How volatility model specification affects volatility targeting performance: Evidence from Taiwan

This research is focused on models for volatility. After the introduction of realized volatility as a consistent estimator for daily volatility, time series models without latent variables have been used to model and forecast volatility. The first part of this research provides a critical review of some of the commonly used realized volatility models and addresses the problem of stationarity and lag selection. In the empirical part we apply our methodology to thirty Dow Jones Industrial Average stocks from the NYSE TAQ dataset. We address the lag selection problem for each of the stocks considered. We find that models based on flexible lag structures do not significantly outperform models based on a fixed lag structure. With respect to latent model specifications for volatility, this study analyzes how the correlation structures in ARCH models relate to those in HARCH models. ARCH models have correlation structures that can be interpreted in the sense of mean reversion. HARCH rely on a specification that includes squared aggregated returns in the conditional variance equation. We find that HARCH is not able to capture correlation scales from ARCH in the mean reverting sense. This finding has implications for persistence. The corresponding persistence measure in HARCH does not capture the persistence of ARCH. In order to address these problems an optimal lag structure is identified. The correspondence between the lag structure and serial correlation is also addressed. In the last part of this study a Bayesian framework is employed in order to investigate the post storm firm survival after hurricanes Katrina and Rita in the Orleans Parish, Louisiana. A novelty of this approach is the spatial component in the model specification. Bayesian techniques are employed in order to draw inferences from a spatial probit model on a dataset containing 8,171 firms from the Orleans Parish. We find evidence indicating the presence of spatial components, especially in the quarters immediately following the storms. Other findings are: larger firms are more likely to survive; also, less flooded firms are more likely to survive; finally, sole proprietorships are more likely to reopen than large chain stores.

List of Figures. List of Tables. 1: Introduction. 2: Asset Return Volatility Models. 2.1. Empirical Stylised Facts of Stock Index Return Series. 2.2. Time-Varying Volatility Models. 2.3. Empirical Applications of Time Varying Volatility Models. 3: The Stochastic Volatility in Mean Model: Empirical Evidence from International Stock Markets. 3.1. Introduction. 3.2. The Stochastic Volatility in Mean Model. 3.3. Some Theory on the Relationship between Returns and Volatility. 3.4. Data. 3.5. Estimation Results for the SVM Model and Some Diagnostics. 3.6. Some Comparisons with GARCH-M Estimation Results. 3.7. Summary and Conclusions. 4: Forecasting with Volatility Models. 4.1. Volatility Models and Their Forecasts. 4.2. An Empirical Study of Six International Stock Indices. 5: Implied Volatility. 5.1. The Black-Scholes Option Pricing Model. 5.2. Forecasting with Implied Volatility: Empirical Evidence. 6: Forecasting the Variability of Stock Index Returns with Stochastic Volatility Models and Implied Volatility. 6.1. Introduction. 6.2. Model Specifications. 6.3. Data Description and Empirical In-Sample Results. 6.4. Volatility Forecasting Methodology. 6.5. Out-of-Sample Results. 6.6. Summary and Conclusions. 7: Stock Index Volatility Forecasting with High-Frequency Data. 7.1. Introduction. 7.2. Stock Return Data and Volatility. 7.3. Realised Volatility Models. 7.4. Daily Time-Varying Volatility Models. 7.5. Forecasting Methodology and Evaluation Criteria. 7.6. Empirical Results. 7.7. Summary and Conclusions. 8: Conclusions. Appendices: A.1. Model. A.2. Likelihood Evaluation Using Importance Sampling. A.3. Approximating Gaussian Model Used for Importance Sampling. A.4. Monte Carlo Evidence of Estimation Procedure. B: Estimation of the SVX Models. B.1. The SVX Model in State Space Form. B.2. Parameter Estimation by Simulated Maximum Likelihood. B.3. Computational Implementation. C: Data and Programs. Bibliography. Index.

Volatility modeling is one of the central issues for theoretical studies and practical applications. In the literature, the conditional volatility model family, i.e. GARCH type model proposed by Engle (1982) (Econometrica 50(4), 987–1007, 1982) and Bollerslev (1986) (J Econom 31, 307–327, 1986) is used to model the fat-tail and the volatility clustering of stock return. On the other hand, the stochastic volatility model (Heston in Rev Financ Stud 6, 327–343, 1993, Heston 1993 and Shephard and Andersen in Stochastic volatility: Origins and overview, 233–254, 2009, Shephard and Andersen 2009) provides an alternative approach to model the time-varying behavior of volatility as a latent state variable. Despite the success of previous models, their predictions of volatility crucially rely on the specification of models used. Therefore, once there exists model misspecification error, the estimates would become inconsistent. Partially inspired by above issues, the model-free volatility approach, including realized volatility and model-free implied volatility, attracts a lot of research attention.

