Econophysics and Financial Economics Econophysics and Financial Economics An Emerging Dialogue Franck Jovanovic and Christophe Schinckus Oxford University Press is a department of the University of Oxford It furthers the University’s objective of excellence in research, scholarship, and education by publishing worldwide Oxford is a registered trade mark of Oxford University Press in the UK and certain other countries Published in the United States of America by Oxford University Press 198 Madison Avenue, New York, NY 10016, United States of America © Oxford University Press 2017 All rights reserved No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, without the prior permission in writing of Oxford University Press, or as expressly permitted by law, by license, or under terms agreed with the appropriate reproduction rights organization Inquiries concerning reproduction outside the scope of the above should be sent to the Rights Department, Oxford University Press, at the address above You must not circulate this work in any other form and you must impose this same condition on any acquirer CIP data is on file at the Library of Congress ISBN 978–0–19–020503–4 1 3 5 7 9 8 6 4 Printed by Edwards Brothers Malloy, United States of America C O N T E N TS Acknowledgments╇ vii Introduction╇ ix 1.╇ Foundations of Financial Economics: The Key Role of the Gaussian Distribution╇ 2.╇ Extreme Values in Financial Economics: From Their Observation to Their Integration into the Gaussian Framework╇ 25 3.╇ New Tools for Extreme-╉Value Analysis: Statistical Physics Goes beyond Its Borders╇ 49 4.╇ The Disciplinary Position of Econophysics: New Opportunities for Financial Innovations╇ 78 5.╇ Major Contributions of Econophysics to Financial Economics╇ 106 6.╇ Toward a Common Framework╇ 139 Conclusion: What Kind of Future Lies in Store for Econophysics?╇ 164 Notes╇ 167 References╇ 185 Index╇ 217 v AC K N O W L E D G M E N TS This book owes a lot to discussions that we had with Anna Alexandrova, Marcel Ausloos, Franỗoise Balibar, Jean-Philippe Bouchaud, Gigel Busca, John Davis, Xavier Gabaix, Serge Galam, Nicolas Gaussel, Yves Gingras, Emmanuel Haven, Philippe Le Gall, Annick Lesne, Thomas Lux, Elton McGoun, Adrian Pagan, Cyrille Piatecki, Geoffrey Poitras, Jeroen Romboust, Eugene Stanley, and Richard Topol We want to thank them We also thank Scott Parris We also want to acknowledge the support of the CIRST (Montréal, Canada), CEREC (University St-Louis, Belgium), GRANEM (Université d’Angers, France), and LÉO (Université d’Orléans, France) We also thank Annick Desmeules Paré, Élise Filotas, Kangrui Wang, and Steve Jones Finally, we wish to acknowledge the financial support of the Social Sciences and Humanities Research Council of Canada, the Fonds québécois de recherche sur la société et la culture, and TELUQ (Fonds Institutionnel de Recherche) for this research We would like to thank the anonymous referees for their helpful comments vii INTRODUCTION Stock market prices exert considerable fascination over the large numbers of people who scrutinize them daily, hoping to understand the mystery of their fluctuations Science was first called in to address this challenging problem 150 years ago In 1863, in a pioneering way, Jules Regnault, a French broker’s assistant, tried for the first time to “tame” the market by creating a mathematical model called the “random walk” based on the principles of social physics (chapter in this book; Jovanovic 2016) Since then, many authors have tried to use scientific models, methods, and tools for the same purpose: to pin down this fluctuating reality Their investigations have sustained a fruitful dialogue between physics and finance They have also fueled a common history In the mid-1990s, in the wake of some of the most recent advances in physics, a new approach to dealing with financial prices emerged This approach is called econophysics Although the name suggests interdisciplinary research, its approach is in fact multidisciplinary This field was created outside financial economics by statistical physicists who study economic phenomena, and more specifically financial markets They use models, methods, and concepts imported from physics From a financial point of view, econophysics can be seen as the application to financial markets of models from particle physics (a subfield of statistical physics) that mainly use stable Lévy processes and power laws This new discipline is original in