Efficient Nested Estimation of CoVaR: A Decoupled Approach

Published Online:https://doi.org/10.1287/opre.2024.1452

References

  • Adrian T, Brunnermeier MK (2016) CoVaR. Amer. Econom. Rev. 106(7):1705–1741.CrossrefGoogle Scholar
  • Bergstra J, Bengio Y (2012) Random search for hyper-parameter optimization. J. Machine Learn. Res. 13(1):281–305.Google Scholar
  • Bischl B, Binder M, Lang M, Pielok T, Richter J, Coors S, Thomas J, et al. (2023) Hyperparameter optimization: Foundations, algorithms, best practices, and open challenges. Wiley Interdisciplinary Rev. Data Mining Knowledge Discovery 13(2):e1484.CrossrefGoogle Scholar
  • Black F, Scholes M (1973) The pricing of options and corporate liabilities. J. Political Econom. 81(3):637–654.CrossrefGoogle Scholar
  • Broadie M, Du Y, Moallemi CC (2015) Risk estimation via regression. Oper. Res. 63(5):1077–1097.LinkGoogle Scholar
  • Caponnetto A, De Vito E (2007) Optimal rates for the regularized least-squares algorithm. Foundations Comput. Math. 7(3):331–368.CrossrefGoogle Scholar
  • Chen QA, Feng MB (2023) Generalized importance sampling for nested simulation. Corlu CG, Hunter SR, Lam H, Onggo BS, Shortle J, Biller B, eds. Proc. Winter Simulation Conf. (Institute of Electrical and Electronics Engineers, Piscataway, NJ), 409–420.Google Scholar
  • Duffie D (2010) Dynamic Asset Pricing Theory (Princeton University Press, Princeton, NJ).Google Scholar
  • Engel E, Dreizler RM (2011) Density Functional Theory (Springer, Berlin).CrossrefGoogle Scholar
  • Feurer M, Hutter F (2019) Hyperparameter optimization. Hutter F, Kotthoff L, Vanschoren J, eds. Automated Machine Learning: Methods, Systems, Challenges (Springer International Publishing, Cham, Switzerland), 3–33.CrossrefGoogle Scholar
  • Gair J (2021) Making sense of data: Introduction to statistics for gravitational-wave astronomy, International Max Planck Research School for Gravitational Wave Astronomy, Lecture Notes (Albert Einstein Institute, Potsdam, Germany).Google Scholar
  • Giles MB, Haji-Ali AL, Spence J (2023) Efficient risk estimation for the credit valuation adjustment. Preprint, submitted January 14, https://arxiv.org/abs/2301.05886.Google Scholar
  • Glasserman P (2004) Monte Carlo Methods in Financial Engineering (Springer, Berlin).CrossrefGoogle Scholar
  • Gordy MB, Juneja S (2010) Nested simulation in portfolio risk measurement. Management Sci. 56(10):1833–1848.LinkGoogle Scholar
  • Györfi L, Kohler M, Krzyżak A, Walk H (2002) A Distribution-Free Theory of Nonparametric Regression (Springer, Berlin).CrossrefGoogle Scholar
  • Hansen BE (2008) Uniform convergence rates for kernel estimation with dependent data. Econom. Theory 24(3):726–748.CrossrefGoogle Scholar
  • Hardt M, Recht B, Singer Y (2016) Train faster, generalize better: Stability of stochastic gradient descent. Balcan MF, Weinberger KQ, eds. Proc. 33rd Internat. Conf. Machine Learn. (PMLR, New York), 1225–1234.Google Scholar
  • Heston SL (1993) A closed-form solution for options with stochastic volatility with applications to bond and currency options. Rev. Financial Stud. 6(2):327–343.CrossrefGoogle Scholar
  • Hong LJ (2009) Estimating quantile sensitivities. Oper. Res. 57(1):118–130.LinkGoogle Scholar
  • Hong LJ, Juneja S, Liu G (2017) Kernel smoothing for nested estimation with application to portfolio risk measurement. Oper. Res. 65(3):657–673.LinkGoogle Scholar
  • Hornik K, Stinchcombe M, White H (1989) Multilayer feedforward networks are universal approximators. Neural Networks 2(5):359–366.CrossrefGoogle Scholar
  • Huang W, Lin N, Hong LJ (2024) Monte Carlo estimation of CoVaR. Oper. Res. 72(6):2337–2357.LinkGoogle Scholar
  • Hull JC (2022) Options, Futures, and Other Derivatives, 11th ed. (Pearson, Harlow, England).Google Scholar
