Realized Volatility

This paper investigates the time-varying volatility patterns of some major commodities as well as the potential factors that drive their long-term volatility component. For this purpose, we make use of a recently proposed GARCH-MIDAS approach which typically allows us to examine the role of economic and financial variables of different frequencies. Using commodity futures for Crude Oil (WTI and Brent), Gold, Silver and Platinum as well as a commodity index, our results show the necessity of disentangling the short-term and long-term components in modeling and forecasting commodity volatility. They also indicate that the long-term volatility of most commodity futures is significantly driven by the level of the global real economic activity as well as the changes in consumer sentiment, industrial production, and economic policy uncertainty. However, the forecasting results are not alike across commodity futures as no single model fits all commodities.

Volatility is a key parameter in currency option pricing. This paper examines alternative specifications of the volatility input to the Black-Scholes option pricing procedure. The focus is the relative performance of implied, realized, and GARCH-based models as predictors of market volatility to forecast currency options prices. Using exchange-traded, daily and intra-daily data for three major European currencies, the results indicate that the realized volatility model tends to outperform the other two specifications, both in-sample and out-of-sample. This result is intuitively appealing and expected to facilitate resolution of other problems in risk management applications.

We forecast the realized and median realized volatility of agricultural commodities using variants of the Heterogeneous AutoRegressive (HAR) model. We obtain tick-by-tick data for five widely traded agricultural commodities (Corn, Rough Rice, Soybeans, Sugar, and Wheat) from the CME/ICE. Real out-of-sample forecasts are produced for 1- up to 66-days ahead. Our in-sample analysis shows that the variants of the HAR model which decompose volatility measures into their continuous path and jump components and incorporate leverage effects offer better fitting in the predictive regressions. However, we convincingly demonstrate that such HAR extensions do not offer any superior predictive ability in the out-of-sample results, since none of these extensions produce significantly better forecasts compared to the simple HAR model. Our results remain robust even when we evaluate them in a Value-at-Risk framework. Thus, there is no benefit by adding more complexity, related to volatility decomposition or relative transformations of volatility, in the forecasting models.

Existing studies on the informational content of at-the-money implied volatility (ATMIV) and past realized volatility (PRV) and the relation between the two have mainly focused on a single short forecast horizon and conclude that ATMIV outperforms PRV. We examine the relation between implied and realized volatility over both short and longer forecasting horizons to provide a forecasting competition. We analytically demonstrate the option maturity effect on the sensitivity of the implied volatility (IV) estimation. As time to maturity increases, vega increases but at a decreasing rate, up to [Formula: see text]. At shorter (longer) maturities, small pricing changes should have greater (smaller) corrective impact on IVs. We find that IV outperforms PRV over a one month forecast horizon. However, as the forecast horizon increases, PRV outperforms IV and subsumes the information contained in it. These mixed results may be attributed to the reduced efficiency of longer dated sections of ...

Asset allocation and risk calculations depend largely on volatile models. The parameters of the volatility models are estimated using either the Maximum Likelihood (ML) or the Quasi-Maximum Likelihood (QML). By comparing the out-of-sample forecasting performance of 68 ARCH-type models using inter-daily data on the peso-dollar exchange rate, this study shows that it is important to correctly specify the distribution of the asset returns and not only focus on the specification of the volatility. The forecasts are compared to the Parkinson Range, an alternative to the Realized Volatility.

Persistence and occasional abrupt changes in the average level characterize the dynamics of high frequency based measures of volatility. Since the beginning of the 2000s, this pattern can be attributed to the dot com bubble, the quiet period of expansion of credit between 2003 and 2006 and then the harsh times after the burst of the subprime mortgage crisis. We conjecture that the inadequacy of many econometric volatility models (a very high level of estimated persistence, serially correlated residuals) can be solved with an ...

The aim of this thesis is to provide a characterization of the statistical properties of estimator of the Hurst parameter of the rough stochastic volatility model following fractional Brownian motion with Hurst index H. For this purpose, we perform a simulation experiment for fractional Brownian motion based on the circulant embedding method. Moreover, the study contributes to make a comparison between the Hurst estimator and the memory parameter estimator, d. The results indicate that the Hurst estimator is superior to considered memory estimators, however, in the presence of microstructure noise, it is downward biased.MSc in Financ

Does volatility re‡ect a continuous reaction to past shocks or changes in the markets induce shifts in the volatility dynamics? In this paper, we introduce price variations as a possible source behind shifts in the level of volatility over some period, with large falls (rises) in prices bringing persistent regimes of high (low) variance in stock returns. We set a ‡exible and systematic modeling strategy to test and estimate this asymmetry, incorporating past cumulated daily returns in a nonlinear framework. The key result of the paper is that this e¤ect is highly signi…cant (we estimate that volatility levels 20% and 60% higher are associated with falls over short horizons) and accounts for high empirical values of long memory parameter estimates. We show that a model based on those …ndings signi…cantly improves out of sample performance in relation to standard methods for all 16 stocks analyzed–specially in periods of high volatility.

