15 years of Adjoint Algorithmic Differentiation (AAD) in finance

References

• Achdou, Y. and Pironneau, O., Computational Methods for Option Pricing, 2005 (SIAM: Philadelphia, PA).
   Google Scholar
• Andersen, L. and Piterbarg, V., Interest Rate Modeling, 2010 (Atlantic Financial Press: London, UK).
   Google Scholar
• Andreasen, J. Bump and run. Wilmott, 2023, 1–10.
   Google Scholar
• Antonov, A., Algorithmic differentiation for callable exotics. 2016. Avaliable at SSRN 2839362.
   Google Scholar
• Antonov, A., Issakov, S. and McClelland, A., Efficient SIMM-MVA calculations for callable exotics. 2017. Available at SSRN 3040061.
   Google Scholar
• Bain, A., Mariapragassam, M. and Reisinger, C., Calibration of local-stochastic and path-dependent volatility models to vanilla and no-touch options. 2019. arXiv preprint arXiv:1911.00877.
   Google Scholar
• Baydin, A.G., Pearlmutter, B.A., Radul, A.A. and Siskind, J.M., Automatic differentiation in machine learning: A survey. J. Mach. Learn. Res., 2018, 18, 1–43.
   Web of Science ®Google Scholar
• Brace, A., Gatarek, D. and Musiela, M., The market model of interest rate dynamics. Math. Finance, 1997, 7, 127–155.
   Web of Science ®Google Scholar
• Brito, J., Goloubentsev, A. and Goncharov, E., Automatic adjoint differentiation for special functions involving expectations. 2022. arXiv preprint arXiv:2204.05204.
   Google Scholar
• Broadie, M. and Glasserman, P., Estimating security price derivatives using simulation. Manag. Sci., 1996, 42, 269–285.
   Web of Science ®Google Scholar
• Capriotti, L., 2008, US Patent 0312530.
   Google Scholar
• Capriotti, L., Fast Greeks by algorithmic differentiation. J. Comput. Finance, 2011, 14, 3–35.
   Web of Science ®Google Scholar
• Capriotti, L., Likelihood ratio method and algorithmic differentiation: Fast second order greeks. Algorithmic Finance, 2015, 4, 81–87.
   Google Scholar
• Capriotti, L. and Giles, M., Fast correlation greeks by adjoint algorithmic differentiation. Risk, 2010, 23, 79.
   Google Scholar
• Capriotti, L. and Giles, M., Adjoint greeks made easy. Risk, 2012, 25, 92.
   Google Scholar
• Capriotti, L., Jiang, Y. and Macrina, A., Real-time risk management: An AAD-PDE approach. Int. J. Financ. Eng., 2015, 2, 1550039.
   Web of Science ®Google Scholar
• Capriotti, L., Jiang, Y. and Macrina, A., AAD and least-square Monte Carlo: Fast bermudan-style options and XVA greeks. Algorithmic Finance, 2017, 6, 35–49.
   Web of Science ®Google Scholar
• Capriotti, L. and Lee, J., Adjoint credit risk management. Risk, 2014, 27, 48.
   Google Scholar
• Capriotti, L., Peacock, M. and Lee, J., Real-time counterparty credit risk management in Monte Carlo. Risk, 2011, 24, 86.
   Google Scholar
• Cesa, M., A brief history of quantitative finance. Probab. Uncertain. Quant. Risk, 2017, 2, 1.
   Google Scholar
• Chan, J.H., Joshi, M.S. and Zhu, D., First- and second-order Greeks in the Heston model. J. Risk, 2015, 17, 19–69.
   Web of Science ®Google Scholar
• Christianson, B., Reverse aumulation and imploicit functions. Optim. Methods Softw., 1998, 9, 307–322.
   Web of Science ®Google Scholar
• Cohen, A.J., Mori-Sánchez, P. and Yang, W., Challenges for density functional theory. Chem. Rev., 2012, 112, 289–320.
   PubMed Web of Science ®Google Scholar
• Denson, N. and Joshi, M., Fast Greeks for Markov-Functional Models Using Adjoint PDE Methods, ( Centre for Actuarial Studies, Fac. of Economics & Commerce, University of Melbourne, Melbourne, Australia). https://books.google.com/books?id=KawXyAEACAAJ.
   Google Scholar
• Denson, N. and Joshi, M., Fast and accurate greeks for the LIBOR market model. J. Comput. Finance, 2011, 14, 115–140.
   Web of Science ®Google Scholar
• Fournié, E., Lasry, J.-M., Lebuchoux, J., Lions, P.-L. and Touzi, N., Applications of Malliavin calculus to Monte Carlo methods in finance. Finance Stoch., 1999, 3, 391–412.