Long-term volatility is a key forecasting input for strategic asset allocation analysis, yet most studies on volatility models have focused on short horizons. The authors use a large sample of global equity and bond indexes since 1934 to test the predictive power of different long-horizon volatility models. Their findings suggest that the best approach to forecasting long-horizon volatility is to use a long historical window and capture both long-term mean reversion and short-term volatility clustering properties. The results show that the authors' model specification does a better job of reducing forecasting errors than does a naïve model based on the simple extrapolation of historical volatility. <b>TOPICS:</b>Portfolio construction, volatility measures, statistical methods, performance measurement <b>Key Findings</b> ▪ This study tests the predictive power of different long-horizon volatility models using a large sample of global equity and bond indexes since 1934. ▪ The best approach to forecasting long-horizon volatility is to use a long historical window and capture both long-term mean reversion and short-term volatility clustering properties. ▪ The results show that the proposed model specification does a better job of reducing forecasting errors than does a naïve model based on the simple extrapolation of historical volatility.

The hedge fund industry has experienced some very troublesome periods in the recent past. In this study, we test the efficiency of simple and advanced risk measures during these difficult market periods according to the Basel II requirements. We concentrate on Fund of Hedge Fund (FoHF) data, as some studies propose that they suffer least from database and measurement biases, and are therefore likely to yield the most representative results compared to other alternative investment data. We examine model stability and risk measure efficiency using unconditional and conditional GMM-based and likelihood ratio tests, as well as independence tests. We find that model stability is very dependent on the successful specification of autoregressive and volatility models. In addition, custom quantile estimation is less susceptible to misspecification than volatility models. Further, we assess the hypothesis of market efficiency for the special case of FoHF. Finally, we find evidence of different level of managerial skill in terms of asset choice, allocation and market timing.

This chapter reviews the possible uses of the Generalized Method of Moments (GMM) to estimate Stochastic Volatility (SV) models. A primary attraction of the method of moments technique is that it is well suited for identifying and estimating volatility models without a complete parametric specification of the probability distributions. Moreover, simulation-based methods of moments are able to exploit a variety of moments, while avoiding limitations due to a lack of closed form expressions. The chapter first highlights the suitability of GMM for popular regression models of volatility forecasting. Then, it reviews the implications of the SV model specification in terms of higher order moments: skewness, kurtosis, variance of the variance, leverage and feedback effects. The chapter examines the ability of a continuous time version of SV models to accommodate data from other sources like option prices or high frequency data on returns and transactions dates. Simulation-based methods are particularly useful for studying continuous time models due to the frequent lack of closed form expressions for their discrete time dynamics. These simulation-based methods of moments are presented within the unifying framework of indirect inference with a special emphasis on misspecification. Likely misspecification of the parametric model used for simulation requires a parsimonious and well-focused choice of the moments to match.

Likelihood-based specification analysis of continuous-time models of the short-term interest rate

We investigate the risk-return relation in the South African stock market using data covering the period from 1973 to 2011. Prior research for several countries reveals high sensitivity of the results to data details and models used. Therefore, our analysis of the risk-return nexus in South Africa are based on three different data frequencies (weekly, monthly and quarterly) and are derived from three different generalized autoregressive conditional heteroskedasticity (GARCH) models in addition to a plain vanilla time-series approach. Similar to the findings of Glosten et al. in 1993 and Harvey in 2001, our results fail to support a significantly positive risk-return relationship in South Africa across various data frequencies and model specifications, and this conclusion survives further robustness checks using different sub-periods and index data. Our results further suggest that the recent global financial crisis may have altered market dynamics and distorted the risk-return relation in the South African stock market.

This study examines several alternative symmetric and asymmetric model specifications of regression-based deterministic volatility models to identify the one that best characterizes the implied volatility functions of S&P 500 Index options in the period 1996–2009. We find that estimating the models with nonlinear least squares, instead of ordinary least squares, always results in lower pricing errors in both in- and out-of-sample comparisons. In-sample, asymmetric models of the moneyness ratio estimated separately on calls and puts provide the overall best performance. However, separating calls from puts violates the put-call-parity and leads to severe model mis-specification problems. Out-of-sample, symmetric models that use the logarithmic transformation of the strike price are the overall best ones. The lowest out-of-sample pricing errors are observed when implied volatility models are estimated consistently to the put-call-parity using the joint data set of out-of-the-money options. The out-of-sample pricing performance of the overall best model is shown to be resilient to extreme market conditions and compares quite favorably with continuous-time option pricing models that admit stochastic volatility and random jump risk factors.

