Forecasting volatility and correlation : the role of option implied measures

Forecasts of volatility and correlation are important inputs into many practical financial problems. Broadly speaking, there are two ways of generating forecasts of these variables. Firstly, time-series models apply a statistical weighting scheme to historical measurements of the variable of interest. The alternative methodology extracts forecasts from the market traded value of option contracts. An efficient options market should be able to produce superior forecasts as it utilises a larger information set of not only historical information but also the market equilibrium expectation of options market participants. While much research has been conducted into the relative merits of these approaches, this thesis extends the literature along several lines through three empirical studies. Firstly, it is demonstrated that there exist statistically significant benefits to taking the volatility risk premium into account for the implied volatility for the purposes of univariate volatility forecasting. Secondly, high-frequency option implied measures are shown to lead to superior forecasts of the intraday stochastic component of intraday volatility and that these then lead on to superior forecasts of intraday total volatility. Finally, the use of realised and option implied measures of equicorrelation are shown to dominate measures based on daily returns.

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.

Are combination forecasts of S&P 500 volatility statistically superior?

Forecasting volatility has received a great deal of research attention, with the relative performances of econometric model based and option implied volatility forecasts often being considered. While many studies find that implied volatility is the pre-ferred approach, a number of issues remain unresolved, including the relative merit of combining forecasts and whether the relative performances of various forecasts are statistically different. By utilising recent econometric advances, this paper considers whether combination forecasts of S&P 500 volatility are statistically superior to a wide range of model based forecasts and implied volatility. It is found that a combination of model based forecasts is the dominant approach, indicating that the implied volatility cannot simply be viewed as a combination of various model based forecasts. Therefore, while often viewed as a superior volatility forecast, the implied volatility is in fact an inferior forecast of S&P 500 volatility relative to model-based forecasts.

Unrealized expectations of jumps in volatility: An explanation to the low and time-varying predictive power of implied volatility

The low predictive power of implied volatility in forecasting the subsequently realized volatility is a well-documented empirical puzzle. As suggested by e.g. Feinstein (1989), Jackwerth and Rubinstein (1996), and Bates (1997), we test whether unrealized expectations of jumps in volatility could explain this phenomenon. Our findings show that expectations of infrequently occurring jumps in volatility are indeed priced in implied volatility. This has two important consequences. First, implied volatility is actually expected to exceed realized volatility over long periods of time only to be greatly less than realized volatility during infrequently occurring periods of very high volatility. Second, the slope coefficient in the classic forecasting regression of realized volatility on implied volatility is very sensitive to the discrepancy between ex ante expected and ex post realized jump frequencies. If the in-sample frequency of positive volatility jumps is lower than ex ante assessed by the market, the classic regression test tends to reject the hypothesis of informational efficiency even if markets are informationally effective.

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).

Semi-parametric forecasting of realized volatility

Forecasts generated by time series models traditionally place greater weight on more recent observations. This paper develops an alternative semi-parametric method for forecasting that does not rely on this convention and applies it to the problem of forecasting asset return volatility. In this approach, a forecast is a weighted average of historical volatility, with the greatest weight given to periods that exhibit similar market conditions to the time at which the forecast is being formed. Weighting is determined by comparing short-term trends in volatility across time (as a measure of market conditions) by means of a multivariate kernel scheme. It is found that the semi-parametric method produces forecasts that are significantly more accurate than a number of competing approaches at both short and long forecast horizons.

Selecting volatility forecasting models for portfolio allocation purposes

Techniques for evaluating and selecting multivariate volatility forecasts are not yet understood as well as their univariate counterparts. This paper considers the ability of different loss functions to discriminate between a set of competing forecasting models which are subsequently applied in a portfolio allocation context. It is found that a likelihood-based loss function outperforms its competitors, including those based on the given portfolio application. This result indicates that considering the particular application of forecasts is not necessarily the most effective basis on which to select models.

Modeling and Forecasting Implied Volatility: Implications for Trading, Pricing, and Risk Management

Modeling and forecasting of implied volatility (IV) is important to both practitioners and academics, especially in trading, pricing, hedging, and risk management activities, all of which require an accurate volatility. However, it has become challenging since the 1987 stock market crash, as implied volatilities (IVs) recovered from stock index options present two patterns: volatility smirk(skew) and volatility term-structure, if the two are examined at the same time, presents a rich implied volatility surface (IVS). This implies that the assumptions behind the Black-Scholes (1973) model do not hold empirically, as asset prices are mostly influenced by many underlying risk factors. This thesis, consists of four essays, is modeling and forecasting implied volatility in the presence of options markets’ empirical regularities. The first essay is modeling the dynamics IVS, it extends the Dumas, Fleming and Whaley (DFW) (1998) framework; for instance, using moneyness in the implied forward price and OTM put-call options on the FTSE100 index, a nonlinear optimization is used to estimate different models and thereby produce rich, smooth IVSs. Here, the constant-volatility model fails to explain the variations in the rich IVS. Next, it is found that three factors can explain about 69-88% of the variance in the IVS. Of this, on average, 56% is explained by the level factor, 15% by the term-structure factor, and the additional 7% by the jump-fear factor. The second essay proposes a quantile regression model for modeling contemporaneous asymmetric return-volatility relationship, which is the generalization of Hibbert et al. (2008) model. The results show strong negative asymmetric return-volatility relationship at various quantiles of IV distributions, it is monotonically increasing when moving from the median quantile to the uppermost quantile (i.e., 95%); therefore, OLS underestimates this relationship at upper quantiles. Additionally, the asymmetric relationship is more pronounced with the smirk (skew) adjusted volatility index measure in comparison to the old volatility index measure. Nonetheless, the volatility indices are ranked in terms of asymmetric volatility as follows: VIX, VSTOXX, VDAX, and VXN. The third essay examines the information content of the new-VDAX volatility index to forecast daily Value-at-Risk (VaR) estimates and compares its VaR forecasts with the forecasts of the Filtered Historical Simulation and RiskMetrics. All daily VaR models are then backtested from 1992-2009 using unconditional, independence, conditional coverage, and quadratic-score tests. It is found that the VDAX subsumes almost all information required for the volatility of daily VaR forecasts for a portfolio of the DAX30 index; implied-VaR models outperform all other VaR models. The fourth essay models the risk factors driving the swaption IVs. It is found that three factors can explain 94-97% of the variation in each of the EUR, USD, and GBP swaption IVs. There are significant linkages across factors, and bi-directional causality is at work between the factors implied by EUR and USD swaption IVs. Furthermore, the factors implied by EUR and USD IVs respond to each others’ shocks; however, surprisingly, GBP does not affect them. Second, the string market model calibration results show it can efficiently reproduce (or forecast) the volatility surface for each of the swaptions markets.

Volatility and VaR Forecasting in the Madrid Stock Exchange

This paper provides an empirical study to assess the forecasting performance of a wide range of models for predicting volatility and VaR in the Madrid Stock Exchange. The models performance was measured by using different loss functions and criteria. The results show that FIAPARCH processes capture and forecast more accurately the dynamics of IBEX-35 returns volatility. It is also observed that assuming a heavy-tailed distribution does not improve models ability for predicting volatility. However, when the aim is forecasting VaR, we find evidence of that the Student’s t FIAPARCH outperforms the models it nests the lower the target quantile.

"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.