   Google Scholar
• Fradkin, E., Kivelson, S.A. and Tranquada, J.M., Colloquium: Theory of intertwined orders in high temperature superconductors. Rev. Mod. Phys., 2015, 87, 457–482.
   Web of Science ®Google Scholar
• Fries, C.P., Stochastic automatic differentiation: Automatic differentiation for Monte-Carlo simulations. Quant. Finance, 2019, 19, 1043–1059.
   Web of Science ®Google Scholar
• Geeraert, S., Lehalle, C.-A., Pearlmutter, B.A., Pironneau, O. and Reghai, A., Mini-symposium on automatic differentiation and its applications in the financial industry. ESAIM: Proc. Surv., 2017, 59, 56–75.
   Google Scholar
• Giering, R. and Kaminski, T., Recipes for adjoint code construction. ACM Trans. Math. Softw., 2006, 24, 437–474.
   Google Scholar
• Giles, M., An extended collection of matrix derivative results for forward and reverse mode automatic differentiation. 2008. Unpublished.
   Google Scholar
• Giles, M., Vibrato Monte Carlo sensitivities. In Monte Carlo and Quasi-Monte Carlo Methods 2008, pp. 369, 2009 (Springer),
   Google Scholar
• Giles, M., Duta, M., Müller, J.-D. and Pierce, N., Algorithm developments for discrete adjoint methods. AIAA J., 2003, 41, 198–205.
   Google Scholar
• Giles, M. and Glasserman, P., Smoking adjoints: Fast Monte Carlo greeks. Risk, 2006, 19, 88–92.
   Google Scholar
• Giles, M. and Pierce, N., An introduction to the adjoint approach to design. Flow Turbul Combust, 2000, 65, 393–415.
   Web of Science ®Google Scholar
• Glasserman, P., Monte Carlo Methods in Financial Engineering, 2004 (Springer: New York).
   Google Scholar
• Glasserman, P. and Yu, B., Simulation for American options: Regression now or regression later? In Monte Carlo and Quasi-Monte Carlo Methods 2002, edited by H. Niederreiter, pp. 213, 2004 (Springer: Berlin, Heidelberg).
   Google Scholar
• Goloubentsev, A., Goloubentsev, D. and Lakshtanov, E., Adjoint differentiation for generic matrix functions. 2021a. arXiv preprint arXiv:2109.04913.
   Google Scholar
• Goloubentsev, D. and Lakshtanov, E., AAD: Breaking the primal barrier. Wilmott, 2019, 2019, 8–11.
   Google Scholar
• Goloubentsev, D. and Lakshtanov, E., Automatic adjoint differentiation for gradient descent and model calibration. Int. J. Wavelets Multiresolut. Inf. Process., 2022, 20(03), 2040004.
   Web of Science ®Google Scholar
• Goloubentsev, D., Lakshtanov, E. and Piterbarg, V., Automatic implicit function theorem. 2021b. Available at SSRN 3984964.
   Google Scholar
• Griewank, A., Evaluating Derivatives: Principles and Techniques of Algorithmic Differentiation (1st edn), 2000 (SIAM: Philadelphia).
   Google Scholar
• Griewank, A. and Walther, A., Evaluating Derivatives: Principles and Techniques of Algorithmic Differentiation (2nd edn), 2008 (SIAM: Philadelphia, PA).
   Google Scholar
• Henrard, M., Adjoint algorithmic differentiation: Calibration and implicit function theorem. OpenGamma Quant. Res., 2011, 1, 1.
   Google Scholar
• Henrard, M., Algorithmic Differentiation in Finance Explained, 2017 (Palgrave Macmillan: London, UK).
   Google Scholar
• Huge, B. and Savine, A., LSM reloaded - Differentiate xVA on your iPad mini. 2017. Available at SSRN 2966155.
   Google Scholar
• Huge, B. and Savine, A., Differential machine learning. 2020. arXiv preprint arXiv:2005.02347.
   Google Scholar
• Hull, J.C., Options, Futures and Other Derivatives, 2002 (Prentice Hall: New Jersey).
   Google Scholar
• Jain, S., Leitao, A. and Oosterlee, C., Rolling adjoints: Fast greeks along Monte Carlo scenarios for early-exercise options. J. Comput. Sci., 2019, 33, 95–112.
   Web of Science ®Google Scholar
• Jain, S. and Oosterlee, C.W., The stochastic grid bundling method: Efficient pricing of Bermudan options and their Greeks. Appl. Math. Comput., 2015, 269, 412–431.
   Web of Science ®Google Scholar
• Joshi, M.S. and Kainth, D., Rapid and accurate development of prices and Greeks for nth to default credit swaps in the Li model. Quant. Finance, 2004, 4, 266–275.
