PREFACE

INTRODUCTION

Difficulties of quantitative finance

Methodological aspects

Why physics?

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PART I. PRICE FORMATION MECHANISM

1.1         Ambiguity of price

1.2         Limitations of stochastic calculus

1.3         Financial transaction as price measurement

1.4         Spread curve of price uncertainty

1.5         Uncertainty scaling

1.6         Basic relationship between spread, volatility and volume

1.6.1          Spread as price uncertainty

1.6.2          Spread as straddle premium

1.6.3          Dimensional considerations

1.6.4          Relation to market data

1.7         Price Impact with low participation

 

PART II. QUANTUM COUPLED-WAVE MODEL OF PRICE DYNAMICS

2.1         Introduction to coupled-wave model

2.2         Price operator and price equation

2.3         Return and spread operators

2.4         Trading algebra

2.5         Uncertainty relation

2.6         Spread and its statistics

2.7         Price process

2.8         State dynamics

2.9         Coupled-wave dynamics

2.10      Execution imbalance

2.11      Order imbalance

2.12      Ergodicity and price formation

2.13      Dynamic coupling

2.13.1        Balanced coupling

2.13.2        XPM coupling

2.13.3        Avalanche coupling regime

2.13.4        Depleting avalanche

2.13.5        Market reaction – conjugate order flow

2.14      Multiperiod scaling

2.15      Price impact

2.16      Risk management for illiquid securities

2.16.1        Market risk components

2.16.2        Liquidation losses and residual positions

 

PART III. QUANTUM THEORY OF PRICE FORMATION

3.1         Linking quantum and diffusion

3.2         Return spectrum

3.3         Quantum dynamics

3.4         Coordinate representation – Dealer’s Equation

3.5         Trade and trade flow operators

3.6         Financial uncertainty principle

3.7         Quantum-diffusion transition

3.8         Price stabilization

3.9         Engineering market environment

3.10      Option pricing for illiquid securities

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PART IV. STATISTICAL MECHANICS OF FINANCIAL MARKETS

4.1         Markets as statistical systems

4.2         Ensemble view of the markets

4.3         Ensemble measures of financial markets

4.3.1          Market and volatility indices

4.3.2          Correlation index

4.3.3          Relation between volatility and correlation

4.3.4          Market drawdown

4.4         What’s wrong with traditional measures of volatility and correlations

4.5         Ensemble measures from quantum framework

4.6         How to interpret ensemble measures in trading

4.7         Measuring market ergodicity

4.8         Second-order phase transitions in financial markets

4.8.1          Ensemble measures in critical events

4.8.2          Order parameter and market phases

4.8.3          Critical hysteresis

4.8.4          Bifurcation of imbalance

4.9         Ensemble theory of price stabilization

4.9.1          Fair value and imbalance field

4.9.2          Market equilibrium equation

4.9.3          Fair value and spread

4.9.4          Price dynamics after fair value shift

4.10      Order imbalance and execution probabilities

4.11      Market impact in ensemble theory

4.12      Simplistic model of execution probabilities

 

APPENDIX A. Behavior of ensemble measures on days with critical events

APPENDIX B. Behavior of ensemble measures on days without critical events

APPENDIX C. Phase diagrams of the market on days with critical events

APPENDIX D. Phase diagrams of the market on days without critical events

Bibliography and References

Index