Physics of Finance Gauge Modelling in Non-Equilibrium Pricing

by Ilinski, Kirill

• ISBN13: 9780471877387
• ISBN10: 0471877387
• Edition: 1st
• Format: Hardcover
• Copyright: 2001-02-08
• Publisher: WILEY

Summary

Uncover an innovative new method of applying contemporary techniques from physics into the financial world. Arguably one of the newest and most controversial approaches in financial analysis, this book uses techniques from modern physics to develop an altogether original method for pricing financial assets

Author Biography

<B>Kirill Ilinski</B> graduated from the Physics Department of Leningrad State University. He received his PhD in mathematical physics from the Leningrad Branch of the Steklov Mathematical Institute of the Russian Academy of Sciences. He spent five years as a Research Fellow in the School of Physics at the University of Birmingham, where he became interested in applications of methods of theoretical physics to financial economics, and attracted the attention of both financial researchers and practitioners by introducing gauge modelling of asset prices out of equilibrium. He has written over 50 articles on financial mathematics, mathematical physics, mathematical methods in statistical physics and the theory of correlated systems. Dr Ilinski has joined the Equity Derivatives Desk at Chase Manhattan in London. <P> <br>

Table of Contents

Preface	xi
Introduction	1	(17)
Dynamics versus Equilibrium	1	(7)
Natural Science versus Social Science	8	(3)
`Fair Game' and the Fractal Market Hypothesis	11	(1)
Dynamics, Volumes, and Money Flows	12	(2)
What Is This Book About?	14	(2)
Summary	16	(1)
Further Reading	17	(1)
Fibre Bundles in Finance: First Contact	18	(23)
Differential Geometry on Fibre Bundles	19	(9)
Fibre Bundles	19	(3)
Parallel Transport	22	(5)
Curvature	27	(1)
Financial Examples	28	(5)
Foreign Exchange	29	(1)
Net Present Value and Discounting as Parallel Transport	30	(2)
Two generalizations: Many Assets and Time	32	(1)
Financial Electrodynamics	33	(7)
Arbitrage as Curvature	35	(1)
Charges, Forces, and Gauge Symmetry	36	(2)
Uncertainty and Quantization	38	(2)
Summary	40	(1)
Further Reading	40	(1)
Fibre Bundles: Mathematics	41	(20)
Manifolds	41	(6)
Fibre Bundles	47	(3)
Connections on Fibre Bundles	50	(2)
Curvature	52	(2)
Transformation Laws	54	(2)
Invariance and Invariants	56	(1)
Lattice Generalizations	57	(1)
For the Curious: Index Theorems	58	(2)
Summary	60	(1)
Further Reading	60	(1)
Fibre Bundles: Physics	61	(21)
Electromagnetism	62	(4)
Gauge Invariance and Geometry	66	(2)
Electrodynamics as a Gauge Theory	68	(2)
Weyl's Gauge Theory	70	(2)
Quantum Electrodynamics	72	(4)
Other Fundamental Gauge Theories	76	(4)
Weak Interactions	76	(1)
Strong Forces	77	(1)
Gravity	78	(2)
Once More on Weyl's Theory	80	(1)
Summary	80	(1)
Further Reading	81	(1)
Fibre Bundles in Finance: Gauge Field Dynamics	82	(32)
Fibre Bundles: Formal Constructions	83	(8)
Construction of the Discrete Base	83	(4)
Structure Group	87	(1)
Fibres	87	(1)
Parallel Transport, Curvature, and Arbitrage	87	(4)
Basic Assumptions	91	(2)
Construction of the Dynamics	93	(5)
Linear Actions	95	(3)
Quadratic Actions	98	(1)
Continuous Fibre Bundles	98	(7)
Gauge Invariance: Practical Issues	105	(8)
Splits and Devaluations	105	(1)
Transaction Costs	106	(1)
Psychological Factors	107	(1)
Uneven Distribution of Numbers in Prices	107	(6)
Summary	113	(1)
Dynamics of Fast Money Flows: I	114	(46)
Introduction	114	(1)
Fast Price Dynamics: Models and Empirics	115	(13)
