scholarly journals CHARACTERIZATION OF THE TAIL BEHAVIOR OF A CLASS OF BEKK PROCESSES: A STOCHASTIC RECURRENCE EQUATION APPROACH

2021 ◽  
pp. 1-34
Author(s):  
Muneya Matsui ◽  
Rasmus Søndergaard Pedersen
Keyword(s):  
Stationary Solutions ◽  
Tail Index ◽  
Recurrence Equation ◽  
Multivariate Garch ◽  
Tail Behavior ◽  
Stochastic Recurrence ◽  
Garch Processes ◽  
Strict Stationarity ◽  
Daily Returns

Abstract We consider conditions for strict stationarity and ergodicity of a class of multivariate BEKK processes $(X_t : t=1,2,\ldots )$ and study the tail behavior of the associated stationary distributions. Specifically, we consider a class of BEKK-ARCH processes where the innovations are assumed to be Gaussian and a finite number of lagged $X_t$ ’s may load into the conditional covariance matrix of $X_t$ . By exploiting that the processes have multivariate stochastic recurrence equation representations, we show the existence of strictly stationary solutions under mild conditions, where only a fractional moment of $X_t$ may be finite. Moreover, we show that each component of the BEKK processes is regularly varying with some tail index. In general, the tail index differs along the components, which contrasts with most of the existing literature on the tail behavior of multivariate GARCH processes. Lastly, in an empirical illustration of our theoretical results, we quantify the model-implied tail index of the daily returns on two cryptocurrencies.

DAY-OF-THE-WEEK EFFECT IN US BIOTECHNOLOGY STOCKS — DO POLICY CHANGES AND ECONOMIC CYCLES MATTER?

2016 ◽  
Vol 11 (02) ◽  
pp. 1650008
Author(s):  
SWARN CHATTERJEE ◽  
AMY HUBBLE
Keyword(s):  
Stock Returns ◽  
Small Firm ◽  
Economic Cycles ◽  
Trading Decisions ◽  
Portfolio Managers ◽  
Small Investors ◽  
Garch Processes ◽  
Day Of The Week ◽  
Firm Effect ◽  
Daily Returns

This study examines the presence of the day-of-the-week effect on daily returns of biotechnology stocks over a 16-year period from January 2002 to December 2015. Using daily returns from the NASDAQ Biotechnology Index (NBI), we find that the stock returns were the lowest on Mondays, and compared to the Mondays the stock returns were significantly higher on Wednesdays, Thursdays, and Fridays. The day-of-the-week effect on returns of biotechnology stocks remained significant even after controlling for the Fama–French and Carhart factors. Moreover, the results from using the asymmetric generalized autoregressive conditional heteroskedastic (GARCH) processes reveal that momentum and small-firm effect were positively associated with the market risk-adjusted returns of the biotechnology stocks during this period. The findings of our study suggest that active portfolio managers need to consider the day of the week, momentum, and small-firm effect when making trading decisions for biotechnology stocks. Implications for portfolio managers, small investors, scholars, and policymakers are included.

scholarly journals Functional ARCH and GARCH Models: A Yule-Walker Approach

2020 ◽  
Author(s):  
Sebastian Kühnert
Keyword(s):  
Financial Time Series ◽  
Sufficient Conditions ◽  
Dimensional Subspace ◽  
Stationary Solutions ◽  
Finite Dimensional Subspace ◽  
Estimation Errors ◽  
Linear Processes ◽  
Finite Dimensional ◽  
Garch Processes ◽  
Asymptotic Upper Bound

Conditional heteroskedastic financial time series are commonly modelled by ARCH and GARCH. ARCH(1) and GARCH processes were recently extended to the function spaces C[0,1] and L2[0,1], their probabilistic features were studied and their parameters were estimated. The projections of the operators on finite-dimensional subspace were estimated, as were the complete operators in GARCH(1,1). An explicit asymptotic upper bound of the estimation errors was stated in ARCH(1). This article provides sufficient conditions for the existence of strictly stationary solutions, weak dependence and finite moments of ARCH and GARCH processes in various Lp[0,1] spaces, C[0,1] and other spaces. In L2[0,1] we deduce explicit asymptotic upper bounds of the estimation errors for the shift term and the complete operators in ARCH and GARCH and for the projections of the operators on a finite-dimensional subspace in ARCH. The operator estimaton is based on Yule-Walker equations. The estimation of the GARCH operators also involves a result concerning the estimation of the operators in invertible, linear processes which is valid beyond the scope of ARCH and GARCH. Through minor modifications, all results in this article regarding functional ARCH and GARCH can be transferred to functional ARMA.

scholarly journals Pricing of Catastrophe Insurance Options Under Immediate Loss Reestimation