We review and synthesize our recent work on realized volatility in financial markets. This includes (1) constructing and interpreting realized volatilities for a variety of asset returns ("understanding"), (2) determining underlying sampling frequencies high enough to produce precise estimates yet low enough to mitigate microstructure bias ("optimizing"), (3) putting realized volatilities to work in various contexts, such as the production of standardized returns series with desirable properties ("using"), and (4) using predictions of realized volatility for improved financial risk management ("forecasting").

This study investigates the practical importance of several VaR modeling and forecasting issues in the context of intraday stock returns. Value-at-Risk (VaR) predictions obtained from daily GARCH models extended with additional information such as the realized volatility and squared overnight returns, are confronted with those from ARFIMA realized volatility models. The out-of-sample evaluation is based on a novel difference-in-proportions test that exploits the frequency of individual VaR rejections and a block-bootstrap unconditional coverage test that is robust to estimation uncertainty and model risk. We find that the overnight surprise does not improve the out-of-sample forecastability of the next-day VaR but there is evidence that intraday jumps have forecasting potential. ARFIMA models produce better backtesting results than GARCH models but the latter fare better in terms of independence of the hits sequence. Encompassing tests further suggest that GARCH and ARFIMA models ca...

Short sale constraints can inflate market prices, as bearish investors cannot act on their market views. The paper uses data from the Indian equity market to test whether opinion dispersion leads to higher overpricing when short sales are prohibited. The Indian ...

It is now recognized that long memory and structural change can easily be confused because the statistical properties of times series of lengths typical of nancial and econometric series are similar for both models. The implications of long memory models or short memory with breaks for the pricing of nancial assets (e.g. options) have been studied by other authorities who have concluded the pricing is signicantly dierent between the two classes of models. Option pricing is also of interest to regulatory authorities. Thus it is of interest both from a nance theory and regulatory point of view whether the data are generated by a true long memory process or by something else. We propose a new approach aimed at distinguishing between long memory and structural change. The approach, which utilizes the computational ecient methods based upon Atheoretical Regression Trees (ART), uses a null hypothesis of the data being a fractionally integrated series. It establishes through simulation the...

Fuzzy rule–based models, a key element in soft computing (SC), have arisen as an alternative for time series analysis and modeling. One difference with preexisting models is their interpretability in terms of human language. Their interactions with other components have also contributed to a huge development in their identification and estimation procedures. In this article, we present fuzzy rule–based models, their links with some regime-switching autoregressive models, and how the use of soft computing concepts can help ...

Fuzzy rule–based models, a key element in soft computing (SC), have arisen as an alternative for time series analysis and modeling. One difference with preexisting models is their interpretability in terms of human language. Their interactions with other components have also contributed to a huge development in their identification and estimation procedures. In this article, we present fuzzy rule–based models, their links with some regime-switching autoregressive models, and how the use of soft computing concepts can help ...

Understanding jump risk is important in risk management and option pricing. This study examines the characteristics of jump risk and the volatility forecasting power of the jump component in a panel of high-frequency intraday stock returns and four index returns from Shanghai Stock Exchange. Across portfolio indexes, jump returns on average account for 45% to 64% of total returns when jumps occur. Market systematic jump risk is an important pricing factor for daily returns. The average jump beta is 62% of the average continuous beta for individual stocks. However, the contribution of jump risk to total risk is limited, indicating that statistically significant jumps in the stochastic process of asset price are rare events but have tremendous impacts on the prices of common stocks in China. We further document that accounting for jump components improves the performance of volatility forecasting for some equity and bond portfolios in China, which is confirmed by in-the-sample and out-of-sample forecasting performance analysis.

Abstract. Credit risk is the most important type of risk in terms of monetary value. Another key risk measure is market risk, which is concerned with stocks and bonds, and related financial derivatives, as well as exchange rates and interest rates. This paper is concerned with ...

Abstract: This paper investigates the economic value of different non-parametric realized volatility estimates in E cient Frontier, Global Minimum Variance, Capital Market Line and Capital Market Line with only positive weights portfolio types. The dataset concerns the ...

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.

Persistence and occasional abrupt changes in the average level characterize the dynamics of high frequency based measures of volatility. Since the beginning of the 2000s, this pattern can be attributed to the dot com bubble, the quiet period of expansion of credit between 2003 and 2006 and then the harsh times after the burst of the subprime mortgage crisis. We conjecture that the inadequacy of many econometric volatility models (a very high level of estimated persistence, serially correlated residuals) can be solved with an adequate representation of such a pattern. We insert a Markovian dynamics in a Multiplicative Error Model to represent the conditional expectation of the realized volatility, allowing us to address the issues of a slow moving average level of volatility and of a different dynamics across regime. We apply the model to realized volatility of the S&P500 index and we gauge the usefulness of such an approach by a more interpretable persistence, better residual proper...