   Web of Science ®Google Scholar
• Joshi, M. and Yang, C., Fast gamma computations for CDO tranches. 2010. Available at SSRN 1689348.
   Google Scholar
• Joshi, M. and Yang, C., Algorithmic Hessians and the fast computation of cross-gamma risk. IIE Trans., 2011, 43, 878–892.
   Web of Science ®Google Scholar
• Käbe, C., Maruhn, J.H. and Sachs, E.W., Adjoint-based Monte Carlo calibration of financial market models. Finance Stoch., 2009, 13, 351–379.
   Web of Science ®Google Scholar
• Kottmann, J.S., Anand, A. and Aspuru-Guzik, A., A feasible approach for automatically differentiable unitary coupled-cluster on quantum computers. Chem. Sci., 2021, 12, 3497–3508.
   PubMed Web of Science ®Google Scholar
• Leclerc, M., Liang, Q. and Schneider, I., Fast Monte Carlo bermudan greeks. Risk, 2009, 22, 84.
   Google Scholar
• Liao, H.-J., Liu, J.-G., Wang, L. and Xiang, T., Differentiable programming tensor networks. Phys. Rev. X, 2019, 9, 031041.
   Web of Science ®Google Scholar
• Longstaff, F.A. and Schwartz, E., Valuing American options by simulation: A simple least-squares approach. Rev. Financ. Stud., 2001, 14, 113–147.
   Web of Science ®Google Scholar
• Ludkovski, M., Statistical machine learning for quantitative finance. Annu. Rev. Stat. Appl., 2023, 10, 271–295.
   Web of Science ®Google Scholar
• Mazzola, G., Yunoki, S. and Sorella, S., Unexpectedly high pressure for molecular dissociation in liquid hydrogen by electronic simulation. Nat. Commun., 2014, 5, 3487.
   PubMed Web of Science ®Google Scholar
• Nakano, K., Attaccalite, C., Barborini, M., Capriotti, L., Casula, M., Coccia, E., Dagrada, M., Genovese, C., Luo, Y., Mazzola, G. and Zen, A., TurboRVB: A many-body toolkit for ab initio electronic simulations by quantum Monte Carlo. J. Chem. Phys., 2020, 152, 234111.
   PubMed Web of Science ®Google Scholar
• Naumann, U., Call tree reversal is NP-complete. In Advances in Automatic Differentiation, edited by C. Bischof et al., pp. 13–22, 2008a (Springer).
   Google Scholar
• Naumann, U., Optimal Jacobian accumulation is NP-complete. Math. Program., 2008b, 112(2), 427–441. https://doi.org/10.1007/s10107-006-0042-z
   Web of Science ®Google Scholar
• Naumann, U., DAG reversal is NP-complete. J. Discrete Algorithms, 2009, 7, 402–410.
   Google Scholar
• Naumann, U., The Art of Differentiating Computer Programs: An Introduction to Algorithmic Differentiation, 2011 (SIAM: Philadelphia, PA).
   Google Scholar
• Naumann, U. and Toit, J., Adjoint algorithmic differentiation tool support for typical numerical patterns in computational finance. J. Comput. Finance, 2018, 21, 23–57.
   Web of Science ®Google Scholar
• Pironneau, O., and Sall, G., Vibrato and automatic differentiation for high order derivatives and sensitivities of financial options. 2016. arXiv preprint arXiv:1606.06143.
   Google Scholar
• Rosenbaum, M. and Zhang, J., Deep calibration of the quadratic rough Heston model. 2021. arXiv preprint arXiv:2107.01611.
   Google Scholar
• Savine, A., Modern Computational Finance: AAD and Parallel Simulations, 2018 (John Wiley & Sons: Hoboken, NJ).
   Google Scholar
• Silotto, L., Scaringi, M. and Bianchetti, M., XVA modelling: Validation, performance and model risk management. Ann. Oper. Res., 2023, 14, 1–92.
   Google Scholar
• Smith, S., Differentiation of the Cholesky algorithm. J. Comput. Graph. Stat., 1995, 4, 134–147.
   Google Scholar
• Sorella, S. and Capriotti, L., Algorithmic differentiation and the calculation of forces by quantum Monte Carlo. J. Chem. Phys., 2010, 133, 234111.
   PubMed Web of Science ®Google Scholar
• Tsitsiklis, J. and Roy, B.V., Regression methods for pricing complex American-style options. IEEE Trans. Neural Netw., 2001, 12, 694–703.
   PubMed Web of Science ®Google Scholar
• Tuckerman, M.E., Ungar, P.J., Von Rosenvinge, T. and Klein, M.L., Ab initio molecular dynamics simulations. J. Phys. Chem., 1996, 100, 12878.
   Web of Science ®Google Scholar