We introduce a new class of semiparametric dynamic autoregressive models for the Amihud illiquidity measure, which captures both the long-run trend in the illiquidity series with a nonparametric component and the short-run dynamics with an autoregressive component. We develop a generalized method of moments (GMM) estimator based on conditional moment restrictions and an efficient semiparametric maximum likelihood (ML) estimator based on an i.i.d. assumption. We derive large sample properties for our estimators. Finally, we demonstrate the model fitting performance and its empirical relevance on an application. We investigate how the different components of the illiquidity process obtained from our model relate to the stock market risk premium using data on the S&P 500 stock market index.
Asymmetric short-rate model without lower bound (with F. Vrins), Quantitative Finance (2023)
We propose a new short-rate process which appropriately captures the salient features of the negative interest rate environment. The model combines the advantages of the Vasicek and Cox-Ingersoll-Ross (CIR) dynamics: it is flexible, tractable and displays positive skewness without imposing a strict lower bound. In addition, a novel calibration procedure is introduced which focuses on minimizing the Jensen–Shannon (JS) divergence between the model- and market-implied forward rate densities rather than focusing on the minimization of price or volatility discrepancies. A thorough empirical analysis based on cap market quotes shows that our model displays superior performance compared to the Vasicek and CIR models regardless of the calibration method. Our proposed calibration procedure based on the JS divergence better captures the entire forward rate distribution compared to competing approaches while maintaining a good fit in terms of pricing and implied volatility errors.
Dynamic portfolio selection with sector-specific regularization (with C.M. Hafner), Econometrics and Statistics (2022)
A new algorithm is proposed for dynamic portfolio selection that takes a sector-specific structure into account. Regularizations with respect to within- and between-sector variations of portfolio weights, as well as sparsity and transaction cost controls, are considered. The model includes two special cases as benchmarks: a dynamic conditional correlation model with shrinkage estimation of the unconditional covariance matrix, and the equally weighted portfolio. An algorithm is proposed for the estimation of the model parameters and the calibration of the penalty terms based on cross-validation. In an empirical study, it is shown that the within-sector regularization contributes significantly to the reduction of out-of-sample volatility of portfolio returns. The model improves the out-of-sample performance of both the DCC with nonlinear shrinkage and the equally-weighted portfolio.
A dynamic conditional score model for the log correlation matrix (with C.M. Hafner), Journal of Econometrics (2021)
This paper proposes a new model for the dynamics of correlation matrices, where the dynamics are driven by the likelihood score with respect to the matrix logarithm of the correlation matrix. In analogy to the exponential GARCH model for volatility, this transformation ensures that the correlation matrices remain positive definite, even in high dimensions. For the conditional distribution of returns, we assume a student-t copula to explain the dependence structure and univariate student-t for the marginals with potentially different degrees of freedom. The separation into volatility and correlation parts allows for a two-step estimation, which facilitates estimation in high dimensions. We derive estimation theory for one-step and two-step estimation. In an application to a set of six asset indices including financial and alternative assets we show that the model performs well in terms of diagnostics, specification tests, and out-of-sample forecasting.
Working Papers
Modeling prices from speculative markets: bursting bubbles or deflating balloons? (with C.M. Hafner and A.C. Harvey), Cambridge Working Papers in Economics (2025)
Speculative markets may be characterized by sharp falls after a slow build up. Sometimes the converse happens. We suggest a number of mechanisms that are able to produce this kind of behaviour and we demonstrate their plausibility by simulation. The models are then fitted to daily data on Bitcoin. In constructing these models we show that it is essential to take account of volatility and non-normality. We also investigate the possibility of a dynamic tail index. The conclusion, at least for Bitcoin, is that speculative markets are more likely to behave like balloons than bubbles. In other words, there is rapid inflation followed by a slow decline.
The permanent and temporary effects of stock splits on liquidity in a dynamic semiparametric model (with C.M. Hafner and O.B. Linton), Cambridge Working Papers in Economics (2024)
We develop a dynamic framework to detect the occurrence of permanent and transitory breaks in the illiquidity process. We propose various tests that can be applied separately to individual events and can be aggregated across different events over time for a given firm or across different firms. We use this methodology to study the impact of forward and reverse stock splits on the illiquidity dynamics of the S&P 500, S&P 400 and S&P 600 index stock constituents. Our empirical results show that stock splits have a positive and significant effect on the permanent component of the illiquidity process while a majority of the stocks engaging in reverse splits experience an improvement in liquidity conditions.