Price and volatility co-jumps (with Roberto Reno') (paper)

Journal of Financial Economics, 2016, 119, 107-146

The nature of the dependence between discontinuities in prices and contemporaneous discontinuities in volatility (co-jumps) has been reported by many as being elusive, in terms of sign, magnitude, and statistical significance. Using a novel identification strategy in continuous time relying on trade-level information for spot variance estimation, as well as infinitesimal cross-moments , we document that a sizeable proportion of discontinuous changes in prices are associated with strongly anti-correlated, contemporaneous, discontinuous changes in volatility. Assuming a possibly non-monotonic pricing kernel, we illustrate the equilibrium implications of price and volatility co-jumps for return and variance risk premia.

Time-varying leverage effects (with Roberto Reno') (paper)

Journal of Econometrics, 2012, 169, 94-113

Vast empirical evidence points to the existence of a negative correlation, named "leverage effect", between shocks to variance and shocks to returns. We provide a nonparametric theory of leverage estimation in the context of a continuous-time stochastic volatility model with jumps in returns, jumps in variance, or both. Leverage is defined as a flexible function of the state of the firm, as summarized by the spot variance level. We show that its point-wise functional estimates have asymptotic properties (in terms of rates of convergence, limiting biases, and limiting variances) which crucially depend on the likelihood of the individual jumps and co-jumps as well as on the features of the jump size distributions. Empirically, we find economically important time-variation in leverage with more negative values associated with higher variance levels.

Nonparametric stochastic volatility (with Roberto Reno') (paper)

Econometric Theory, 2018, 34, 1207-1255

We provide nonparametric methods for stochastic volatility modelling. Our methods allow for the joint evaluation of return and volatility dynamics with nonlinear drift and diffusion functions, nonlinear leverage effects, and jumps in returns and volatility with possibly state-dependent jump intensities. In the first stage, we identify spot volatility by virtue of jump-robust nonparametric estimates. Using observed prices and estimated spot volatilities, the second stage extracts the functions and parameters driving price and volatility dynamics from nonparametric estimates of the bivariate process’ infinitesimal moments. We present a complete asymptotic theory under recurrence, thereby accommodating the persistence properties of volatility in finite samples.

Realized volatility forecasting in the presence of time-varying noise (with Jeff Russell and Chen Yang) (paper)

Journal of Business and Economic Statistics, 2013, 31, 331-345

Observed high-frequency financial prices can be considered as comprising two components, a true price and a market microstructure noise perturbation. It is an empirical regularity, coherent with classical market microstructure theories of price determination, that the second moment of market microstructure noise is time-varying. We study the optimal, from a finite-sample forecast MSE standpoint, frequency selection for realized variance in linear variance forecasting models with time-varying market microstructure noise. We show that the resulting sampling frequencies are generally considerably lower than those that would be optimally chosen when time-variation in the second moment of the noise is unaccounted for. These optimal, lower frequencies have the potential to translate into considerable out-of-sample MSE gains. When forecasting using high-frequency variance estimates, we recommend treating the relevant frequency as a parameter and evaluating it jointly with the parameters of the forecasting model. The proposed joint solution is robust to the features of the true price formation mechanism and generally applicable to a variety of forecasting models and high-frequency variance estimators, including those for which the typical choice variable is a smoothing parameter, rather than a frequency.

Realized volatility forecasting and option pricing (with Jeff Russell and Chen Yang) (paper)

Journal of Econometrics, 2008, 147, 34-46

A growing literature advocates the use of microstructure noise-contaminated high-frequency data for the purpose of volatility estimation. This paper evaluates and compares the quality of several recently-proposed estimators in the context of a relevant economic metric, i.e., profits from option pricing and trading. Using forecasts obtained by virtue of alternative volatility estimates, agents price short-term options on the S&P 500 index before trading with each other at average prices. The agents' average profits and the Sharpe ratios of the profits constitute the criteria used to evaluate alternative volatility estimates and the corresponding forecasts. For our data, we find that estimators with superior finite sample mean-squared-error properties generate higher average profits and higher Sharpe ratios, in general. We confirm that, even from a forecasting standpoint, there is scope for optimizing the finite sample properties of alternative volatility estimators as advocated by Bandi and Russell (2005, 2008b) in recent work.

