Tim Bollerslev - Academia.edu (original) (raw)

Papers by Tim Bollerslev

A rapidly growing literature has documented important improvements in financial return volatility... more A rapidly growing literature has documented important improvements in financial return volatility measurement and forecasting performance through the use of realized variation measures constructed from the summation of high-frequency squared returns coupled with relatively simple reduced-form time series modeling procedures. Building on recent theoretical results in Barndorff-Nielsen and Shephard (2004a, 2005) for related bi-power variation measures involving the sum of adjacent absolute high-frequency returns, the present paper provides a practical and robust framework for non-parametrically measuring and assessing the statistical significance of the jump component in asset return volatility. Exploiting these ideas for a decade of high-frequency five-minute returns for the DM/$ exchange rate, the S&P500 market index, and the 30-year U.S. Treasury bond yield, we find the jump component of the price process to be distinctly less persistent than the continuous sample path variation process. Also, the occurrences of many of the most significant jumps appear to be directly associated with specific macroeconomic news announcements. Moreover, including the time series of significant jumps along with the measurements of the corresponding continuous sample path variability in an easy-to-implement reduced form HAR-RV-CJ volatility forecasting model, we find that almost all of the predictability in the daily, weekly and monthly volatilities come from the lagged continuous variation process. 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 total return variation process.

Ssrn Electronic Journal, 2000

Page 1. HIGH-FREQUENCY DATA, FREQUENCY DOMAIN INFERENCE, AND VOLATILITY FORECASTING Tim Bollersle... more Page 1. HIGH-FREQUENCY DATA, FREQUENCY DOMAIN INFERENCE, AND VOLATILITY FORECASTING Tim Bollerslev and Jonathan H. Wright* Abstract—Although it is clear that the volatility of asset returns is serially correlated ...

Current industry practice largely follows one of two restrictive approaches to market risk manage... more Current industry practice largely follows one of two restrictive approaches to market risk management: historical simulation or RiskMetrics. In contrast, exploiting recent developments in financial econometrics we propose flexible methods which are likely to produce more accurate assessments of market risk. Clearly, the demands of real-world risk management in financial institutions -in particular, real-time risk tracking in very high-dimensional situations -impose strict limits on model complexity. Hence we stress parsimonious models that are easily estimated, and we discuss a variety of practical approaches for high-dimensional covariance matrix modeling, along with what we see as some of the pitfalls and problems in current practice. In so doing we hope to encourage further dialog between the academic and practitioner communities and to stimulate the development of improved market risk management technologies that draw on the best of both worlds. _________________ * This paper is prepared for Mark Carey and René Stulz (eds.), Risks of Financial Institutions, University of Chicago Press for NBER. For helpful comments we would like to thank

Journal of Econometrics, 2010

The Hansen-Lunde (HL) research program is generally first-rate, displaying a rare blend of theore... more The Hansen-Lunde (HL) research program is generally first-rate, displaying a rare blend of theoretical prowess and applied sense. The present paper is no exception. In a major theoretical advance, HL allow for correlation between microstructure (MS) noise and latent price. (I prefer "latent price" to terms such as "efficient price" or "true price," which carry lots of excess baggage.) In a parallel major substantive advance, HL provide a pioneering empirical investigation of the nature of the correlation between MS noise and latent price, documenting a negative correlation at high frequencies. My admiration of the paper hinges on the contributions noted above and is indeed most genuine. Nevertheless, much of what follows is rather critical of the extant literature, including certain key elements of the HL approach.

This paper provides a simple unified framework for assessing the empirical linkages between retur... more This paper provides a simple unified framework for assessing the empirical linkages between returns and realized and implied volatilities. First, we show that whereas the volatility feedback effect as measured by the sign of the correlation between contemporaneous return and realized volatility depends importantly on the underlying structural model parameters, the correlation between return and implied volatility is unambiguously positive for all reasonable parameter configurations. Second, the lagged return-volatility asymmetry, or the leverage effect, is always stronger for implied than realized volatility. Third, implied volatilities generally provide downward biased forecasts of subsequent realized volatilities. Our results help explain previous findings reported in the extant empirical literature, and is further corroborated by new estimation results for a sample of monthly returns and implied and realized volatilities for the aggregate S&P market index.

