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.

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

This article introduces a new nonparametric test to detect jump arrival times and realized jump sizes in asset prices up to the intra-day level. We demonstrate that the likelihood of misclassification of jumps becomes negligible when we use high-frequency 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 company-specific 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, so-called 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

A rapidly growing literature has documented important improvements in volatility measurement and forecasting performance through the use of realized volatilities constructed from high-frequency returns coupled with relatively simple reduced form time series modeling procedures. Building on recent theoretical results from Barndorff-Nielsen and Shephard (2003c) for related bi-power 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 the realized volatility measurements. Exploiting these ideas for a decade of high-frequency five-minute returns for the DM/ $ exchange rate, the S&P500 aggregate market index, and the 30-year 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 easy-to-implement 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.

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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 first-order asymptotic validity under general assumptions on the log-price 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 second-order asymptotic refinement when volatility is constant, but not otherwise. The WB yields a second-order asymptotic refinement under stochastic volatility provided we choose the external random variable used to construct the WB data appropriately. None of these methods provide third-order asymptotic refinements. Both methods improve upon the first-order asymptotic theory in finite samples.

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.

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 high-frequency 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 high-yield 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.

This paper provides a methodology for computing optimal filtering distributions in discretely observed continuous-time jump-diffusion 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 time-discretization schemes with Monte Carlo methods to compute the optimal filtering distribution. Our approach is very general, applying in multivariate jump-diffusion models with nonlinear characteristics and even non-analytic 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.