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Journal ArticleDOI

Semiparametric Conditional Quantile Models for Financial Returns and Realized Volatility

TL;DR: In this article, the conditional quantiles of future returns and volatility of financial assets vary with various measures of ex-post variation in asset prices as well as option-implied volatility.
Abstract: This paper investigates how the conditional quantiles of future returns and volatility of financial assets vary with various measures of ex-post variation in asset prices as well as option-implied volatility. We work in the flexible quantile regression framework and rely on recently developed model-free measures of integrated variance, upside and downside semivariance, and jump variation. Our results for the S&P 500 and WTI Crude Oil futures contracts show that simple linear quantile regressions for returns and heterogenous quantile autoregressions for realized volatility perform very well in capturing the dynamics of the respective conditional distributions, both in absolute terms as well as relative to a couple of well-established benchmark models. The models can therefore serve as useful risk management tools for investors trading the futures contracts themselves or various derivative contracts written on realized volatility.
Citations
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Journal ArticleDOI
TL;DR: In this paper, the authors comprehensively examined the existence and significance of a contemporaneous/intertemporal risk-return trade-off for crude oil futures using high-frequency transaction data.

60 citations

Journal ArticleDOI
TL;DR: In this paper, the authors assess the value-at-risk (VaR) forecasting performance of recently proposed realized volatility models combined with alternative parametric and semi-parametric quantile estimation methods, and find that statistical accuracy and regulatory compliance is essentially improved when they use quantile methods which account for the fat tails and the asymmetry of the innovations distribution.

55 citations

Journal ArticleDOI
TL;DR: In this article, quantile regression theory is used to obtain a combination of individual potentially-biased VaR forecasts that is optimal because it meets by construction ex post the correct out-of-sample conditional coverage criterion.
Abstract: We make use of quantile regression theory to obtain a combination of individual potentially-biased VaR forecasts that is optimal because it meets by construction ex post the correct out-of-sample conditional coverage criterion. This enables a Wald-type conditional quantile forecast encompassing test for any finite set of competing (semi/non)parametric models which can be nested. Two attractive properties of this backtesting approach are robustness to model risk and estimation uncertainty. We deploy the techniques to confront inter-day and high frequency intra-day VaR models for equity, FOREX, fixed income and commodity trading desks. Forecast combination of both types of models is especially warranted for more extreme-tail risks. Overall our empirical analysis supports the use of high frequency 5-minute price information for daily risk management.

42 citations

Journal ArticleDOI
TL;DR: In this article, quantile regression theory is used to obtain a combination of individual potentially-biased VaR forecasts that is optimal because, by construction, it meets the correct out-of-sample conditional coverage criterion ex post.

37 citations

Journal ArticleDOI
TL;DR: In this article, the authors adopt a semi-parametric model for the distribution by assuming that the return quantiles depend on the realized measures and evaluate the distribution, quantile and interval forecasts of the quantile model in comparison to a benchmark GARCH model.
Abstract: The aim of this paper is to forecast (out-of-sample) the distribution of financial returns based on realized volatility measures constructed from high-frequency returns. We adopt a semi-parametric model for the distribution by assuming that the return quantiles depend on the realized measures and evaluate the distribution, quantile and interval forecasts of the quantile model in comparison to a benchmark GARCH model. The results suggest that the model outperforms an asymmetric GARCH specification when applied to the S&P 500 futures returns, in particular on the right tail of the distribution. However, the model provides similar accuracy to a GARCH (1, 1) model when the 30-year Treasury bond futures return is considered.

17 citations

References
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TL;DR: The authors describes the advantages of these studies and suggests how they can be improved and also provides aids in judging the validity of inferences they draw, such as multiple treatment and comparison groups and multiple pre- or post-intervention observations.
Abstract: Using research designs patterned after randomized experiments, many recent economic studies examine outcome measures for treatment groups and comparison groups that are not randomly assigned. By using variation in explanatory variables generated by changes in state laws, government draft mechanisms, or other means, these studies obtain variation that is readily examined and is plausibly exogenous. This paper describes the advantages of these studies and suggests how they can be improved. It also provides aids in judging the validity of inferences they draw. Design complications such as multiple treatment and comparison groups and multiple pre- or post-intervention observations are advocated.

7,222 citations


"Semiparametric Conditional Quantile..." refers methods in this paper

  • ...To test for equal predictive ability we use the Diebold & Mariano (1995) test with the Newey-West variance in the case of multi-step-ahead quantile forecasts....

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Posted Content
TL;DR: Simulation results show that the HAR-RV model successfully achieves the purpose of reproducing the main empirical features of financial returns in a very tractable and parsimonious way and empirical results show remarkably good forecasting performance.
Abstract: The paper proposes an additive cascade model of volatility components defined over different time periods. This volatility cascade leads to a simple AR-type model in the realized volatility with the feature of considering different volatility components realized over different time horizons and thus termed Heterogeneous Autoregressive model of Realized Volatility (HAR-RV). In spite of the simplicity of its structure and the absence of true long-memory properties, simulation results show that the HAR-RV model successfully achieves the purpose of reproducing the main empirical features of financial returns (long memory, fat tails, and self-similarity) in a very tractable and parsimonious way. Moreover, empirical results show remarkably good forecasting performance.

493 citations


"Semiparametric Conditional Quantile..." refers background or methods in this paper

  • ...In a comparison with two competing models, the CAViaR of Engle and Manganelli (2004) and the lognormal-normal mixture of Andersen et al....