New methodologies for diagnostic analysis and adaptive tuning based on sensitivity information of the Multivariate Stochastic Volatility (MSV) model are established in this dissertation. The main focus is on obtaining optimal conditional volatilities from a time series set of financial data observed in the market by specifying a State-Space model with error covariance adaptive tuning of the MSV model. Variational Data Assimilation methods are used in this research as tools for obtaining the optimal a posteriori estimates of the multivariate series of volatilities. Calculus of Variations techniques are then applied to a forecast score function to derive the sensitivities of the forecasted volatilities in terms of the input parameters. In summary, this dissertation achieves the development of these new methodologies by 1.Developing the sensitivity information of the multivariate conditional volatilities to observations, covariance specifications and prior estimates, 2.Developing tools for assessing multivariate volatility forecasts. For each time period, sensitivity information provides forecasted volatility diagnostics of the MSV model to give guidance on model performance, and 3.Developing an adaptive tuning procedure based on the multivariate volatility sensitivity information to update the observation error covariance matrix during each assimilation with the main objective of providing improved results in an online manner. Applications of the new sensitivity diagnostics and adaptive tuning procedures of the MSV model are explored in two experiments. The first experiment is a proof-of-concept experiment where a multivariate series of volatilities is simulated through the specification of a MSV model and serves as a placeholder for true volatilities. The MSV model is then estimated on the resulting time series dataset and the adaptive tuning procedure is performed to demonstrate superior estimation results over the current literature methodologies. In the second experiment, a time series set of Foreign Exchange (FX) rate data is used to estimate the MSV model to provide a time series of conditional volatility estimates of each FX rate. The sensitivity information of each FX rate's conditional volatility forecasts is implemented to derive model performance diagnostics, while the adaptive tuning procedure is implemented to provide improved conditional volatility estimates. Furthermore, an objective assessment and validation of the newly developed methodology is achieved by using an extended data set that is independent on the training set used to calibrate the model.

Specification and estimation of discrete time quadratic stochastic volatility models

This paper uses the specific-to-general methodological approach that is widely used in science, in which problems with existing theories are resolved as the need arises, to illustrate a number of important developments in the modeling of univariate and multivariate financial volatility. Some of the difficulties in analyzing time-varying univariate and multivariate conditional volatility and stochastic volatility include the number of parameters to be estimated and the computational complexities associated with multivariate conditional volatility models and both univariate and multivariate stochastic volatility models. For these reasons, among others, automated inference in its present state requires modifications and extensions for modeling in empirical financial econometrics. As a contribution to the development of automated inference in modeling volatility, 20 important issues in the specification, estimation, and testing of conditional and stochastic volatility models are discussed. A “potential for automation rating” (PAR) index and recommendations regarding the possibilities for automated inference in modeling financial volatility are given in each case.

This paper aims to select the best model or set of models for modelling volatility of the four most popular cryptocurrencies, i.e. Bitcoin, Ethereum, Ripple and Litecoin. More than 1,000 GARCH models are fitted to the log returns of the exchange rates of each of these cryptocurrencies to estimate a one-step ahead prediction of Value-at-Risk (VaR) and Expected Shortfall (ES) on a rolling window basis. The best model or superior set of models is then chosen by backtesting VaR and ES as well as using a Model Confidence Set (MCS) procedure for their loss functions. The results imply that using standard GARCH models may yield incorrect VaR and ES predictions, and hence result in ineffective risk-management, portfolio optimisation, pricing of derivative securities etc. These could be improved by using instead the model specifications allowing for asymmetries and regime switching suggested by our analysis, from which both investors and regulators can benefit.

This paper aims to select the best model or set of models for modelling volatility of the four most popular cryptocurrencies, i.e. Bitcoin, Ethereum, Ripple and Litecoin. More than 1000 GARCH models are fitted to the log returns of the exchange rates of each of these cryptocurrencies to estimate a one-step ahead prediction of Value-at-Risk (VaR) and Expected Shortfall (ES) on a rolling window basis. The best model or superior set of models is then chosen by backtesting VaR and ES as well as using a Model Confidence Set (MCS) procedure for their loss functions. The results imply that using standard GARCH models may yield incorrect VaR and ES predictions, and hence result in ineffective risk-management, portfolio optimisation, pricing of derivative securities etc. These could be improved by using instead the model specifications allowing for asymmetries and regime switching suggested by our analysis, from which both investors and regulators can benefit.

Risk and Return in Stochastic Volatility Models: Volatility Feedback Matters!