Forecasting volatility using a continuous time model

This paper evaluates the forecasting performance of a continuous stochastic volatility model with two factors of volatility (SV2F) and compares it to those of GARCH and ARFIMA models. The empirical results show that the volatility forecasting ability of the SV2F model is better than that of the GARCH and ARFIMA models, especially when volatility seems to change pattern. We use ex-post volatility as a proxy of the realized volatility obtained from intraday data and the forecasts from the SV2F are calculated using the reprojection technique proposed by Gallant and Tauchen (1998).

Measuring, Modeling, and Forecasting Volatility and Correlations from High-Frequency Data

This dissertation contains four essays that all share a common purpose: developing new methodologies to exploit the potential of high-frequency data for the measurement, modeling and forecasting of financial assets volatility and correlations. The first two chapters provide useful tools for univariate applications while the last two chapters develop multivariate methodologies. In chapter 1, we introduce a new class of univariate volatility models named FloGARCH models. FloGARCH models provide a parsimonious joint model for low frequency returns and realized measures, and are sufficiently flexible to capture long memory as well as asymmetries related to leverage effects. We analyze the performances of the models in a realistic numerical study and on the basis of a data set composed of 65 equities. Using more than 10 years of high-frequency transactions, we document significant statistical gains related to the FloGARCH models in terms of in-sample fit, out-of-sample fit and forecasting accuracy compared to classical and Realized GARCH models. In chapter 2, using 12 years of high-frequency transactions for 55 U.S. stocks, we argue that combining low-frequency exogenous economic indicators with high-frequency financial data improves the ability of conditionally heteroskedastic models to forecast the volatility of returns, their full multi-step ahead conditional distribution and the multi-period Value-at-Risk. Using a refined version of the Realized LGARCH model allowing for time-varying intercept and implemented with realized kernels, we document that nominal corporate profits and term spreads have strong long-run predictive ability and generate accurate risk measures forecasts over long-horizon. The results are based on several loss functions and tests, including the Model Confidence Set. Chapter 3 is a joint work with David Veredas. We study the class of disentangled realized estimators for the integrated covariance matrix of Brownian semimartingales with finite activity jumps. These estimators separate correlations and volatilities. We analyze different combinations of quantile- and median-based realized volatilities, and four estimators of realized correlations with three synchronization schemes. Their finite sample properties are studied under four data generating processes, in presence, or not, of microstructure noise, and under synchronous and asynchronous trading. The main finding is that the pre-averaged version of disentangled estimators based on Gaussian ranks (for the correlations) and median deviations (for the volatilities) provide a precise, computationally efficient, and easy alternative to measure integrated covariances on the basis of noisy and asynchronous prices. Along these lines, a minimum variance portfolio application shows the superiority of this disentangled realized estimator in terms of numerous performance metrics. Chapter 4 is co-authored with Niels S. Hansen, Asger Lunde and Kasper V. Olesen, all affiliated with CREATES at Aarhus University. We propose to use the Realized Beta GARCH model to exploit the potential of high-frequency data in commodity markets. The model produces high quality forecasts of pairwise correlations between commodities which can be used to construct a composite covariance matrix. We evaluate the quality of this matrix in a portfolio context and compare it to models used in the industry. We demonstrate significant economic gains in a realistic setting including short selling constraints and transaction costs.

Aikasarja-analyysimenetelmien soveltuvuus maakaasun; hinnoittelussa käytettyjen sidonnaisuustekijöiden ennustamisessa: Case Gasum Oy