New York University Leonard N Stern School Finance Department Working Paper Seires, 1999

Using high-frequency data on Deutschemark and Yen returns against the dollar, we construct model-... more Using high-frequency data on Deutschemark and Yen returns against the dollar, we construct model-free estimates of daily exchange rate volatility and correlation, covering an entire decade. In addition to being model-free, our estimates are also approximately free of measurement error under general conditions, which we delineate. Hence, for all practical purposes, we can treat the exchange rate volatilities and correlations as observed rather than latent. We do so, and we characterize their joint distribution, both unconditionally and conditionally. Noteworthy results include a simple normality-inducing volatility transformation, high contemporaneous correlation across volatilities, high correlation between correlation and volatilities, pronounced and highly persistent temporal variation in both volatilities and correlation, clear evidence of long-memory dynamics in both volatilities and correlation, and remarkably precise scaling laws under temporal aggregation.

This paper bridges the gap between traditional ARCH modelling and recent advances on realized vol... more This paper bridges the gap between traditional ARCH modelling and recent advances on realized volatilities. Based on a ten-year sample of five-minute returns for the ECU basket currencies versus the US dollar, we find that the realized volatilities constructed from the summation of the high-frequency intraday squared returns conditional on the lagged squared daily returns are approximately Inverse Gaussian (IG) distributed, while the distribution of the daily returns standardized by their realized volatilities is approximately normal. Moreover, the implied daily GARCH model with Normal Inverse Gaussian (NIG) errors estimated for the ECU returns results in very accurate out-of-sample predictions for the three years of actual daily Euro/US dollar exchange rates.

Nber Working Papers, May 17, 2012

We examine the relationship between volatility and past and future returns in highfrequency equit... more We examine the relationship between volatility and past and future returns in highfrequency equity market data. Consistent with a prolonged "leverage" effect, we find the correlations between absolute high-frequency returns and current and past high-frequency returns to be significantly negative for several days, while the reverse cross-correlations between absolute returns and future returns are generally negligible. Based on a simple aggregation formula, we demonstrate how the high-frequency data may similarly be used in more effectively assessing volatility asymmetries over longer daily return horizons. Motivated by the striking cross-correlation patterns uncovered in the high-frequency data, we investigate the ability of some popular continuous-time stochastic volatility models for explaining the observed asymmetries. Our results clearly highlight the importance of allowing for multiple latent volatility factors at very fine time scales in order to adequately describe and understand the patterns in the data.

Journal of Econometrics, 2010

This paper proposes a method for constructing a volatility risk premium, or investor risk aversio... more This paper proposes a method for constructing a volatility risk premium, or investor risk aversion, index. The method is intuitive and simple to implement, relying on the sample moments of the recently popularized model-free realized and option-implied volatility measures. A small-scale Monte Carlo experiment confirms that the procedure works well in practice. Implementing the procedure with actual S&P500 optionimplied volatilities and high-frequency five-minute-based realized volatilities indicates significant temporal dependencies in the estimated stochastic volatility risk premium, which we in turn relate to a set of macro-finance state variables. We also find that the extracted volatility risk premium helps predict future stock market returns.

Volatility and Time Series Econometrics, 2010

The market's risk neutral probability distribution for the value of an asset on a future date can... more The market's risk neutral probability distribution for the value of an asset on a future date can be extracted from the prices of a set of options that mature on that date, but two key technical problems arise. In order to obtain a full well-behaved density, the option market prices must be smoothed and interpolated, and some way must be found to complete the tails beyond the range spanned by the available options. This paper develops an approach that solves both problems, with a combination of smoothing techniques from the literature modified to take account of the market's bid-ask spread, and a new method of completing the density with tails drawn from a Generalized Extreme Value distribution. We extract twelve years of daily risk neutral densities from S&P 500 index options and find that they are quite different from the lognormal densities assumed in the Black-Scholes framework, and that their shapes change in a regular way as the underlying index moves. Our approach is quite general and has the potential to reveal valuable insights about how information and risk preferences are incorporated into prices in many financial markets.