many points and diverges from previous works Although econophysicists concretized the project initiated by Mandelbrot in the 1960s, who sought to extend statistical physics to finance by modeling stock price variations through Lévy stable processes, econophysicists took a different path to get there Therefore, they provide new perspectives that this book investigates Over the past two decades, econophysics has carved out a place in the scientific analysis of financial markets, providing new theoretical models, methods, and results The framework that econophysicists have developed describes the evolution of financial markets in a way very different from that used by the current standard financial models Today, although less visible than financial economics, econophysics influences financial markets and practices Many “quants” (quantitativists) trained in statistical physics have carried their tools and methodology into the financial world According to several trading-room managers and directors, econophysicists’ phenomenological approach has modified the practices and methods of analyzing financial data Hitherto, these practical changes have concerned certain domains of finance: hedging, portfolio management, financial crash predictions, and software dedicated to finance In the coming decades, however, econophysics could contribute to profound changes in the entire financial industry Performance measures, risk management, and all financial ix 227 Index price indices calculus, 172n7 price-return models, 143–53, 154t–163t prices, 23, 168n10, 173n24, 181n16, 182n29, 182n34 See also law of one price; volatility pricing, 108 primes, 168n15 probability space, 170n36 probability theory, 169n23 profit, 169n29 psychology, 182n36 pure-jump processes, 174n32 qualitative tests, 95 Quantitative Finance, 82, 88, 102 quantitative tests, 95, 134–37 quants, ix–x , 107 Quételet, Adolphe, 2–3 Quieros, Silvio, 137 radar, 182n25 random growth, generative models, 124–26 random number table, 169n26 random size, 34 random-walk model, 7–9, 12–13, 103, 174n30 random walks, ix, 3–4, 168n7, 168n19, 170n37 rational traders, 116–17 raw observations, 92–93 RBC models See real business cycle models Reagan administration, 79 real business cycle (RBC) models, 94, 179n21 Redelico, Francisco, 137 Reed, William, 94–95, 125 Regnault, Jules, 6, 9, 167n3, 168n11, 169n31 See also random walks Gaussian distribution introduced by, 29 normal law named by, 167n5 stochastic modeling and, 2–4 renormalization group theory overview, 51–58, 52f, 54f, 55f, 56f, 57f stochastic process application, 54f replicating portfolio, 97 returns, 65, 170n34, 174n27 risk, 22, 171n52 power laws’ pertinence to estimating, 113–14 return’s relationship with, 170n34, 174n27 risk management, 109 RiskMetrics, 109 Rmetrics, 108 Roberts, Harry, 9, 12–13, 169n30 Rochet, Jean-Charles, 171n53 Roehner, Bertrand, 82 Roll, Richard, 40, 173n23, 173n25 Rosenfeld, Lawrence, 180n36 Ross, Stephen, 20, 45, 171n53 Rosser, J Barkley, 88, 180n34 rough data, 98 Roy, A. D., 10 Roychowdhury, Vwani, 176n34 Russian financial crisis, 181n15 Rybski, Diego, 177n37 St Petersburg paradox, 177n44 Saley, Hadiza, 18 samples, 177n45, 180n36 Samuelson, Paul, 11, 18, 37, 45, 169n31, 170n37 Santa Fe Institute, xii–xiii, 80, 130, 181n21, 183n41 SAS See Statistical Analysis System scale factor, 37, 173n20 scale invariance, 67–68, 176n28, 176n29 See also critical phenomena definition, 52, 64, 173n17 overview, 64 scaling hypothesis, 116 scaling laws, 174n6, 181n13 scaling properties, 176n28, 176n29 Schabas, Margaret, 50 Schinckus, Christophe, 84, 129 Scholes, Myron, 20–21, 44–45, 149–50, 181n15 Schwert, G William, 182n32 sciences analogies in, 175n14 computerization of, 60–62, 61f 228 Index scientific innovations, opportunity for, 96–102, 99f, 100f, 101f scientificity, 102–3 securities, 169n31, 170n45 See also random walk Seemann, Lars, 106 Seibold, Goetz, 183n40 self-criticality theory, 132–34 self-organized criticality, 131–34 separation theorem, 170n35 SGF See Statistique Générale de la France Shalizi, Rohilla, 136–37 Shannon, Donald, 38 Sharpe, William, 20 Shefrin, Hersh, 183n37 Shiller, Robert 48 Shinohara, Shuji, 183n40 short-term time dependence, 184n11 short-term valuations, 3 Simkin, Mikhail, 176n34 Simon, Herbert, 94, 124, 177n37 Sims, Christopher, 179n21 single-factor model, 20 size models, 177n40 skewness, 34 Slanina, František, 132 Slutsky, Eugen, 8, 169n27, 169n30 Sneppen, Kim, 183n40 Society