Market microstructure noise, integrated variance estimators, and the accuracy of asymptotic approximations (with Jeff Russell) (paper)

Journal of Econometrics, 2011, 160, 145-159

A growing literature has advocated consistent kernel estimation of integrated variance in the presence of financial market microstructure noise. We find that, for realistic sample sizes encountered in practice, the asymptotic results derived for these estimators may provide unsatisfactory representations of their finite sample properties. In addition, the existing asymptotic results might not offer sufficient guidance for practical implementations. We show how to optimize the finite sample properties of kernel-based integrated variance estimators. Empirically, we find that their sub-optimal implementation can, in some cases, lead to little or no finite sample gains when compared to the classical realized variance estimator. Significant statistical and economic gains can, however, be recovered by using our proposed finite sample methods.

Using high-frequency data in dynamic portfolio choice (with Jeff Russell and Julia Zhu) (paper)

Econometric Reviews, 2008, 27, 163-198

This paper evaluates the economic benefit of methods that have been suggested to optimally sample (in an MSE sense) high-frequency return data for the purpose of realized variance/covariance estimation in the presence of market microstructure noise (Bandi and Russell, 2004, 2005a). We compare certainty equivalents derived from volatility-timing trading strategies relying on optimally-sampled realized variances and covariances, on realized variances and covariances obtained by sampling every 5 minutes, and on realized variances and covariances obtained by sampling every 15 minutes. In our sample, we show that a risk-averse investor who is given the option of choosing variance/covariance forecasts derived from MSE-based optimal sampling methods versus forecasts obtained from 5- and 15-minute intervals (as generally proposed in the literature) would be willing to pay up to about 80 basis points per year to achieve the level of utility that is guaranteed by optimal sampling. We find that the gains yielded by optimal sampling are economically large, statistically significant, and robust to realistic transaction costs.

Separating microstructure noise from volatility (with Jeff Russell) (paper)

Journal of Financial Economics, 2006, 79, 655-692

There are two variance components embedded in the returns constructed using high frequency asset prices: the time-varying variance of the unobservable efficient returns that would prevail in a frictionless economy and the variance of the equally unobservable microstructure noise. Using sample moments of high frequency return data recorded at different frequencies, we provide a simple and robust technique to identify both variance components. In the context of a volatility-timing trading strategy, we show that careful (optimal) separation of the two volatility components of the observed stock returns yields substantial utility gains.

Microstructure noise, realized variance, and optimal sampling (with Jeff Russell) (paper)

Review of Economic Studies, 2008, 75, 339-369, lead article

A recent and extensive literature has pioneered the summing of squared observed intradaily returns, "realized variance," to estimate the daily integrated variance of financial asset prices, a traditional object of economic interest. We show that, in the presence of market microstructure noise, realized variance does not identify the daily integrated variance of the frictionless equilibrium price. However, we demonstrate that the noise-induced bias at very high sampling frequencies can be appropriately traded off with the variance reduction obtained by high frequency sampling and derive an MSE optimal sampling theory for the purpose of integrated variance estimation. We show how our theory naturally leads to an identification procedure which allows us to recover the moments of the unobserved noise; this procedure may be useful in other applications. Finally, using the profits obtained by option traders on the basis of alternative variance forecasts as our economic metric, we find that explicit optimization of realized variance's finite sample MSE properties results in accurate forecasts and considerable economic gains.

Comment on "Realized Variance and Microstructure Noise" by Hansen and Lunde (with Jeff Russell) (paper)

Journal of Business and Economic Statistics, 2006, 24, 167-173

Volatility (with Jeff Russell) (paper)

Handbook of Financial Engineering, Elsevier, 2007

We provide a unified framework to understand current advances in two important fields in empirical finance: volatility estimation by virtue of microstructure noise-contaminated asset price data and transaction cost evaluation. In this framework, we review recently-proposed identification procedures relying on the unique possibilities furnished by asset price data sampled at high frequency. While discussing these procedures, we offer our perspective on the existing methods and findings, as well as on directions for future work.