Asymmetric Information and Quantization in Financial Economics

We show how a quantum formulation of financial economics can be derived from asymmetries with respect to Fisher information. Our approach leverages statistical derivations of quantum mechanics which provide a natural basis for interpreting quantum formulations of social sciences generally and of economics in particular. We illustrate the utility of this approach by deriving arbitrage-free derivative-security dynamics.

[1]  H. Kleinert.  Path Integrals in Quantum Mechanics, Statistics, Polymer Physics, and Financial Markets , 2006 .

[2]  Jonathan M. Karpoff.  The Relation between Price Changes and Trading Volume: A Survey , 1987, Journal of Financial and Quantitative Analysis.

[3]  Edward Nelson.  Dynamical Theories of Brownian Motion , 1967 .

[4]  Robert A. Gatenby,et al.  Exploratory Data Analysis Using Fisher Information , 2006 .

[5]  Andrei Khrennivov,et al.  Classical and Quantum Mechanics on Information Spaces with Applications to Cognitive, Psychological, Social, and Anomalous Phenomena , 1999, quant-ph/0003016.

[6]  E. T. Jaynes,et al.  Papers on probability, statistics and statistical physics , 1983 .

[7]  Ron Wright.  Statistical Structures Underlying Quantum Mechanics and Social Science , 2003 .

[8]  Lev Davidovich Landau,et al.  Quantum Mechanics, Non‐Relativistic Theory: Vol. 3 of Course of Theoretical Physics , 1958 .

[9]  R. C. Merton,et al.  On the Pricing of Corporate Debt: The Risk Structure of Interest Rates , 1974, World Scientific Reference on Contingent Claims Analysis in Corporate Finance.

[10]  Edward Nelson.  Derivation of the Schrodinger equation from Newtonian mechanics , 1966 .

[11]  M. Ausloos,et al.  Mechanistic approach to generalized technical analysis of share prices and stock market indices , 2002, cond-mat/0201587.

[12]  F. Knight.  The economic nature of the firm: From Risk, Uncertainty, and Profit , 2009 .

[13]  Andrei Khrennikov,et al.  Ubiquitous Quantum Structure , 2010 .

[14]  J. Zinn-Justin.  Path integrals in quantum mechanics , 2005 .

[15]  Arieh Ben-Naim,et al.  A Farewell to Entropy:Statistical Thermodynamics Based on Information , 1992 .

[16]  H Frank,et al.  Knight, Risk, Uncertainty, and Profit. , 1921 .

[17]  Emmanuel Haven.  Pilot-Wave Theory and Financial Option Pricing , 2005 .

[18]  G. White,et al.  Damodaran, Aswath. 2002. Investment Valuation: Tools and Techniques for Determining Value of Any Asset. Canada : John Wiley & Sons,Inc., 2002. Daltario, Tony. 2009. World Cement Industry. Investment U Research , 2009 .

[19]  U. Klein,et al.  The Statistical Origins of Quantum Mechanics , 2008, 0810.2394.

[20]  J. Stiglitz.  The Contributions of the Economics of Information to Twentieth Century Economics , 2000 .

[21]  Quantum modeling of nonlinear dynamics of stock prices: Bohmian approach , 2007 .

[22]  Olga Al. Choustova.  Quantum Bohmian model for financial market , 2001 .

[23]  E. Haven.  Elementary Quantum Mechanical Principles and Social Science: Is There a Connection? , 2008 .

[24]  D. Sornette.  Critical Phenomena in Natural Sciences: Chaos, Fractals, Selforganization and Disorder: Concepts and Tools , 2000 .

[25]  Jerome S. Fons.  Using Default Rates to Model the Term Structure of Credit Risk , 1994 .

[26]  E. Haven.  The Blackwell and Dubins Theorem and Rényi’s Amount of Information Measure: Some Applications , 2010 .

[27]  D. Foley.  Statistical Equilibrium in Economics: Method, Interpretation, and an Example , 1999 .

[28]  B. Frieden.  Science from Fisher Information , 2004 .

[29]  J. Keynes,et al.  The General Theory of Employment, Interest and Money. , 1936 .

[30]  V. Yakovenko,et al.  Colloquium: Statistical mechanics of money, wealth, and income , 2009, 0905.1518.

[31]  Philip Mirowski,et al.  More Heat than Light: Economics as Social Physics, Physics as Nature's Economics , 1991 .

[32]  P. Pochet.  A Quantitative Analysis , 2006 .

[33]  青木 正直,et al.  Reconstructing macroeconomics : a perspective from statistical physics and combinatorial stochastic processes , 2007 .

