arXiv subjects

Peter Reinhard Hansen

Publications and source records attributed to Peter Reinhard Hansen.

29 records · Page 2Linked to original sources

arXiv2025

A Multivariate Realized GARCH Model

We propose a novel class of multivariate GARCH models that incorporate realized measures of volatility and correlations. The key innovation is an unconstrained vector parametrization of the conditional correlation matrix, which enables the use of factor models for correlations. This approach elegantly addresses the main challenge faced by multivariate GARCH models in high-dimensional settings. As an illustration, we explore block correlation matrices that naturally simplify to linear factor models for the conditional correlations. The model is applied to the returns of nine assets, and its in-sample and out-of-sample performance compares favorably against several popular benchmarks.

econ.EM↗

arXiv2024

Cluster GARCH

We introduce a novel multivariate GARCH model with flexible convolution-t distributions that is applicable in high-dimensional systems. The model is called Cluster GARCH because it can accommodate cluster structures in the conditional correlation matrix and in the tail dependencies. The expressions for the log-likelihood function and its derivatives are tractable, and the latter facilitate a score-drive model for the dynamic correlation structure. We apply the Cluster GARCH model to daily returns for 100 assets and find it outperforms existing models, both in-sample and out-of-sample. Moreover, the convolution-t distribution provides a better empirical performance than the conventional multivariate t-distribution.

econ.EM↗

arXiv2024

Convolution-t Distributions

We introduce a new class of multivariate heavy-tailed distributions that are convolutions of heterogeneous multivariate t-distributions. Unlike commonly used heavy-tailed distributions, the multivariate convolution-t distributions embody cluster structures with flexible nonlinear dependencies and heterogeneous marginal distributions. Importantly, convolution-t distributions have simple density functions that facilitate estimation and likelihood-based inference. The characteristic features of convolution-t distributions are found to be important in an empirical analysis of realized volatility measures and help identify their underlying factor structure.

econ.EM↗

arXiv2023

Characterizing Correlation Matrices that Admit a Clustered Factor Representation

The Clustered Factor (CF) model induces a block structure on the correlation matrix and is commonly used to parameterize correlation matrices. Our results reveal that the CF model imposes superfluous restrictions on the correlation matrix. This can be avoided by a different parametrization, involving the logarithmic transformation of the block correlation matrix.

econ.EM↗

arXiv2022

A New Method for Generating Random Correlation Matrices

We propose a new method for generating random correlation matrices that makes it simple to control both location and dispersion. The method is based on a vector parameterization, gamma = g(C), which maps any distribution on R^d, d = n(n-1)/2 to a distribution on the space of non-singular nxn correlation matrices. Correlation matrices with certain properties, such as being well-conditioned, having block structures, and having strictly positive elements, are simple to generate. We compare the new method with existing methods.

econ.EM↗

arXiv2022

Option Pricing with State-dependent Pricing Kernel

We introduce a new volatility model for option pricing that combines Markov switching with the Realized GARCH framework. This leads to a novel pricing kernel with a state-dependent variance risk premium and a pricing formula for European options, which is derived with an analytical approximation method. We apply the Markov switching Realized GARCH model to S&P 500 index options from 1990 to 2019 and find that investors' aversion to volatility-specific risk is time-varying. The proposed framework outperforms competing models and reduces (in-sample and out-of-sample) option pricing errors by 15% or more.

q-fin.PR↗

arXiv2022

Relative Contagiousness of Emerging Virus Variants: An Analysis of the Alpha, Delta, and Omicron SARS-CoV-2 Variants

We propose a simple dynamic model for estimating the relative contagiousness of two virus variants. Maximum likelihood estimation and inference is conveniently invariant to variation in the total number of cases over the sample period and can be expressed as a logistic regression. We apply the model to Danish SARS-CoV-2 variant data. We estimate the reproduction numbers of Alpha and Delta to be larger than that of the ancestral variant by a factor of 1.51 [CI 95%: 1.50, 1.53] and 3.28 [CI 95%: 3.01, 3.58], respectively. In a predominately vaccinated population, we estimate Omicron to be 3.15 [CI 95%: 2.83, 3.50] times more infectious than Delta. Forecasting the proportion of an emerging virus variant is straight forward and we proceed to show how the effective reproduction number for a new variant can be estimated without contemporary sequencing results. This is useful for assessing the state of the pandemic in real time as we illustrate empirically with the inferred effective reproduction number for the Alpha variant.

econ.EM↗

arXiv2021

Realized GARCH, CBOE VIX, and the Volatility Risk Premium

We show that the Realized GARCH model yields close-form expression for both the Volatility Index (VIX) and the volatility risk premium (VRP). The Realized GARCH model is driven by two shocks, a return shock and a volatility shock, and these are natural state variables in the stochastic discount factor (SDF). The volatility shock endows the exponentially affine SDF with a compensation for volatility risk. This leads to dissimilar dynamic properties under the physical and risk-neutral measures that can explain time-variation in the VRP. In an empirical application with the S&P 500 returns, the VIX, and the VRP, we find that the Realized GARCH model significantly outperforms conventional GARCH models.

econ.EM↗

arXiv2021

A Canonical Representation of Block Matrices with Applications to Covariance and Correlation Matrices

We obtain a canonical representation for block matrices. The representation facilitates simple computation of the determinant, the matrix inverse, and other powers of a block matrix, as well as the matrix logarithm and the matrix exponential. These results are particularly useful for block covariance and block correlation matrices, where evaluation of the Gaussian log-likelihood and estimation are greatly simplified. We illustrate this with an empirical application using a large panel of daily asset returns. Moreover, the representation paves new ways to regularizing large covariance/correlation matrices, test block structures in matrices, and estimate regressions with many variables.

econ.EM↗

arXiv2021

Periodicity in Cryptocurrency Volatility and Liquidity

We study recurrent patterns in volatility and volume for major cryptocurrencies, Bitcoin and Ether, using data from two centralized exchanges (Coinbase Pro and Binance) and a decentralized exchange (Uniswap V2). We find systematic patterns in both volatility and volume across day-of-the-week, hour-of-the-day, and within the hour. These patterns have grown stronger over the years and can be related to algorithmic trading and funding times in futures markets. We also document that price formation mainly takes place on the centralized exchanges while price adjustments on the decentralized exchanges can be sluggish.

q-fin.TR↗

arXiv2020

A New Parametrization of Correlation Matrices

We introduce a novel parametrization of the correlation matrix. The reparametrization facilitates modeling of correlation and covariance matrices by an unrestricted vector, where positive definiteness is an innate property. This parametrization can be viewed as a generalization of Fisther's Z-transformation to higher dimensions and has a wide range of potential applications. An algorithm for reconstructing the unique n x n correlation matrix from any d-dimensional vector (with d = n(n-1)/2) is provided, and we derive its numerical complexity.

econ.EM↗