ABSTRACT This paper extends the class of stochastic volatility diffusions for asset returns to encompass Poisson jumps of time‐varying intensity. We find that any reasonably descriptive continuous‐time model for equity‐index returns must allow for discrete jumps as well as stochastic volatility with a pronounced negative relationship between return and volatility innovations. We also find that the dominant empirical characteristics of the return process appear to be priced by the option market. Our analysis indicates a general correspondence between the evidence extracted from daily equity‐index returns and the stylized features of the corresponding options market prices.

We study the dynamic relation between market risks and risk premia using time series of index option surfaces. We find that priced left tail risk cannot be spanned by market volatility (and its components) and introduce a new tail factor. This tail factor has no incremental predictive power for future volatility and jump risks, beyond current and past volatility, but is critical in predicting future market equity and variance risk premia. Our findings suggest a wide wedge between the dynamics of market risks and their compensation, which typically displays a far more persistent reaction following market crises.

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.

This paper provides a detailed characterization of the volatility in the deutsche mark–dollar foreign exchange market using an annual sample of five‐minute returns. The approach captures the intraday activity patterns, the macroeconomic announcements, and the volatility persistence (ARCH) known from daily returns. The different features are separately quantified and shown to account for a substantial fraction of return variability, both at the intraday and daily level. The implications of the results for the interpretation of the fundamental “driving forces” behind the volatility process is also discussed.

Recent empirical evidence suggests that the long-run dependence in financial market volatility is best characterized by a slowly mean-reverting fractionally integrated process. At the same time, much shorter-lived volatility dependencies are typically observed with high-frequency intradaily returns.

We develop a new parametric estimation procedure for option panels observed with error. We exploit asymptotic approximations assuming an ever increasing set of option prices in the moneyness (cross-sectional) dimension, but with a fixed time span. We develop consistent estimators for the parameters and the dynamic realization of the state vector governing the option price dynamics. The estimators converge stably to a mixed-Gaussian law and we develop feasible estimators for the limiting variance. We also provide semiparametric tests for the option price dynamics based on the distance between the spot volatility extracted from the options and one constructed nonparametrically from high-frequency data on the underlying asset. Furthermore, we develop new tests for the day-by-day model fit over specific regions of the volatility surface and for the stability of the risk-neutral dynamics over time. A comprehensive Monte Carlo study indicates that the inference procedures work well in empirically realistic settings. In an empirical application to S&P 500 index options, guided by the new diagnostic tests, we extend existing asset pricing models by allowing for a flexible dynamic relation between volatility and priced jump tail risk. Importantly, we document that the priced jump tail risk typically responds in a more pronounced and persistent manner than volatility to large negative market shocks.

A Framework for Exploring the Macroeconomic Determinants of Systematic Risk by Torben G. Andersen, Tim Bollerslev, Francis X. Diebold and Jin Wu. Published in volume 95, issue 2, pages 398-404 of American Economic Review, May 2005

Some fundamental questions regarding equity-index return dynamics are difficult to address due to the latent character of spot volatility. We exploit tick-by-tick option quotes to compute a novel “Corridor Volatility” index which may serve as an observable proxy for short-term volatility. Exploiting this index, we find that equity-index volatility jumps are common, symmetrically distributed, and cojump with the underlying returns. Moreover, the return-volatility asymmetry is more pronounced than is generally recognized and is in force for both diffusive and jump innovations in volatility. Finally, the index performs admirably during turbulent market conditions, constituting a useful real-time gauge of market stress.

ABSTRACT We study short‐maturity (“weekly”) S&P 500 index options, which provide a direct way to analyze volatility and jump risks. Unlike longer‐dated options, they are largely insensitive to the risk of intertemporal shifts in the economic environment. Adopting a novel seminonparametric approach, we uncover variation in the negative jump tail risk, which is not spanned by market volatility and helps predict future equity returns. As such, our approach allows for easy identification of periods of heightened concerns about negative tail events that are not always “signaled” by the level of market volatility and elude standard asset pricing models.

ABSTRACT Variance‐ratio tests are routinely employed to assess the variation in return volatility over time and across markets. However, such tests are not statistically robust and can be seriously misleading within a high‐frequency context. We develop improved inference procedures using a Fourier Flexible Form regression framework. The practical significance is illustrated through tests for changes in the FX intraday volatility pattern following the removal of trading restrictions in Tokyo. Contrary to earlier evidence, we find nodiscernible changes outside of the Tokyo lunch period. We ascribe the difference to the fragile finite‐sample inference of conventional variance‐ratio procedures and a single outlier.