Tässä tutkielmassatarkastellaan maakaasun hinnoittelussa käytettyjen sidonnaisuustekijöiden hintadynamiikkaa ja niiden vaikutusta maakaasun hinnanmuodostukseen. Pääasiallisena tavoitteena on arvioida eri aikasarjamenetelmien soveltuvuutta sidonnaisuustekijöiden ennustamisessa. Tämä toteutettiin analysoimalla eri mallien ja menetelmien ominaisuuksia sekä yhteen sovittamalla nämä eri energiamuotojen hinnanmuodostuksen erityispiirteisiin. Tutkielmassa käytetty lähdeaineisto on saatu Gasum Oy:n tietokannasta. Maakaasun hinnoittelussa käytetään kolmea sidonnaisuustekijää seuraavilla painoarvoilla: raskaspolttoöljy 50%, indeksi E40 30% ja kivihiili 20%. Kivihiilen ja raskaan polttoöljyn hinta-aineisto koostuu verottomista dollarimääräisistä kuukausittaisista keskiarvoista periodilta 1.1.1997 - 31.10.2004. Kotimarkkinoiden perushintaindeksin alaindeksin E40 indeksi-aineisto, joka kuvaa energian tuottajahinnan kehitystä Suomessa ja koostuu tilastokeskuksen julkaisemista kuukausittaisista arvoista periodilta 1.1.2000 - 31.10.2004. Tutkimuksessa tarkasteltujen mallien ennustuskyky osoittautui heikoksi. Kuitenkin tuloksien perusteella voidaan todeta, että lyhyellä aikavälillä EWMA-malli antoi harhattomimman ennusteen. Muut testatuista malleista eivät kyenneet antamaan riittävän luotettavia ja tarkkoja ennusteita. Perinteinen aikasarja-analyysi kykeni tunnistamaan aikasarjojen kausivaihtelut sekä trendit. Lisäksi liukuvan keskiarvon menetelmä osoittautui jossain määrin käyttökelpoiseksi aikasarjojen lyhyen aikavälin trendien identifioinnissa.

A Comprehensive Portfolio Construction Under Stochastic Environment

Prior research has established that idiosyncratic volatility of the securities prices exhibits a positive trend. This trend and other factors have made the merits of investment diversification and portfolio construction more compelling. A new optimization technique, a greedy algorithm, is proposed to optimize the weights of assets in a portfolio. The main benefits of using this algorithm are to: a) increase the efficiency of the portfolio optimization process, b) implement large-scale optimizations, and c) improve the resulting optimal weights. In addition, the technique utilizes a novel approach in the construction of a time-varying covariance matrix. This involves the application of a modified integrated dynamic conditional correlation GARCH (IDCC - GARCH) model to account for the dynamics of the conditional covariance matrices that are employed. The stochastic aspects of the expected return of the securities are integrated into the technique through Monte Carlo simulations. Instead of representing the expected returns as deterministic values, they are assigned simulated values based on their historical measures. The time-series of the securities are fitted into a probability distribution that matches the time-series characteristics using the Anderson-Darling goodness-of-fit criterion. Simulated and actual data sets are used to further generalize the results. Employing the S&P500 securities as the base, 2000 simulated data sets are created using Monte Carlo simulation. In addition, the Russell 1000 securities are used to generate 50 sample data sets. The results indicate an increase in risk-return performance. Choosing the Value-at-Risk (VaR) as the criterion and the Crystal Ball portfolio optimizer, a commercial product currently available on the market, as the comparison for benchmarking, the new greedy technique clearly outperforms others using a sample of the S&P500 and the Russell 1000 securities. The resulting improvements in performance are consistent among five securities selection methods (maximum, minimum, random, absolute minimum, and absolute maximum) and three covariance structures (unconditional, orthogonal GARCH, and integrated dynamic conditional GARCH).

Volatility forecasting with range models: An evaluation of new alternatives to the CARR model

The aim of this paper is to analyze the forecasting ability of the CARR model proposed by Chou (2005) using the S&P 500. We extend the data sample, allowing for the analysis of different stock market circumstances and propose the use of various range estimators in order to analyze their forecasting performance. Our results show that there are two range-based models that outperform the forecasting ability of the GARCH model. The Parkinson model is better for upward trends and volatilities which are higher and lower than the mean while the CARR model is better for downward trends and mean volatilities.

"Empirical Analysis of Jumps Contribution to Volatility Forecasting Using High Frequency Data".

Rapport de recherche présenté à la Faculté des arts et des sciences en vue de l'obtention du grade de Maîtrise en sciences économiques.

Volatility forecasting for risk management

Recent research has suggested that forecast evaluation on the basis of standard statistical loss functions could prefer models which are sub-optimal when used in a practical setting. This paper explores a number of statistical models for predicting the daily volatility of several key UK financial time series. The out-of-sample forecasting performance of various linear and GARCH-type models of volatility are compared with forecasts derived from a multivariate approach. The forecasts are evaluated using traditional metrics, such as mean squared error, and also by how adequately they perform in a modern risk management setting. We find that the relative accuracies of the various methods are highly sensitive to the measure used to evaluate them. Such results have implications for any econometric time series forecasts which are subsequently employed in financial decisionmaking.