  • Imaizumi M (2023) Sup-norm convergence of deep neural network estimator for nonparametric regression by adversarial training. Preprint, submitted July 8, https://arxiv.org/abs/2307.04042.Google Scholar
  • James G, Witten D, Hastie T, Tibshirani R (2013) An Introduction to Statistical Learning (Springer, Berlin).CrossrefGoogle Scholar
  • Kanagawa M, Hennig P, Sejdinovic D, Sriperumbudur BK (2018) Gaussian processes and kernel methods: A review on connections and equivalences. Preprint, submitted July 6, https://arxiv.org/abs/1807.02582.Google Scholar
  • Lin N, Hong LJ (2025) The FA–SAA algorithm for CVaR optimization. Asia-Pacific J. Oper. Res. 42(6):2540002.CrossrefGoogle Scholar
  • Liu M, Staum J (2010) Stochastic kriging for efficient nested simulation of expected shortfall. J. Risk 12(3):3–27.CrossrefGoogle Scholar
  • Nadaraya EA (1964) On estimating regression. Theory Probability Its Appl. 9(1):141–142.CrossrefGoogle Scholar
  • Nirenberg L (1959) On elliptic partial differential equations. Annali Della Scuola Normale Superiore Pisa-Scienze Fisiche Matematiche 13(2):115–162.Google Scholar
  • Platen E, Bruti-Liberati N (2010) Numerical Solution of Stochastic Differential Equations with Jumps in Finance (Springer Science & Business Media, Boston).CrossrefGoogle Scholar
  • Schölkopf B, Herbrich R, Smola AJ (2001) A generalized representer theorem. Helmbold D, Williamson B, eds. Computational Learning Theory: COLT 2001, Lecture Notes in Computer Science, vol. 2111 (Springer, Berlin, Heidelberg), 416–426.Google Scholar
  • Serfling RJ (2009) Approximation Theorems of Mathematical Statistics (John Wiley & Sons, New York).Google Scholar
  • Shreve SE (2004) Stochastic Calculus for Finance II: Continuous-Time Models (Springer, Berlin).CrossrefGoogle Scholar
  • Snoek J, Larochelle H, Adams RP (2012) Practical bayesian optimization of machine learning algorithms. Pereira F, Burges CJC, Bottou L, Weinberger KQ, eds. Proc. 26th Annual Conf. Neural Information Processing Systems (Curran Associates, Inc., Red Hook, NY), 2951–2959.Google Scholar
  • Srivastava N, Hinton G, Krizhevsky A, Sutskever I, Salakhutdinov R (2014) Dropout: A simple way to prevent neural networks from overfitting. J. Machine Learn. Res. 15(1):1929–1958.Google Scholar
  • Steinwart I, Hush DR, Scovel C (2009) Optimal rates for regularized least squares regression. Proc. 22nd Annual Conf. Learning Theory (COLT 2009) (Conference on Learning Theory, Montreal), 79–93.Google Scholar
  • Syed Y, Wang G (2023) Optimal randomized multilevel Monte Carlo for repeatedly nested expectations. Krause A, Brunskill E, Cho K, Engelhardt B, Sabato S, Scarlett J, eds. Proc. 40th Internat. Conf. Machine Learn. (PMLR, New York), 33343–33364.Google Scholar
  • Tsybakov AB (2008) Introduction to Nonparametric Estimation (Springer, Berlin).Google Scholar
  • Wang W, Wang Y, Zhang X (2024) Smooth nested simulation: Bridging cubic and square root convergence rates in high dimensions. Management Sci. 70(12):9031–9057.LinkGoogle Scholar
  • Watson GS (1964) Smooth regression analysis. Indian J. Statist. Ser. A 26(4):359–372.Google Scholar
  • Yang L, Shami A (2020) On hyperparameter optimization of machine learning algorithms: Theory and practice. Neurocomputing (Amsterdam) 415:295–316.CrossrefGoogle Scholar
  • Yang Y, Bhattacharya A, Pati D (2017) Frequentist coverage and sup-norm convergence rate in Gaussian process regression. Preprint, submitted August 16, https://arxiv.org/abs/1708.04753.Google Scholar
  • Yarotsky D (2017) Error bounds for approximations with deep ReLU networks. Neural Networks 94:103–114.CrossrefGoogle Scholar
INFORMS site uses cookies to store information on your computer. Some are essential to make our site work; Others help us improve the user experience. By using this site, you consent to the placement of these cookies. Please read our Privacy Statement to learn more.