Research on continuous-time econometrics and finance

Research on high-frequency econometrics and finance

Research on microstructure frictions

Research on low-frequency asset pricing

Research on nonlinear, nonstationary time series

If you are looking for a paper which is not posted here, please do not hesitate to get in touch.

Local Edgeworth expansions (with Roberto Reno') (SSRN draft) 

We derive local (over a small time interval) Edgeworth expansions of the bivariate conditional characteristic function of the level/volatility increments of a Brownian semimartingale. We do so without and with compound Poisson discontinuities (idiosyncratic and joint) in levels and volatility. In a first order expansion, the proposed local approximation to the bivariate Gaussian characteristic function of the level/volatility changes adds skewness through the time-varying correlations between the level/volatility changes and the volatility/volatility-of-volatility changes. In a second-order expansion, the local approximation adds kurtosis through, among other quantities, the volatility-of-volatility and the volatility of the volatility-of-volatility. All discontinuities only affect the second order. We show how Fourier-inversion of the proposed expansion (and recovery of the local conditional density) is intimately related to the differentiability properties of the assumed process. We formalize these properties through the concept of W-differentiability, with W defining the leading Brownian motion.

0DTE option pricing (with Nicola Fusari and Roberto Reno')  (SSRN draft)

Trading in 0-Days-To-Expiry (0DTE) options has grown exponentially over the last few years. After describing this exploding market, we present novel closed-form pricing formulae that accurately capture the 0DTE implied-volatility surface. We use a local-in-time approach, relying on Edgeworth-like expansions of the log-return characteristic function, explicitly suited to price ultra-short-tenor instruments. The expansions provide skewness and kurtosis adjustments which depend on the underlying non-affine return characteristics in closed form. We show significant improvements in pricing and hedging as compared to state-of-the-art models. We conclude by providing suggestive results on nearly instantaneous predictability by estimating 0DTE-based risk premia.

Conditional spectral methods (with Yinan Su)  (SSRN draft)

Journal of Econometrics, forthcoming

We model predictive scale-specific cycles. By employing suitable matrix representations, we express the forecast errors of covariance-stationary multivariate time series in terms of conditionally orthonormal scale-specific basis. The representations yield conditionally orthogonal decompositions of these forecast errors. They also provide decompositions of their variances and betas in terms of scale-specific variances and betas capturing predictive variability and co-variability over cycles of alternative lengths without spillovers across cycles. Making use of the proposed representations within the classical family of time-varying conditional volatility models, we document the role of time-varying volatility forecasts in generating orthogonal predictive scale-specific cycles in returns. We conclude by providing suggestive evidence that the conditional variances of the predictive return cycles may (i) be priced over short-to-medium horizons and (ii) offer economically-relevant trading signals over these same horizons.

Spectral financial econometrics (with Andrea Tamoni)  (paper)

Econometric Theory, 2022, 38, 1175-1220

We survey the literature on spectral regression estimation. We present a cohesive framework designed to model dependence on frequency in the response of economic time series to changes in the explanatory variables. Our emphasis is on the statistical structure and on the economic interpretation of time-domain specifications needed to obtain horizon effects over frequencies, over scales, or upon aggregation. To this end, we articulate our discussion around the role played by lead-lag effects in the explanatory variables as drivers of differential information across horizons. We provide perspectives for future work throughout.

Spectral factor models (with Shomesh Chaudhuri, Andrew W. Lo and Andrea Tamoni) (paper)

Journal of Financial Economics, 2021, 142, 214-238.

We represent risk factors as sums of orthogonal components capturing fluctuations with cycles of different length. The representation leads to novel spectral factor models in which systematic risk is allowed—without being forced—to vary across frequencies. Frequency-specific systematic risk is captured by a notion of spectral beta. We show that traditional factor models restrict the spectral betas to be constant across frequencies. The restriction can hide horizon-specific pricing effects that spectral factor models are designed to reveal. We illustrate how the methods may lead to economically meaningful dimensionality reduction in the factor space.

Structural stochastic volatility (with Nicola Fusari and Roberto Reno') (SSRN draft)

A novel closed-form pricing formula for short-maturity options is employed to jointly identify equity characteristics (spot volatility, spot leverage, and spot volatility of volatility) which have been the focus of large, but separate, strands of the literature. Interpreting equity as a call option on asset values, all equity characteristics should depend on structural sources of risk, such as the variance of the firm’s assets and the extent of the firm’s financial leverage. We confirm the implications of theory with data, thereby providing support for relations (like the link between spot leverage and the firm’s financial leverage) broadly considered empirically ambiguous.

Return predictability with endogenous growth (with Lorenzo Bretscher and Andrea Tamoni) (paper)

Journal of Financial Economics, 2023, 150.

The component of the volatility of total factor productivity (TFP) that is orthogonal to the dividend price ratio is shown to have long-run predictive ability for market returns. This finding implies that TFP volatility should also predict real cash flows and/or real interest rates: it is found to mainly predict real cash flows through inflation. A model with endogenous growth, Epstein-Zin preferences and price rigidities reconciles both TFP volatility-driven long-run predictability and its real implications. Within the model, we justify the cross-sectional pricing of TFP volatility risk in alternative asset classes as well as the similar (to that of TFP volatility) predictive ability of a suitable low-frequency notion of market volatility.

Systematic staleness (with Davide Pirino and Roberto Reno') (paper)

Journal of Econometrics, 2024, 238.

Asset prices are stale. We define a measure of systematic (market-wide) staleness as the percentage of small price adjustments over multiple assets. A notion of idiosyncratic (asset-specific) staleness is also established. For both systematic and idiosyncratic staleness, we provide a limit theory based on joint asymptotics relying on increasingly-frequent observations over a fixed time span and an increasing number of assets. Using systematic and idiosyncratic staleness as moment conditions, we introduce novel structural estimates of systematic and idiosyncratic measures of liquidity obtained from transaction prices only. The economic signal contained in the latter is assessed by virtue of suitable metrics.

Beta in the tails (with Roberto Reno') (paper)

Journal of Econometrics, 2022, 227, 134-150

Do hedge funds hedge? In negative states of the world, often not as much as they should. For several styles, we report larger market betas when market returns are low (i.e., “beta in the tails”). We justify this finding through a combination of negative-mean jumps in the market returns and large market jump betas: when moving to the left tail of the market return distribution jump dynamics dominate continuous dynamics and the overall systematic risk of the fund is driven by the higher systematic risk associated with return discontinuities. Methodologically, the separation of continuous and discontinuous dynamics is conducted by exploiting the informational content of the high-order infinitesimal cross-moments of hedge-fund and market returns.