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136
Roughing It Up: Including Jump Components in the Measurement, Modeling and Forecasting of Return Volatility
 REVIEW OF ECONOMICS AND STATISTICS, FORTHCOMING
, 2006
"... A rapidly growing literature has documented important improvements in financial return volatility measurement and forecasting via use of realized variation measures constructed from highfrequency returns coupled with simple modeling procedures. Building on recent theoretical results in BarndorffNi ..."
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Cited by 79 (7 self)
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A rapidly growing literature has documented important improvements in financial return volatility measurement and forecasting via use of realized variation measures constructed from highfrequency returns coupled with simple modeling procedures. Building on recent theoretical results in BarndorffNielsen and Shephard (2004a, 2005) for related bipower variation measures, the present paper provides a practical and robust framework for nonparametrically measuring the jump component in asset return volatility. In an application to the DM/ $ exchange rate, the S&P500 market index, and the 30year 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 nonjump 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 nonjump 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.
A central limit theorem for realised power and bipower variations of continuous semimartingales
 In
, 2006
"... Summary. Consider a semimartingale of the form Yt = Y0 + ∫ t 0 asds + ∫ t σs − dWs, 0 where a is a locally bounded predictable process and σ (the “volatility”) is an adapted right–continuous process with left limits and W is a Brownian motion. We consider the realised bipower variation process V (Y; ..."
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Cited by 38 (17 self)
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Summary. Consider a semimartingale of the form Yt = Y0 + ∫ t 0 asds + ∫ t σs − dWs, 0 where a is a locally bounded predictable process and σ (the “volatility”) is an adapted right–continuous process with left limits and W is a Brownian motion. We consider the realised bipower variation process V (Y; r, s) n t = n r+s
Jumps in financial markets: A new nonparametric test and jump clustering
, 2007
"... This article introduces a new nonparametric test to detect jump arrival times and realized jump sizes in asset prices up to the intraday level. We demonstrate that the likelihood of misclassification of jumps becomes negligible when we use highfrequency returns. Using our test, we examine jump dyn ..."
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Cited by 36 (2 self)
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This article introduces a new nonparametric test to detect jump arrival times and realized jump sizes in asset prices up to the intraday level. We demonstrate that the likelihood of misclassification of jumps becomes negligible when we use highfrequency returns. Using our test, we examine jump dynamics and their distributions in the U.S. equity markets. The results show that individual stock jumps are associated with prescheduled earnings announcements and other companyspecific news events. Additionally, S&P 500 Index jumps are associated with general market news announcements. This suggests different pricing models for individual equity options versus index options. (JEL G12, G22, G14) Financial markets sometimes generate significant discontinuities, socalled jumps, in financial variables. A number of recent empirical and theoretical studies proved the existence of jumps and their substantial impact on financial management, from portfolio and risk management to option and bond pricing
Some Like it Smooth, and Some Like it Rough: Untangling Continuous and Jump Components in Measuring, Modeling, and Forecasting Asset Return Volatility
, 2003
"... 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 th ..."
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Cited by 24 (3 self)
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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 BarndorffNielsen and Shephard (2003c) for related bipower variation measures involving the sum of highfrequency absolute returns, the present paper provides a practical framework for nonparametrically measuring the jump component in the realized volatility measurements. Exploiting these ideas for a decade of highfrequency fiveminute returns for the DM/ $ exchange rate, the S&P500 aggregate market index, and the 30year U.S. Treasury Bond, we find the jump components to be distinctly less persistent than the contribution to the overall return variability originating from the continuous sample path component of the price process. Explicitly including the jump measure as an additional explanatory variable in an easytoimplement reduced form model for the realized volatilities results in highly significant jump coefficient estimates at the daily, weekly and quarterly forecasts 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 the total return variability.