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  • ...Given the recent evidence on the predictive power of contemporaneous jumps for future volatility (Andersen, Bollerslev & Diebold, 2007, Corsi, Pirino & Renò, 2010) and the finding of Todorov & Tauchen (2011) that prices and volatility tend to jump together seems to suggests that jumps may perhaps contain information about quantiles of future returns and volatility as well....

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  • ...Inspired by the success of the of the heterogenous autoregressive model (HAR) for realized volatility developed by Corsi (2009) and extended by Andersen et al. (2007), we write the conditional α-quantile of the realized quadratic variation RVt+1,M as qα(RVt+1,M |Ωt) = β0(α)+βv1(α)′vt,M…...

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  • ...This model can be viewed as an extension of the heterogeneous autoregression, originally proposed by Corsi (2009) for modeling the conditional mean of realized volatility, to conditional quantiles....

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  • ...Following the suggestions of the referees, we compare the return regressions with the CAViaR model proposed by Engle and Manganelli (2004), augmented by the various realized measures and option-implied volatility, and the lognormal-normal mixture of Andersen et al....

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Journal ArticleDOI
TL;DR: In this paper, the authors provide a framework for non-parametric measurement of the jump component in asset return volatility and find that jumps are both highly prevalent and distinctly less persistent than the continuous sample path variation process.
Abstract: A rapidly growing literature has documented important improvements in financial return volatility measurement and forecasting via use of realized variation measures constructed from high-frequency returns coupled with simple modeling procedures. Building on recent theoretical results in Barndorff-Nielsen and Shephard (2004a, 2005) for related bi-power variation measures, the present paper provides a practical and robust framework for non-parametrically measuring the jump component in asset return volatility. In an application to the DM/$ exchange rate, the S&P500 market index, and the 30-year U.S. Treasury bond yield, we find that jumps are both highly prevalent and distinctly less persistent than the continuous sample path variation process. Moreover, many jumps appear directly associated with specific macroeconomic news announcements. Separating jump from non-jump movements in a simple but sophisticated volatility forecasting model, we find that almost all of the predictability in daily, weekly, and monthly return volatilities comes from the non-jump component. Our results thus set the stage for a number of interesting future econometric developments and important financial applications by separately modeling, forecasting, and pricing the continuous and jump components of the total return variation process.

323 citations

Journal ArticleDOI
TL;DR: In this paper, the authors provide a general framework for integration of high-frequency intraday data into the measurement, modeling, and forecasting of daily and lower frequency volatility and return distributions.
Abstract: This paper provides a general framework for integration of high-frequency intraday data into the measurement, modeling, and forecasting of daily and lower frequency volatility and return distributions. Most procedures for modeling and forecasting financial asset return volatilities, correlations, and distributions rely on restrictive and complicated parametric multivariate ARCH or stochastic volatility models, which often perform poorly at intraday frequencies. Use of realized volatility constructed from high-frequency intraday returns, in contrast, permits the use of traditional time series procedures for modeling and forecasting. Building on the theory of continuous-time arbitrage-free price processes and the theory of quadratic variation, we formally develop the links between the conditional covariance matrix and the concept of realized volatility. Next, using continuously recorded observations for the Deutschemark / Dollar and Yen / Dollar spot exchange rates covering more than a decade, we find that forecasts from a simple long-memory Gaussian vector autoregression for the logarithmic daily realized volatilities perform admirably compared to popular daily ARCH and related models. Moreover, the vector autoregressive volatility forecast, coupled with a parametric lognormal-normal mixture distribution implied by the theoretically and empirically grounded assumption of normally distributed standardized returns, gives rise to well-calibrated density forecasts of future returns, and correspondingly accurate quantile estimates. Our results hold promise for practical modeling and forecasting of the large covariance matrices relevant in asset pricing, asset allocation and financial risk management applications.

315 citations

Journal ArticleDOI
TL;DR: In this paper, the authors study the forecasting of future realized volatility in the stock, bond, and foreign exchange markets, as well as the continuous sample path and jump components of this, from variables in the information set, including implied volatility backed out from option prices.
Abstract: We study the forecasting of future realized volatility in the stock, bond, and foreign exchange markets, as well as the continuous sample path and jump components of this, from variables in the information set, including implied volatility backed out from option prices. Recent nonparametric statistical techniques of Barndor-Nielsen & Shephard (2004, 2006) are used to separate realized volatility into its continuous and jump components, which enhances forecasting performance, as shown by Andersen, Bollerslev & Diebold (2005). We generalize the heterogeneous autoregressive (HAR) model of Corsi (2004) 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 issues in the forecasting equations. We show that implied volatility contains incremental information about future volatility relative to both continuous and jump components of past realized volatility. Indeed, in the foreign exchange market, implied volatility completely subsumes the information content of daily, weekly, and monthly realized volatility measures, when forecasting future realized volatility or its continuous component. In addition, implied volatility is an unbiased forecast of future realized volatility in the foreign exchange and stock markets. Perhaps surprisingly, the jump component of realized return volatility is, to some extent, predictable, and options appear to be calibrated to incorporate information about future jumps in all three markets.

276 citations


"Semiparametric Conditional Quantile..." refers background in this paper

  • ...ion models. Besides modeling conditional quantiles of future returns, we propose simple models for the quantiles of future realized volatility. We follow Andersen, Bollerslev & Diebold (2007) and Bush et al. (2011) and consider a heterogeneous quantile autoregressive model (HQAR) with jumps and implied volatility. This model can be viewed as an extension of the heterogeneous autoregression, originally proposed ...

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