Models	116	(3)
Empirical Results	119	(9)
Money Flows: First Principles	128	(3)
Dynamics Construction for a Single Investment Horizon	131	(7)
Single-Investor Case	131	(2)
Risk Factors	133	(1)
Many-Investors Case	134	(3)
Lattice Gauge Theory	137	(1)
Farmer's Term	138	(3)
Interaction	141	(3)
Comparison with Other Microscopic Models	144	(3)
Statistical Properties of the Model	147	(5)
Summary	152	(1)
Probability Distribution Function - Analytics	153	(7)
Dynamics of Fast Money Flows: II	160	(18)
Introduction	160	(1)
Technical Analysis	161	(3)
Efficient Market Hypothesis	164	(2)
Short-Time Dynamical Equations	166	(7)
Econometric Issues of Price Adjustment	173	(2)
Final Remarks on Chapter 6 and 7	175	(2)
Summary	177	(1)
Virtual Arbitrage Pricing Theory	178	(20)
Equilibrium Asset Pricing	179	(4)
Gauge Model: Corrections to APT	183	(4)
Effective Equation for a Riskless Portfolio in the Presence of Virtual Arbitrage	187	(3)
Corrections to APT	190	(4)
Basis in the Space of Riskless Portfolios	191	(3)
Corrections to CAPM	194	(1)
Discussion	195	(2)
Summary	197	(1)
Derivatives	198	(66)
Derivative Pricing Under the No-Arbitrage Assumption	202	(2)
Arbitage or No-Arbitage: Some Empirical Results	204	(17)
Evidence from Index-Futures Arbitrage	205	(10)
Arbitrage and Extreme Market Events	215	(6)
Gauge Model for Derivative Pricing	221	(15)
Derivation of the Black-Scholes Equation	226	(2)
Boundary Conditions	228	(2)
Connection with Black-Scholes Analysis	230	(1)
Arbitrage Money Flows	231	(2)
Other Money Flows	233	(3)
Phenomenological Model of Derivative Pricing with Virtual Arbitrage	236	(4)
Effective Equation for Derivative Price	238	(1)
Discussion of the Model	239	(1)
Partial Differential Equations Framework	240	(3)
Explicit Solutions	243	(7)
Pure Ornstein-Uhlenbeck Process	245	(1)
Generating Function for Restricted Brownian Motion	246	(2)
Compound Process	248	(1)
Particular Derivatives	249	(1)
Transaction Costs and Arbitrage Strategies	250	(5)
Derivative Pricing Far From Equilibrium	255	(8)
Underlying Price Stochastic Dynamics	256	(3)
Pricing Equation	259	(3)
Final Remarks	262	(1)
Summary	263	(1)
Conclusions	264	(45)
APPENDIX: METHODS OF QUANTUM FIELD THEORY AND THEIR FINANCIAL APPLICATIONS
1. Primer on Creation--Annihilation Operators	267	(7)
1.1. Occupation Number Representation in a Simple Case	267	(3)
1.2. Multicoordinate generalization	270	(1)
1.3. Why Do We Need Creation-Annihilation Operators?	271	(2)
1.4. Famous Example: the Harmonic Oscillator	273	(1)
2. Functional Integrals	274	(8)
2.1. Feynman Path Integral	276	(1)
2.2. Coherent State Representation and Functional Integrals	277	(4)
2.3. Proof of Fact (18) from Chapter 6	281	(1)
3. Exact Results for Functional Integrals	282	(7)
3.1. Gaussian Integrals	282	(2)
3.2. Path Integrals for the Harmonic Oscillator	284	(3)
3.3. Derivation of Equation (50) of Chapter 9 Using Path Integrals	287	(2)
4. Financial Applications	289	(7)
4.1. Short-Term Interest Rate Models	289	(1)
4.2. Exact Results for the Vasicek Model from Path Integrals	290	(3)
4.3. Saloman Brothers Model	293	(3)
5. Calculation of Functional Integrals	296	(8)
5.1. Perturbation Theory and Feynman Diagrams	297	(2)
5.2. Quasiclassical Approach and Effective Action	299	(2)
5.3. Numerical Methods	301	(3)
6. Functional Integrals and Ito Calculus	304	(5)
6.1. Functional Integrals for Quasi-Brownian Processes	304	(1)
6.2. Fokker-Planck Equation	305	(1)
6.3. Ito Lemma	306	(3)
Glossary	309	(6)
References	315	(8)
Index	323