A rapidly growing literature has documented important improvements in volatility measurement and ... more A rapidly growing literature has documented important improvements in volatility measurement and forecasting performance through the use of realized volatilities constructed from highfrequency returns coupled with relatively simple reduced-form time series modeling procedures. Building on recent theoretical results from Barndorff-Nielsen and Shephard (2003c,d) for related bipower variation measures involving the sum of high-frequency absolute returns, the present paper provides a practical framework for non-parametrically measuring the jump component in realized volatility measurements. Exploiting these ideas for a decade of high-frequency five-minute returns for the DM/$ exchange rate, the S&P500 market index, and the 30-year U.S. Treasury bond yield, we find the jump component of the price process to be distinctly less persistent than the continuous sample path component. Explicitly including the jump measure as an additional explanatory variable in an easy-toimplement reduced form model for realized volatility results in highly significant jump coefficient estimates at the daily, weekly and quarterly forecast horizons. As such, our results hold promise for improved financial asset allocation, risk management, and derivatives pricing, by separate modeling, forecasting and pricing of the continuous and jump components of total return variability. that the conditional variance of many assets is best described by a combination of a smooth and very slowly mean-reverting continuous sample path process, along with a much less persistent jump component.

Journal of Econometrics 52 (1992) 5-59. North-Holland ARCH modeling in finance* A review of the t... more Journal of Econometrics 52 (1992) 5-59. North-Holland ARCH modeling in finance* A review of the theory and empirical evidence Tim Bollerslev Northwestern University, Euanston, IL 60208, USA Щ" Ray Y. Chou Georgia Institute of Technology, Atlanta, GA 30332, USA ...

A rapidly growing literature has documented important improvements in financial return volatility... more A rapidly growing literature has documented important improvements in financial return volatility measurement and forecasting performance through the use of realized variation measures constructed from the summation of high-frequency squared returns coupled with relatively simple reduced-form time series modeling procedures. Building on recent theoretical results in Barndorff-Nielsen and Shephard (2004a, 2005) for related bi-power variation measures involving the sum of adjacent absolute high-frequency returns, the present paper provides a practical and robust framework for non-parametrically measuring and assessing the statistical significance of the jump component in asset return volatility. Exploiting these ideas for a decade of high-frequency five-minute returns for the DM/$ exchange rate, the S&P500 market index, and the 30-year U.S. Treasury bond yield, we find the jump component of the price process to be distinctly less persistent than the continuous sample path variation process. Also, the occurrences of many of the most significant jumps appear to be directly associated with specific macroeconomic news announcements. Moreover, including the time series of significant jumps along with the measurements of the corresponding continuous sample path variability in an easy-to-implement reduced form HAR-RV-CJ volatility forecasting model, we find that almost all of the predictability in the daily, weekly and monthly volatilities come from the lagged continuous variation process. 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 total return variation process.

Ssrn Electronic Journal, 2000

Page 1. HIGH-FREQUENCY DATA, FREQUENCY DOMAIN INFERENCE, AND VOLATILITY FORECASTING Tim Bollersle... more Page 1. HIGH-FREQUENCY DATA, FREQUENCY DOMAIN INFERENCE, AND VOLATILITY FORECASTING Tim Bollerslev and Jonathan H. Wright* Abstract—Although it is clear that the volatility of asset returns is serially correlated ...