[34]  Charles M. C. Lee,et al.  Price Momentum and Trading Volume , 1998 .

[35]  Ab initio yield curve dynamics , 2005, physics/0507098.

[36]  Emmanuel Haven,et al.  Private Information and the ‘Information Function’: A Survey of Possible Uses , 2008 .

[37]  B. Frieden,et al.  Fisher Information and Equilibrium Distributions in Econophysics , 2004 .

[38]  Melville S. Green.  Principles of Statistical Mechanics. The Information Theory Approach. Amnon Katz. Freeman, San Francisco, 1967. xii + 188 pp., illus. $8 , 1968 .

[39]  M. Potters,et al.  Theory of Financial Risk , 1997 .

[40]  B. Frieden,et al.  Physics from Fisher Information by B. Roy Frieden , 1998 .

[41]  F. Black,et al.  The Pricing of Options and Corporate Liabilities , 1973, Journal of Political Economy.

[42]  Martin Schaden.  Interest Rates and Coupon Bonds in Quantum Finance , 2009 .

[43]  J. Keynes,et al.  The General Theory of Employment, Interest and Money. , 1936 .

[44]  Hermann Haken,et al.  Information and Self-Organization: A Macroscopic Approach to Complex Systems , 2010 .

[45]  T. Lux.  Applications of Statistical Physics in Finance and Economics , 2007 .

[46]  Kirill Ilinski,et al.  Physics of Finance: Gauge Modelling in Non-Equilibrium Pricing , 2001 .

[47]  E. Haven,et al.  Information in asset pricing: a wave function approach , 2009 .

[48]  Duncan K. Foley,et al.  A Statistical Equilibrium Theory of Markets , 1994 .

[49]  Olga Choustova,et al.  Quantum probability and financial market , 2009, Inf. Sci..

[50]  B. Frieden,et al.  Physics from Fisher Information: A Unification , 1998 .

[51]  O. Choustova.  Application of Bohmian Mechanics to Dynamics of Prices of Shares: Stochastic Model of Bohm–Vigier from Properties of Price Trajectories , 2008 .

[52]  Financial Economics from Fisher Information , 2007 .

[53]  Fernando Estrada,et al.  Theory of financial risk , 2011 .

[54]  Philip Mirowski,et al.  More Heat Than Light. Economics as Social Physics: Physics as Nature's Economics. , 1991 .

[55]  C. R. Rao,et al.  Information and the Accuracy Attainable in the Estimation of Statistical Parameters , 1992 .

[56]  E. Madelung,et al.  Quantentheorie in hydrodynamischer Form , 1927 .

[57]  B. Roy Frieden,et al.  Asymmetric information and economics , 2010 .

[58]  R. Fisher,et al.  THE INHERITANCE OF STYLE LENGTH IN LYTHRUM SALICARIA , 1943 .

[59]  J. Keynes.  The General Theory of Employment , 1937 .

[60]  Martin Schaden.  Quantum Finance , 2002 .

[61]  R. Lourie,et al.  The Statistical Mechanics of Financial Markets , 2002 .

[62]  Roger Balian.  Information Theory and Statistical Entropy , 1991 .

[63]  O. Choustova.  Quantum-like Viewpoint on the Complexity and Randomness of the Financial Market , 2009 .

[64]  E. M. Lifshitz,et al.  Quantum mechanics: Non-relativistic theory, , 1959 .

[65]  J. Stiglitz.  Information and the Change in the Paradigm in Economics, Part 1 , 2003 .

[66]  F. Black,et al.  VALUING CORPORATE SECURITIES: SOME EFFECTS OF BOND INDENTURE PROVISIONS , 1976 .

[67]  E. Haven.  The Variation of Financial Arbitrage via the Use of an Information Wave Function , 2008 .

[68]  C. DeWitt-Morette,et al.  Techniques and Applications of Path Integration , 1981 .

[69]  J. Stiglitz.  Information and the Change in the Paradigm in Economics, Part 2 , 2004 .

[70]  Marcel Reginatto,et al.  Derivation of the equations of nonrelativistic quantum mechanics using the principle of minimum Fisher information , 1998 .

[71]  B. Frieden,et al.  Asymmetric information and macroeconomic dynamics , 2010 .

[72]  D. Bohm.  A SUGGESTED INTERPRETATION OF THE QUANTUM THEORY IN TERMS OF "HIDDEN" VARIABLES. II , 1952 .

[73]  Maureen O'Hara,et al.  Market Statistics and Technical Analysis: The Role of Volume , 1994 .

[74]  A. Damodaran.  Investment Valuation: Tools and Techniques for Determining the Value of Any Asset , 1995 .