Radical Complexity

This is an informal and sketchy review of five topical, somewhat unrelated subjects in quantitative finance and econophysics: (i) models of price changes; (ii) linear correlations and random matrix theory; (iii) non-linear dependence copulas; (iv) high-frequency trading and market stability; and finally—but perhaps most importantly—(v) “radical complexity” that prompts a scenario-based approach to macroeconomics heavily relying on Agent-Based Models. Some open questions and future research directions are outlined.

[1]  Jean-Philippe Bouchaud,et al.  Self Referential Behaviour, Overreaction and Conventions in Financial Markets , 2003 .

[2]  J. Bouchaud,et al.  Theory of financial risks : from statistical physics to risk management , 2000 .

[3]  J. Bouchaud,et al.  V–, U–, L– or W–shaped economic recovery after Covid-19: Insights from an Agent Based Model , 2021, PloS one.

[4]  A. Turrell,et al.  An Interdisciplinary Model for Macroeconomics , 2017 .

[6]  Jean-Philippe Bouchaud,et al.  Risk premia: asymmetric tail risks and excess returns , 2014, 1409.7720.

[7]  J. Bouchaud,et al.  Zooming In on Equity Factor Crowding , 2020, 2001.04185.

[8]  Mathieu Rosenbaum,et al.  Rough fractional diffusions as scaling limits of nearly unstable heavy tailed Hawkes processes , 2015, 1504.03100.

[9]  M. Rosenbaum,et al.  Volatility is rough , 2018 .

[10]  Julien Guyon.  The Joint S&P 500/VIX Smile Calibration Puzzle Solved , 2019, SSRN Electronic Journal.

[11]  J. Bouchaud,et al.  A First Course in Random Matrix Theory , 2020 .

[12]  Olivier Ledoit,et al.  Nonlinear Shrinkage of the Covariance Matrix for Portfolio Selection: Markowitz Meets Goldilocks , 2017 .

[13]  J. Bouchaud,et al.  Out-of-Equilibrium Dynamics and Excess Volatility in Firm Networks , 2020, Journal of Economic Dynamics and Control.

[14]  Michael J. Gerhardt.  The End of Theory , 2001 .

[15]  M. Wątorek,et al.  Financial Return Distributions: Past, Present, and COVID-19 , 2021, Entropy.

[16]  E. Bacry,et al.  Modelling fluctuations of financial time series: from cascade process to stochastic volatility model , 2000, cond-mat/0005400.

[17]  Thomas Mikosch,et al.  Copulas: Tales and facts , 2006 .

[18]  Stephen J. Hardiman,et al.  Critical reflexivity in financial markets: a Hawkes process analysis , 2013, 1302.1405.

[19]  A. Turrell,et al.  Drawing on different disciplines: macroeconomic agent-based models , 2019 .

[20]  Jean-Philippe Bouchaud,et al.  Principal regression analysis and the index leverage effect , 2010, 1011.5810.

[21]  Pablo Jensen,et al.  Competition between collective and individual dynamics , 2009, Proceedings of the National Academy of Sciences.

[22]  Jean-Philippe Bouchaud,et al.  Cleaning large correlation matrices: tools from random matrix theory , 2016, 1610.08104.

[23]  L. Bachelier,et al.  Theory of Speculation , 1964 .

[24]  Jean-Philippe Bouchaud,et al.  Goodness-of-fit tests with dependent observations , 2011, 1106.3016.

[25]  J. Bouchaud,et al.  Stock price jumps: news and volume play a minor role , 2008, 0803.1769.

[26]  J. Bouchaud,et al.  Co-impact: crowding effects in institutional trading activity , 2018, Quantitative Finance.

[27]  J. Bouchaud,et al.  Tipping Points in Macroeconomic Agent-Based Models , 2013, 1307.5319.

[28]  G. Dosi,et al.  More is different ... and complex! the case for agent-based macroeconomics , 2019, Journal of Evolutionary Economics.

[29]  J. Bouchaud,et al.  Tâtonnement, Approach to Equilibrium and Excess Volatility in Firm Networks , 2020, SSRN Electronic Journal.

[30]  J. Bouchaud,et al.  Trades, Quotes and Prices: Financial Markets Under the Microscope , 2018 .

[31]  S. Péché,et al.  Eigenvectors of some large sample covariance matrix ensembles , 2009 .

[32]  J. Bouchaud,et al.  Exogenous and endogenous price jumps belong to different dynamical classes , 2021, SSRN Electronic Journal.

[33]  Jean-Philippe Bouchaud,et al.  Relation between bid–ask spread, impact and volatility in order-driven markets , 2006, physics/0603084.

[34]  Time reversal invariance in finance , 2009 .

[35]  J. Bouchaud,et al.  Quadratic Hawkes processes for financial prices , 2015, 1509.07710.

[36]  Jean-Philippe Bouchaud,et al.  Rotational Invariant Estimator for General Noisy Matrices , 2015, IEEE Transactions on Information Theory.

[37]  E. Bacry,et al.  Hawkes Processes in Finance , 2015, 1502.04592.

[38]  J. Bouchaud,et al.  Optimal cleaning for singular values of cross-covariance matrices , 2019, 1901.05543.

[39]  Jean-Philippe Bouchaud,et al.  Tipping points in macroeconomic Agent-Based models , 2013 .

[40]  V. Plerou,et al.  Institutional Investors and Stock Market Volatility , 2005 .

[41]  Jean-Philippe Bouchaud,et al.  A nested factor model for non-linear dependencies in stock returns , 2013 .

[42]  Charles M. Jones,et al.  A Century of Stock Market Liquidity and Trading Costs , 2002 .

[43]  J. Bouchaud,et al.  Confidence collapse in a multihousehold, self-reflexive DSGE model , 2020, Proceedings of the National Academy of Sciences.

[44]  M. Rosenbaum,et al.  From quadratic Hawkes processes to super-Heston rough volatility models with Zumbach effect , 2019, 1907.06151.

[45]  M. Rosenbaum,et al.  The Quadratic Rough Heston Model and the Joint S&P 500/VIX Smile Calibration Problem , 2020, SSRN Electronic Journal.