This is a compilation of research papers employed throughout my academic research internship during the summer of 2022 under the supervision of Dr Robert Gaunt. My main focus is the generalised hyperbolic (GH) distribution, concentrating on both its properties and its applications to the modelling of financial returns.

Properties

[1] Podgórski, Krzysztof, and Jonas Wallin. "Convolution-invariant subclasses of generalized hyperbolic distributions." Communications in Statistics-Theory and Methods 45.1 (2016): 98-103.

[2] Fotopoulos, Stergios B., Venkata K. Jandhyala, and Alex Paparas. "Some Properties of the Multivariate Generalized Hyperbolic Models." Data Analysis and Applications 3: Computational, Classification, Financial, Statistical and Stochastic Methods 5 (2020): 177-194.

[3] Gaunt, Robert E., and Milan Merkle. "On bounds for the mode and median of the generalized hyperbolic and related distributions." Journal of Mathematical Analysis and Applications 493.1 (2021): 124508.

[4] Gaunt, Robert E., and Milan Merkle. "On the mode and median of the generalized hyperbolic and related distributions." arXiv preprint arXiv:2002.01884 (2020).

[5] Barndorff-Nielsen, Ole. "Hyperbolic distributions and distributions on hyperbolae." Scandinavian Journal of statistics (1978): 151-157.

[6] Barndorff-Nielsen, Ole, John Kent, and Michael Sørensen. "Normal variance-mean mixtures and z distributions." International Statistical Review/Revue Internationale de Statistique (1982): 145-159.

[7] Scott, David J., et al. "Moments of the generalized hyperbolic distribution." Computational statistics 26.3 (2011): 459-476.

[8] Galea, Manuel, Filidor Vilca, and Camila Borelli Zeller. "Hypotheses tests on the skewness parameter in a multivariate generalized hyperbolic distribution." Brazilian Journal of Probability and Statistics 35.3 (2021): 630-655.

Applications to Finance

[1] Chinhamu, Knowledge, and Delson Chikobvu. "Value-at-risk estimation of gold market with stable generalised hyperbolic distributions." Journal of Economic and Financial Sciences 10.3 (2017): 508-521.

[2] Cong, Duc Tran, and Jo Yu Wang. "Risk Management and VaR with Application on ASIAN Market." ICFE 2017 (2017): 240.

[3] Zhang, Yuanyuan, et al. "The generalised hyperbolic distribution and its subclass in the analysis of a new era of cryptocurrencies: Ethereum and its financial risk." Physica A: Statistical Mechanics and its Applications 526 (2019): 120900.

[4] Ignatieva, Katja, and Zinoviy Landsman. "Conditional tail risk measures for the skewed generalised hyperbolic family." Insurance: Mathematics and Economics 86 (2019): 98-114.

[5] Ignatieva, Katja, and Zinoviy Landsman. "Estimating the tails of loss severity via conditional risk measures for the family of symmetric generalised hyperbolic distributions." Insurance: Mathematics and Economics 65 (2015): 172-186.

[6] Breckling, Jens, Ernst Eberlein, and Philip Kokic. "A tailored suit for risk management: Hyperbolic model." Measuring Risk in Complex Stochastic Systems (2000): 189-202.

[7] Hammerstein, Ernst August V. Generalized hyperbolic distributions: theory and applications to CDO pricing. Diss. Albert-Ludwigs-Universitat Freiburg, 2010.

[8] Hammerstein, Ernst August V. "Tail behaviour and tail dependence of generalized hyperbolic distributions." Advanced modelling in mathematical finance. Springer, Cham, 2016. 3-40.

[9] Hu, Wenbo. Calibration of multivariate generalized hyperbolic distributions using the EM algorithm, with applications in risk management, portfolio optimization and portfolio credit risk. The Florida State University, 2005.

[10] Pathmanathan, Thinesh. Dimension Reduction and Clustering of High Dimensional Data using a Mixture of Generalized Hyperbolic Distributions. Diss. 2018.

[11] Rüschendorf, Ludger, and Viktor Wolf. "Cost-efficiency in multivariate Lévy models." Dependence Modeling 3.1 (2015).

[12] Eberlein, Ernst, and Ulrich Keller. "Hyperbolic distributions in finance." Bernoulli (1995): 281-299.

[13] Behr, Andreas, and Ulrich Pötter. "Alternatives to the normal model of stock returns: Gaussian mixture, generalised logF and generalised hyperbolic models." Annals of Finance 5.1 (2009): 49-68.

[14] Hurst, Simon R., and Eckhard Platen. "The marginal distributions of returns and volatility." Lecture Notes-Monograph Series (1997): 301-314.

[15] Maina, Calvin Bitange. Dependence modelling of financial data using genenalised hyperbolic distribution. Diss. 2013.

[16] Bauer, Christian. "Value at risk using hyperbolic distributions." Journal of Economics and Business 52.5 (2000): 455-467.

[17] Alexeev, Vitali, Katja Ignatieva, and Thusitha Liyanage. "Dependence Modelling in Insurance via Copulas with Skewed Generalised Hyperbolic Marginals." Studies in Nonlinear Dynamics & Econometrics 25.2 (2021).

[18] Adubisi, Obinna Damian, et al. "Financial Data and a New Generalization of the Skew-T Distribution." Covenant Journal of Physical and Life Sciences (2021).

[19] Eberlein, Ernst, and Ernst August V. Hammerstein. "Generalized hyperbolic and inverse Gaussian distributions: limiting cases and approximation of processes." Seminar on stochastic analysis, random fields and applications IV. Birkhäuser, Basel, 2004.