for Economic Science with Heterogeneous Interacting Agents (ESHIA), 83 sociophysics, 175n15 See also econophysics software, 108 sophisticated traders, 16–17, 170n45 Sornette, Didier, 66, 116, 149, 150, 180n26 source papers, 178n7 Sprenkle, Case, 21, 32 Sputnik era, 79 square root of time, law of, 3 stability, 66–67, 173n22 stable distributions package, 108 stable Lévy processes, x–xi, 38, 41, 49, 53–55, 54f, 62, 66–67, 74–76, 75f, 91, 144–145, 173n3, 184n12 See also nonstable Lévy distribution; truncated stable Lévy distribution Fama on, 39–40 Mandelbrot on, 33–37 non-Gaussian stable Lévy processes and, 72–73 power law characterizing, 176n31 stable nonnormal process, 173n23 stable Paretian distributions, 39–40 Standard & Poor’s 500 Index, 21–22 Standler, Ronald, 178n2 Stanford University, 169n25 Stanley, Eugene, 74, 145– 46, 148, 179n14, 180n24 on econophysics, 59, 79, 81, 82, 178n1 on scaling invariance, 67–68 on universality class, 110 “The State of the Finance Field” (Weston), 12 Statistical Analysis System (SAS), 108 statistical dependence, 170n44 statistical econophysics, xiii statistical equilibrium, 180n28 statistical patterns, 181n23 statistical physics, 80, 179n18 application, 58–60 borders, 49–77, 52f, 54f, 55f, 56f, 57f, 61f, 69f, 71f, 75f golden age, 50–58, 52f, 54f, 55f, 56f, 57f methods, 58–60 power laws’ role in, 63–65 statistical tests, 19 Statistique Générale de la France (SDF), 30–31 Stauffer, Dietrich, xii, 132 Steiger, William, 14–15 Stigler, George, 130 Stiglitz, Joseph, 19 Stinchcombe, Robin, 132 Stirling, James, 4 stochastic modeling, 2–4 stochastic processes, 171n57, 171n58 efficient-market hypothesis and, 15–20 power laws as linked with, 66 stock market, 2–4, 167n1 See also random walks 229 Index stock market crash, 1929, 7–8 stock prices, 169n29, 172n9 stock price variations, 2–4, 26–29, 26f, 27f, 28f, 169n30, 172n3, 179n19 stress tests, 113 string theory, 183n2 student distribution, 173n21 subjectivism, 112 system of markets, 171n53 Tan, Abby, 149–50, 152 technical analysis, 179n23 technical formations, 9 temperature-pressure phase diagram, 52f Texas Instruments, 22 textbooks, on econophysics, 82 Thaler, Richard, 129 Theiler, James, 137 theorems, 171n57 theoretical characteristic function, 173n26 Théorie de la spéculation (Bachelier), 4–5 “Théorie mathématique du jeu” (Bachelier), 5 time, square root of, 3 time-dependence dynamic, 174n34 time series, 181n13 Tippett, Leonard, 169n26 Tippett table, 169n26 Toronto Stock Exchange, 175n17 traders, 16–17, 116–17, 132, 170n45 trades, 182n34 trading, 107–8 trading rooms, econophysics used by, 106–17, 110f, 115t transdisciplinarity, 121–22, 147f transdisciplinary analysis, 147 Trans-Lux Movie Ticker, 168n10 trends, 14–15 Treynor, Jack, 20, 129 tribes, 170n36 truncated stable Lévy distribution, 144, 145, 148–52 truncation, 158n51, 177n44, 177n46, 178n50, 178n52 overview, 72–76, 75f of power law, 72–76 Tversky, Amos, 129 two-block model, 44–45 unconditional distributions, 47–48, 100, 111–12, 114, 179n13 universality classes, 58, 64–65, 68, 109–10 University of Budapest, 82 University of Chicago, 14, 32, 170n43, 179n16 University of Houston, 83 University of Silesia, 83 University of Warsaw, 83 University of Wroclaw, 83 Upton, David, 38 upward, 3 value-at-risk (VAR), 109, 179n21, 181n11 van der Vaart, Aad W., 73 Vanguard 500 Index fund, 21–22 van Tassel, John, 32, 38 VAR See value-at-risk variability, 174n29 variance, 184n11 variation correlation length, 175n13 vector autoregressions (VARs) modeling, 94 visual linearity, 132–33 visual tests, 119, 134–35, 183n42 Vitanov, Nikolay, 177n36 volatility, 110–15, 115t volatility clustering, 112 von Smoluchowski, Marian, 6, 168n19 Wall Street Journal, 168n10 Wang, Bing-Hong, 132 Weintraub, Robert, 14–15 Weston, Paul, 12 Whitley, Richard, 92 Widom, Benjamin, 53, 176n28 Wiener, Norbert, 6, 169n20 Wiener process See Brownian motion Williams, John, 170n34 Willis, J. C., 70 230 Index Wilson, Kenneth Nobel Prize in Physics received by, 51–58, 52f, 54f, 55f, 56f, 57f overview, 51–58, 52f, 54f, 55f, 56f, 57f Woodard, Ryan, 116 Working, Holbrook, 169n25, 169n30, 170n44 random-walk model research of, 7–8, 9, 12–13 on trends, 15 Wyart, Matthieu, 130–31 Yale University, 172n6 Yoshikawa, Hiroshi, 128 Yule, George Udny, 70, 124, 125–26 Zanin, Massimiliano, 137 Zhang, Yi-Chen, 103 Zhao, Xin, 181n11 Zipf, George, 70, 177n37, 177n38 Zipf ’s Law, 70 ... 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