Abstract
Generative moment matching networks (GMMNs) are suggested for modeling the cross-sectional dependence between stochastic processes. The stochastic processes considered are geometric Brownian motions and ARMA–GARCH models. Geometric Brownian motions lead to an application of pricing American basket call options under dependence and ARMA–GARCH models lead to an application of simulating predictive distributions. In both types of applications the benefit of using GMMNs in comparison to parametric dependence models is highlighted and the fact that GMMNs can produce dependent quasi-random samples with no additional effort is exploited to obtain variance reduction.
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References
Bollerslev, T.: Generalized autoregressive conditional heteroskedasticity 31(3), 307–327 (1986)
Dziugaite, G.K., Roy, D.M., Ghahramani, Z.: Training generative neural networks via maximum mean discrepancy optimization. In: Proceedings of the Thirty-First Conference on Uncertainty in Artificial Intelligence, pp. 258–267. AUAI Press (2015). http://www.auai.org/uai2015/proceedings/papers/230.pdf
Embrechts, P., McNeil, A.J., Straumann, D.: Correlation and dependency in risk management: Properties and pitfalls. In: Dempster, M. (ed.) Risk Management: Value at Risk and Beyond, pp. 176–223. Cambridge University Press, Cambridge (2002)
Genest, C., Segers, J.: On the covariance of the asymptotic empirical copula process 101(8), 1837–1845 (2010)
Hofert, M., Kojadinovic, I., Maechler, M., Yan, J.: Elements of Copula Modeling with R. Springer Use R! Series (2018). https://doi.org/10.1007/978-3-319-89635-9, http://www.springer.com/de/book/9783319896342
Hofert, M., Prasad, A., Zhu, M.: Quasi-random sampling for multivariate distributions via generative neural networks, pp. 1–24 (2021)
Jondeau, E., Rockinger, M.: The copula-GARCH model of conditional dependencies: An international stock market application 25, 827–853 (2006)
Lemieux, C.: Monte Carlo and Quasi–Monte Carlo Sampling. Springer, Berlin (2009)
Li, Y., Swersky, K., Zemel, R.: Generative moment matching networks. In: International Conference on Machine Learning, pp. 1718–1727 (2015)
Longstaff, F.A., Schwartz, E.S.: Valuing american options by simulation: a simple least-squares approach 14(1), 113–147 (2001)
McNeil, A.J., Frey, R., Embrechts, P.: Quantitative Risk Management: Concepts, Techniques, Tools, 2 edn. Princeton University Press (2015)
Nelsen, R.B.: An Introduction to Copulas. Springer, Berlin (2006)
Patton, A.J.: Modelling asymmetric exchange rate dependence 47(2), 527–556 (2006). http://public.econ.duke.edu/~ap172/Patton_IER_2006.pdf
Rémillard, B., Scaillet, O.: Testing for equality between two copulas 100(3), 377–386 (2009)
Scheuerer, M., Hamill, T.M.: Variogram-based proper scoring rules for probabilistic forecasts of multivariate quantities 143(4), 1321–1334 (2015)
Sklar, A.: Fonctions de répartition à n dimensions et leurs marges 8, 229–231 (1959)
Weiss, A.: Arma models with arch errors 5(2), 129–143 (1984)
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Hofert, M., Prasad, A., Zhu, M. (2022). Applications of Multivariate Quasi-Random Sampling with Neural Networks. In: Keller, A. (eds) Monte Carlo and Quasi-Monte Carlo Methods. MCQMC 2020. Springer Proceedings in Mathematics & Statistics, vol 387. Springer, Cham. https://doi.org/10.1007/978-3-030-98319-2_14
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