework for estimating realized volatilities, a simple discrete time model is presented in order to motivate the main results. A continuous time specification provides the theoretical foundation for the main results in this literature. Cases with and without microstructure noise are considered, and it is shown how microstructure noise can cause severe problems in terms of consistent estimation of the daily realized volatility. Independent and dependent noise processes are examined. The most important methods for providing consistent estimators are presented, and a critical exposition of different techniques is given. The finite sample properties are discussed in comparison with their asymptotic properties. A multivariate model is presented to discuss estimation of the realized covariances. Various issues relating to modelling and forecasting realized volatilities are considered. The main empirical findings using univariate and multivariate methods are summarized.

Multivariate Realized Stock Market Volatility

We present a new matrix-logarithm model of the realized covariance matrix of stock returns. The model uses latent factors which are functions of both lagged volatility and returns. The model has several advantages: it is parsimonious; it does not require imposing parameter restrictions; and, it results in a positive-definite covariance matrix. We apply the model to the covariance matrix of size-sorted stock returns and find that two factors are sufficient to capture most of the dynamics. We also introduce a new method to track an index using our model of the realized volatility covariance matrix.Econometric and statistical methods; Financial markets

What tames the Celtic tiger? portfolio implications from a multivariate Markov switching model

We use multivariate regime switching vector autoregressive models to characterize the time-varying linkages among the Irish stock market, one of the top world performers of the 1990s, and the US and UK stock markets. We find that two regimes, characterized as bear and bull states, are required to characterize the dynamics of excess equity returns both at the univariate and multivariate level. This implies that the regimes driving the small open economy stock market are largely synchronous with those typical of the major markets. However, despite the existence of a persistent bull state in which the correlations among Irish and UK and US excess returns are low, we find that state comovements involving the three markets are so relevant to reduce the optimal mean variance weight carried by ISEQ stocks to at most one-quarter of the overall equity portfolio. We compute time-varying Sharpe ratios and recursive mean-variance portfolio weights and document that a regime switching framework produces out-of-sample portfolio performance that outperforms simpler models that ignore regimes. These results appear robust to endogenizing the effects of dynamics in spot exchange rates on excess stock returns.Stock exchanges