2008 ◽  
Vol 45 (03) ◽  
pp. 831-845 ◽  
Author(s):  
Francesca Biagini ◽  
Yuliya Bregman ◽  
Thilo Meyer-Brandis
Keyword(s):  
Fourier Transform ◽  
Option Pricing ◽  
Heavy Tails ◽  
Initial Estimate ◽  
Tail Behavior ◽  
Catastrophe Insurance ◽  
Catastrophe Modeling ◽  
Loss Distributions ◽  
Loss Index

We specify a model for a catastrophe loss index, where the initial estimate of each catastrophe loss is reestimated immediately by a positive martingale starting from the random time of loss occurrence. We consider the pricing of catastrophe insurance options written on the loss index and obtain option pricing formulae by applying Fourier transform techniques. An important advantage is that our methodology works for loss distributions with heavy tails, which is the appropriate tail behavior for catastrophe modeling. We also discuss the case when the reestimation factors are given by positive affine martingales and provide a characterization of positive affine local martingales.

Subsampling Inference for the Autocorrelations of GARCH Processes*

2017 ◽  
Vol 17 (3) ◽  
pp. 495-515 ◽  
Author(s):  
Tucker McElroy ◽  
Agnieszka Jach
Keyword(s):  
Growth Rate ◽  
Asymptotic Distributions ◽  
Higher Moments ◽  
Rate Dependent ◽  
Convergence Results ◽  
Empirical Coverage ◽  
Cross Correlations ◽  
Garch Processes ◽  
Coverage Rates ◽  
Daily Returns

Abstract We provide self-normalization for the sample autocorrelations of power GARCH(p, q) processes whose higher moments might be infinite. To validate the studentization, whose goal is to match the growth rate dependent on the index of regular variation of the process, we substantially extend existing weak-convergence results. Since asymptotic distributions are non-pivotal, we construct subsampling-based confidence intervals for the autocorrelations and cross-correlations, which are shown to have satisfactory empirical coverage rates in a simulation study. The methodology is further applied to daily returns of CAC40 and FTSA100 indices and their squares.

scholarly journals DYNAMIC ASSET CORRELATIONS BASED ON VINES

2018 ◽  
Vol 35 (1) ◽  
pp. 167-197 ◽  
Author(s):  
Benjamin Poignard ◽  
Jean-David Fermanian
Keyword(s):  
Maximum Likelihood ◽  
Partial Correlation ◽  
Asset Returns ◽  
Multivariate Garch ◽  
Conditional Correlation ◽  
Correlation Matrices ◽  
New Family ◽  
Partial Correlations ◽  
Garch Processes ◽  
Quasi Maximum Likelihood

We develop a new method for generating dynamics of conditional correlation matrices of asset returns. These correlation matrices are parameterized by a subset of their partial correlations, whose structure is described by a set of connected trees called “vine”. Partial correlation processes can be specified separately and arbitrarily, providing a new family of very flexible multivariate GARCH processes, called “vine-GARCH” processes. We estimate such models by quasi-maximum likelihood. We compare our models with DCC and GAS-type specifications through simulated experiments and we evaluate their empirical performances.

The Tail Behavior due to the Presence of the Risk Premium in AR-GARCH-in-Mean, GARCH-AR, and Double-Autoregressive-in-Mean Models*

2020 ◽  
Author(s):  
Christian M Dahl ◽  
Emma M Iglesias
Keyword(s):  
Simulation Study ◽  
Risk Premium ◽  
Tail Index ◽  
Parametric Models ◽  
Ar Model ◽  
Behavior Changes ◽  
Tail Behavior ◽  
Strong Stationarity ◽  
The Mean ◽  
Ar Process

Abstract We extend the results in Borkovec (2000), Basrak, David, and Mikosch (2002a), Lange (2011), and Francq and Zakoïan (2015) by describing the tail behavior when a risk premium component is added in the mean equation of different conditional heteroskedastic processes. We study three types of parametric models: the traditional generalized autoregressive conditional heteroskedastic (GARCH)-M model, the double autoregressive (AR) model with risk premium, and the GARCH-AR model. We find that if an AR process is introduced in the mean equation of a traditional GARCH-M process, the tail behavior is the same as if it is not introduced. However, if we add a risk premium component to the double AR model, then the tail behavior changes with respect to the GARCH-M. The GARCH-AR model also has a different tail index than the traditional AR-GARCH model. In a simulation study, we show that larger tail indexes are associated with the traditional GARCH-M model. When the size of the risk premium component increases, the tail index tends to fall. The only exception to this rule occurs in the double AR model when the risk premium depends on log-volatility. Parameter configurations where the strong stationarity condition of the risk premium models fails are also illustrated and discussed.

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