Pitfalls of the Cholesky Decomposition for Forecasting Multivariate Volatility

2015 ◽  
Author(s):  
Moritz Daniel Heiden
Keyword(s):  
Cholesky Decomposition ◽  
Multivariate Volatility

scholarly journals COVID-19 pandemic and the crude oil market risk: hedging options with non-energy financial innovations

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Afees A. Salisu ◽  
Kingsley Obiora
Keyword(s):  
Crude Oil ◽  
Structural Breaks ◽  
Exchange Traded Funds ◽  
Modeling Framework ◽  
Risk Hedging ◽  
Financial Innovations ◽  
Oil Market ◽  
Price Series ◽  
Hedging Effectiveness ◽  
Multivariate Volatility

AbstractThis study examines the hedging effectiveness of financial innovations against crude oil investment risks, both before and during the COVID-19 pandemic. We focus on the non-energy exchange traded funds (ETFs) as proxies for financial innovations given the potential positive correlation between energy variants and crude oil proxies. We employ a multivariate volatility modeling framework that accounts for important statistical features of the non-energy ETFs and oil price series in the computation of optimal weights and optimal hedging ratios. Results show evidence of hedging effectiveness for the financial innovations against oil market risks, with higher hedging performance observed during the pandemic. Overall, we show that sectoral financial innovations provide resilient investment options. Therefore, we propose that including the ETFs in an investment portfolio containing oil could improve risk-adjusted returns, especially in similar financial crisis as witnessed during the pandemic. In essence, our results are useful for investors in the global oil market seeking to maximize risk-adjusted returns when making investment decisions. Moreover, by exploring the role of structural breaks in the multivariate volatility framework, our attempts at establishing robustness for the results reveal that ignoring the same may lead to wrong conclusions about the hedging effectiveness.

A multivariate volatility vine copula model

2016 ◽  
Vol 37 (4) ◽  
pp. 281-308 ◽  
Author(s):  
E. C. Brechmann ◽  
M. Heiden ◽  
Y. Okhrin
Keyword(s):  
Copula Model ◽  
Vine Copula ◽  
Multivariate Volatility

An efficient Cholesky decomposition and applications for the simulation of large-scale random wind velocity fields

2018 ◽  
Vol 22 (6) ◽  
pp. 1255-1265 ◽  
Author(s):  
Yongle Li ◽  
Chuanjin Yu ◽  
Xingyu Chen ◽  
Xinyu Xu ◽  
Koffi Togbenou ◽  
...  
Keyword(s):  
Wind Velocity ◽  
Large Scale ◽  
Spectral Representation ◽  
Cholesky Decomposition ◽  
Velocity Fields ◽  
Data Driven ◽  
Long Span Bridges ◽  
Long Span ◽  
Spectral Representation Method ◽  
Representation Method

A growing number of long-span bridges are under construction across straits or through valleys, where the wind characteristics are complex and inhomogeneous. The simulation of inhomogeneous random wind velocity fields on such long-span bridges with the spectral representation method will require significant computation resources due to the time-consuming issues associated with the Cholesky decomposition of the power spectrum density matrixes. In order to improve the efficiency of the decomposition, a novel and efficient formulation of the Cholesky decomposition, called “Band-Limited Cholesky decomposition,” is proposed and corresponding simulation schemes are suggested. The key idea is to convert the coherence matrixes into band matrixes whose decomposition requires less computational cost and storage. Subsequently, each decomposed coherence matrix is also a band matrix with high sparsity. As the zero-valued elements have no contribution to the simulation calculation, the proposed method is further expedited by limiting the calculation to the non-zero elements only. The proposed methods are data-driven ones, which can be applicable broadly for simulating many complicated large-scale random wind velocity fields, especially for the inhomogeneous ones. Through the data-driven strategies presented in the study, a numerical example involving inhomogeneous random wind velocity field simulation on a long-span bridge is performed. Compared to the traditional spectral representation method, the simulation results are with high accuracy and the entire simulation procedure is about 2.5 times faster by the proposed method for the simulation of one hundred wind velocity processes.

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