Optimal filtering of jump diffusions: extracting latent states from asset prices”, Working Paper, http://wwwstat.wharton.upenn.edu/ stroud/pubs.html
, 2006
"... This paper provides a methodology for computing optimal filtering distributions in discretely observed continuoustime jumpdiffusion models. Although it has received little attention, the filtering distribution is useful for estimating latent states, forecasting volatility and returns, computing mo ..."
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Cited by 20 (5 self)
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This paper provides a methodology for computing optimal filtering distributions in discretely observed continuoustime jumpdiffusion models. Although it has received little attention, the filtering distribution is useful for estimating latent states, forecasting volatility and returns, computing model diagnostics such as likelihood ratios, and parameter estimation. Our approach combines timediscretization schemes with Monte Carlo methods to compute the optimal filtering distribution. Our approach is very general, applying in multivariate jumpdiffusion models with nonlinear characteristics and even nonanalytic observation equations, such as those that arise when option prices are available. We provide a detailed analysis of the performance of the filter, and analyze four applications: disentangling jumps from stochastic volatility, forecasting realized volatility, likelihood based model comparison, and filtering using both option prices and underlying returns. 2 1
BOOTSTRAPPING REALIZED VOLATILITY
 SUBMITTED TO ECONOMETRICA
"... We propose bootstrap methods for a general class of nonlinear transformations of realized volatility which includes the raw version of realized volatility and its logarithmic transformation as special cases. We consider the i.i.d. bootstrap and the wild bootstrap (WB) and prove their firstorder asy ..."
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Cited by 20 (3 self)
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We propose bootstrap methods for a general class of nonlinear transformations of realized volatility which includes the raw version of realized volatility and its logarithmic transformation as special cases. We consider the i.i.d. bootstrap and the wild bootstrap (WB) and prove their firstorder asymptotic validity under general assumptions on the logprice process that allow for drift and leverage effects. We derive Edgeworth expansions in a simpler model that rules out these effects. The i.i.d. bootstrap provides a secondorder asymptotic refinement when volatility is constant, but not otherwise. The WB yields a secondorder asymptotic refinement under stochastic volatility provided we choose the external random variable used to construct the WB data appropriately. None of these methods provide thirdorder asymptotic refinements. Both methods improve upon the firstorder asymptotic theory in finite samples.
Explaining credit default swap spreads with equity volatility and jump risks of individual firms. Working Paper, Fitch Ratings
, 2005
"... This paper tries to explain the credit default swap (CDS) premium, using a novel approach to identify the volatility and jump risks of individual firms from highfrequency equity prices. Our empirical results suggest that the volatility risk alone predicts 50 percent of the variation in CDS spread l ..."
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Cited by 18 (0 self)
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This paper tries to explain the credit default swap (CDS) premium, using a novel approach to identify the volatility and jump risks of individual firms from highfrequency equity prices. Our empirical results suggest that the volatility risk alone predicts 50 percent of the variation in CDS spread levels, while the jump risk alone forecasts 19 percent. After controlling for credit ratings, macroeconomic conditions, and firms ’ balance sheet information, we can explain 77 percent of the total variation. Moreover, the pricing effects of volatility and jump measures vary consistently across investmentgrade and highyield entities. The estimated nonlinear effects of volatility and jump risks on credit spreads are in line with the implications from a calibrated structural model with stochastic volatility and jumps, although the challenge of simultaneously matching credit spreads and default probabilities remains.
Power Variation & Stochastic Volatility: a review and some new results
, 2003
"... In this paper we review some recent work on limit results on realised power variation, that is sums of powers of absolute increments of various semimartingales. A special case of this analysis is realised variance and its probability limit, quadratic variation. Such quantities often appear in fin ..."
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Cited by 15 (2 self)
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In this paper we review some recent work on limit results on realised power variation, that is sums of powers of absolute increments of various semimartingales. A special case of this analysis is realised variance and its probability limit, quadratic variation. Such quantities often appear in financial econometrics in the analysis of volatility. The paper also provides some new results and discusses open issues.