Current industry practice largely follows one of two restrictive approaches to market risk manage... more Current industry practice largely follows one of two restrictive approaches to market risk management: historical simulation or RiskMetrics. In contrast, exploiting recent developments in financial econometrics we propose flexible methods which are likely to produce more accurate assessments of market risk. Clearly, the demands of real-world risk management in financial institutions -in particular, real-time risk tracking in very high-dimensional situations -impose strict limits on model complexity. Hence we stress parsimonious models that are easily estimated, and we discuss a variety of practical approaches for high-dimensional covariance matrix modeling, along with what we see as some of the pitfalls and problems in current practice. In so doing we hope to encourage further dialog between the academic and practitioner communities and to stimulate the development of improved market risk management technologies that draw on the best of both worlds. _________________ * This paper is prepared for Mark Carey and René Stulz (eds.), Risks of Financial Institutions, University of Chicago Press for NBER. For helpful comments we would like to thank

Journal of Econometrics, 2010

The Hansen-Lunde (HL) research program is generally first-rate, displaying a rare blend of theore... more The Hansen-Lunde (HL) research program is generally first-rate, displaying a rare blend of theoretical prowess and applied sense. The present paper is no exception. In a major theoretical advance, HL allow for correlation between microstructure (MS) noise and latent price. (I prefer "latent price" to terms such as "efficient price" or "true price," which carry lots of excess baggage.) In a parallel major substantive advance, HL provide a pioneering empirical investigation of the nature of the correlation between MS noise and latent price, documenting a negative correlation at high frequencies. My admiration of the paper hinges on the contributions noted above and is indeed most genuine. Nevertheless, much of what follows is rather critical of the extant literature, including certain key elements of the HL approach.

This paper provides a simple unified framework for assessing the empirical linkages between retur... more This paper provides a simple unified framework for assessing the empirical linkages between returns and realized and implied volatilities. First, we show that whereas the volatility feedback effect as measured by the sign of the correlation between contemporaneous return and realized volatility depends importantly on the underlying structural model parameters, the correlation between return and implied volatility is unambiguously positive for all reasonable parameter configurations. Second, the lagged return-volatility asymmetry, or the leverage effect, is always stronger for implied than realized volatility. Third, implied volatilities generally provide downward biased forecasts of subsequent realized volatilities. Our results help explain previous findings reported in the extant empirical literature, and is further corroborated by new estimation results for a sample of monthly returns and implied and realized volatilities for the aggregate S&P market index.

New York University Leonard N Stern School Finance Department Working Paper Seires, 1999

Using high-frequency data on Deutschemark and Yen returns against the dollar, we construct model-... more Using high-frequency data on Deutschemark and Yen returns against the dollar, we construct model-free estimates of daily exchange rate volatility and correlation, covering an entire decade. In addition to being model-free, our estimates are also approximately free of measurement error under general conditions, which we delineate. Hence, for all practical purposes, we can treat the exchange rate volatilities and correlations as observed rather than latent. We do so, and we characterize their joint distribution, both unconditionally and conditionally. Noteworthy results include a simple normality-inducing volatility transformation, high contemporaneous correlation across volatilities, high correlation between correlation and volatilities, pronounced and highly persistent temporal variation in both volatilities and correlation, clear evidence of long-memory dynamics in both volatilities and correlation, and remarkably precise scaling laws under temporal aggregation.

This paper bridges the gap between traditional ARCH modelling and recent advances on realized vol... more This paper bridges the gap between traditional ARCH modelling and recent advances on realized volatilities. Based on a ten-year sample of five-minute returns for the ECU basket currencies versus the US dollar, we find that the realized volatilities constructed from the summation of the high-frequency intraday squared returns conditional on the lagged squared daily returns are approximately Inverse Gaussian (IG) distributed, while the distribution of the daily returns standardized by their realized volatilities is approximately normal. Moreover, the implied daily GARCH model with Normal Inverse Gaussian (NIG) errors estimated for the ECU returns results in very accurate out-of-sample predictions for the three years of actual daily Euro/US dollar exchange rates.