Forecasting exchange rate volatility using conditional variance models selected by information criteria

This paper uses appropriately modified information criteria to select models from the GARCH family, which are subsequently used for predicting US dollar exchange rate return volatility. The out of sample forecast accuracy of models chosen in this manner compares favourably on mean absolute error grounds, although less favourably on mean squared error grounds, with those generated by the commonly used GARCH(1, 1) model. An examination of the orders of models selected by the criteria reveals that (1, 1) models are typically selected less than 20% of the time.

The importance of the volatility risk premium for volatility forecasting

In this paper, we study the role of the volatility risk premium for the forecasting performance of implied volatility. We introduce a non-parametric and parsimonious approach to adjust the model-free implied volatility for the volatility risk premium and implement this methodology using more than 20 years of options and futures data on three major energy markets. Using regression models and statistical loss functions, we find compelling evidence to suggest that the risk premium adjusted implied volatility significantly outperforms other models, including its unadjusted counterpart. Our main finding holds for different choices of volatility estimators and competing time-series models, underlying the robustness of our results.

Do jumps matter for volatility forecasting? Evidence from energy markets

This paper characterizes the dynamics of jumps and analyzes their importance for volatility forecasting. Using high-frequency data on four prominent energy markets, we perform a model-free decomposition of realized variance into its continuous and discontinuous components. We find strong evidence of jumps in energy markets between 2007 and 2012. We then investigate the importance of jumps for volatility forecasting. To this end, we estimate and analyze the predictive ability of several Heterogenous Autoregressive (HAR) models that explicitly capture the dynamics of jumps. Conducting extensive in-sample and out-of-sample analyses, we establish that explicitly modeling jumps does not significantly improve forecast accuracy. Our results are broadly consistent across our four energy markets, forecasting horizons, and loss functions

Estimating and forecasting the volatility of Brazilian finance series using arch models (Preliminary Version)

The goal of this paper is to present a comprehensive emprical analysis of the return and conditional variance of four Brazilian …nancial series using models of the ARCH class. Selected models are then compared regarding forecasting accuracy and goodness-of-…t statistics. To help understanding the empirical results, a self-contained theoretical discussion of ARCH models is also presented in such a way that it is useful for the applied researcher. Empirical results show that although all series share ARCH and are leptokurtic relative to the Normal, the return on the US$ has clearly regime switching and no asymmetry for the variance, the return on COCOA has no asymmetry, while the returns on the CBOND and TELEBRAS have clear signs of asymmetry favoring the leverage e¤ect. Regarding forecasting, the best model overall was the EGARCH(1; 1) in its Gaussian version. Regarding goodness-of-…t statistics, the SWARCH model did well, followed closely by the Student-t GARCH(1; 1)

Forecasting daily volatility using high frequency financial data

Aiming at empirical findings, this work focuses on applying the HEAVY model for daily volatility with financial data from the Brazilian market. Quite similar to GARCH, this model seeks to harness high frequency data in order to achieve its objectives. Four variations of it were then implemented and their fit compared to GARCH equivalents, using metrics present in the literature. Results suggest that, in such a market, HEAVY does seem to specify daily volatility better, but not necessarily produces better predictions for it, what is, normally, the ultimate goal. The dataset used in this work consists of intraday trades of U.S. Dollar and Ibovespa future contracts from BM&FBovespa.

Estimating and forecasting generalized fractional Long memory stochastic volatility models

In recent years fractionally differenced processes have received a great deal of attention due to its flexibility in financial applications with long memory. This paper considers a class of models generated by Gegenbauer polynomials, incorporating the long memory in stochastic volatility (SV) components in order to develop the General Long Memory SV (GLMSV) model. We examine the statistical properties of the new model, suggest using the spectral likelihood estimation for long memory processes, and investigate the finite sample properties via Monte Carlo experiments. We apply the model to three exchange rate return series. Overall, the results of the out-of-sample forecasts show the adequacy of the new GLMSV model.

Forecasting Elections with High Volatility

This article uses data from the social survey Allbus 1998 to introduce a method of forecasting elections in a context of electoral volatility. The approach models the processes of change in electoral behaviour, exploring patterns in order to model the volatility expressed by voters. The forecast is based on the matrix of transition probabilities, following the logic of Markov chains. The power of the matrix, and the use of the mover-stayer model, is debated for alternative forecasts. As an example of high volatility, the model uses data from the German general election of 1998. The unification of two German states in 1990 caused the incorporation of around 15 million new voters from East Germany who had limited familiarity and no direct experience of the political culture in West Germany. Under these circumstances, voters were expected to show high volatility.

Forecasting the term structure of volatility of crude oil price changes

Peer reviewed