Nber Working Papers, May 17, 2012

We examine the relationship between volatility and past and future returns in highfrequency equit... more We examine the relationship between volatility and past and future returns in highfrequency equity market data. Consistent with a prolonged "leverage" effect, we find the correlations between absolute high-frequency returns and current and past high-frequency returns to be significantly negative for several days, while the reverse cross-correlations between absolute returns and future returns are generally negligible. Based on a simple aggregation formula, we demonstrate how the high-frequency data may similarly be used in more effectively assessing volatility asymmetries over longer daily return horizons. Motivated by the striking cross-correlation patterns uncovered in the high-frequency data, we investigate the ability of some popular continuous-time stochastic volatility models for explaining the observed asymmetries. Our results clearly highlight the importance of allowing for multiple latent volatility factors at very fine time scales in order to adequately describe and understand the patterns in the data.

Journal of Econometrics, 2010

This paper proposes a method for constructing a volatility risk premium, or investor risk aversio... more This paper proposes a method for constructing a volatility risk premium, or investor risk aversion, index. The method is intuitive and simple to implement, relying on the sample moments of the recently popularized model-free realized and option-implied volatility measures. A small-scale Monte Carlo experiment confirms that the procedure works well in practice. Implementing the procedure with actual S&P500 optionimplied volatilities and high-frequency five-minute-based realized volatilities indicates significant temporal dependencies in the estimated stochastic volatility risk premium, which we in turn relate to a set of macro-finance state variables. We also find that the extracted volatility risk premium helps predict future stock market returns.

Volatility and Time Series Econometrics, 2010

The market's risk neutral probability distribution for the value of an asset on a future date can... more The market's risk neutral probability distribution for the value of an asset on a future date can be extracted from the prices of a set of options that mature on that date, but two key technical problems arise. In order to obtain a full well-behaved density, the option market prices must be smoothed and interpolated, and some way must be found to complete the tails beyond the range spanned by the available options. This paper develops an approach that solves both problems, with a combination of smoothing techniques from the literature modified to take account of the market's bid-ask spread, and a new method of completing the density with tails drawn from a Generalized Extreme Value distribution. We extract twelve years of daily risk neutral densities from S&P 500 index options and find that they are quite different from the lognormal densities assumed in the Black-Scholes framework, and that their shapes change in a regular way as the underlying index moves. Our approach is quite general and has the potential to reveal valuable insights about how information and risk preferences are incorporated into prices in many financial markets.

A rapidly growing literature has documented important improvements in volatility measurement and ... more A rapidly growing literature has documented important improvements in volatility measurement and forecasting performance through the use of realized volatilities constructed from highfrequency returns coupled with relatively simple reduced-form time series modeling procedures. Building on recent theoretical results from Barndorff-Nielsen and Shephard (2003c,d) for related bipower variation measures involving the sum of high-frequency absolute returns, the present paper provides a practical framework for non-parametrically measuring the jump component in realized volatility measurements. Exploiting these ideas for a decade of high-frequency five-minute returns for the DM/$ exchange rate, the S&P500 market index, and the 30-year U.S. Treasury bond yield, we find the jump component of the price process to be distinctly less persistent than the continuous sample path component. Explicitly including the jump measure as an additional explanatory variable in an easy-toimplement reduced form model for realized volatility results in highly significant jump coefficient estimates at the daily, weekly and quarterly forecast horizons. As such, our results hold promise for improved financial asset allocation, risk management, and derivatives pricing, by separate modeling, forecasting and pricing of the continuous and jump components of total return variability. that the conditional variance of many assets is best described by a combination of a smooth and very slowly mean-reverting continuous sample path process, along with a much less persistent jump component.

Journal of Econometrics 52 (1992) 5-59. North-Holland ARCH modeling in finance* A review of the t... more Journal of Econometrics 52 (1992) 5-59. North-Holland ARCH modeling in finance* A review of the theory and empirical evidence Tim Bollerslev Northwestern University, Euanston, IL 60208, USA Щ" Ray Y. Chou Georgia Institute of Technology, Atlanta, GA 30332, USA ...