The Statistical Mechanics of Financial Markets

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ISBN: 9783540262855 | 3540262857
Cover: Hardcover
Copyright: 11/1/2005

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This highly praised introductory treatment describes the parallels between statistical physics and finance - both those established in the 100-year long interaction between these disciplines, as well as new research results on financial markets.

1. Introduction

(12)

1.1 Motivation

(3)

1.2 Why Physicists? Why Models of Physics?

(2)

1.3 Physics and Finance - Historical

(2)

1.4 Aims of this Book

(5)

2. Basic Information on Capital Markets

(14)

2.1 Risk

(1)

2.2 Assets

(2)

2.3 Three Important Derivatives

(4)

2.3.1 Forward Contracts

(1)

2.3.2 Futures Contract

(1)

2.3.3 Options

(2)

2.4 Derivative Positions

(1)

2.5 Market Actors

(1)

2.6 Price Formation at Organized Exchanges

(6)

2.6.1 Order Types

(1)

2.6.2 Price Formation by Auction

(1)

2.6.3 Continuous Trading: The XETRA Computer Trading System

(4)

3. Random Walks in Finance and Physics

(24)

3.1 Important Questions

(1)

3.2 Bachelier's "Théorie de la Spéculation"

(13)

3.2.1 Preliminaries

(4)

3.2.2 Probabilities in Stock Market Operations

(7)

3.2.3 Empirical Data on Successful Operations in Stock Markets

(1)

3.2.4 Biographical Information on Louis Bachelier (1870-1946)

(1)

3.3 Einstein's Theory of Brownian Motion

(3)

3.3.1 Osmotic Pressure and Diffusion in Suspensions

(2)

3.3.2 Brownian Motion

(1)

3.4 Experimental Situation

(7)

3.4.1 Financial Data

(2)

3.4.2 Perrin's Observations of Brownian Motion

(1)

3.4.3 One-Dimensional Motion of Electronic Spins

(4)

4. The Black—Scholes Theory of Option Prices

(50)

4.1 Important Questions

(1)

4.2 Assumptions and Notation

(1)

4.2.1 Assumptions

(1)

4.2.2 Notation

(1)

4.3 Prices for Derivatives

(5)

4.3.1 Forward Price

(1)

4.3.2 Futures Price

(1)

4.3.3 Limits on Option Prices

(2)

4.4 Modeling Fluctuations of Financial Assets

(14)

4.4.1 Stochastic Processes

(8)

4.4.2 The Standard Model of Stock Prices

(1)

4.4.3 The Itô Lemma

(2)

4.4.4 Log-normal Distributions for Stock Prices

(2)

4.5 Option Pricing

(29)

4.5.1 The Black—Scholes Differential Equation

(3)

4.5.2 Solution of the Black—Scholes Equation

(5)

4.5.3 Risk-Neutral Valuation

(1)

4.5.4 American Options

(2)

4.5.5 The Greeks

(4)

4.5.6 Synthetic Replication of Options

(1)

4.5.7 Implied Volatility

(5)

4.5.8 Volatility Indices

(8)

5. Scaling in Financial Data and in Physics

101

(72)

5.1 Important Questions

101

(1)

5.2 Stationarity of Financial Markets

102

(4)

5.3 Geometric Brownian Motion

106

(14)

5.3.1 Price Histories

106

(1)

5.3.2 Statistical Independence of Price Fluctuations

106

(5)

5.3.3 Statistics of Price Changes of Financial Assets

111

(9)

5.4 Pareto Laws and Lévy Flights

120

(11)

5.4.1 Definitions

121

(2)

5.4.2 The Gaussian Distribution and the Central Limit Theorem

123

(3)

5.4.3 Lévy Distributions

126

(3)

5.4.4 Non-stable Distributions with Power Laws

129

(2)

5.5 Scaling, Lévy Distributions, and Lévy Flights in Nature

131

(15)

5.5.1 Criticality and Self-Organized Criticality, Diffusion and Superdiffusion

131

(2)

5.5.2 Micelles

133

(1)

5.5.3 Fluid Dynamics

134

(3)

5.5.4 The Dynamics of the Human Heart

137

(1)

5.5.5 Amorphous Semiconductors and Glasses

138

(3)

5.5.6 Superposition of Chaotic Processes

141

(1)

5.5.7 Tsallis Statistics

142

(4)

5.6 New Developments: Non-stable Scaling, Temporal and Interasset Correlations in Financial Markets

146

(27)

5.6.1 Non-stable Scaling in Financial Asset Returns

147

(4)

5.6.2 The Breadth of the Market

151

(3)

5.6.3 Non-linear Temporal Correlations

154

(5)

5.6.4 Stochastic Volatility Models

159

(2)

5.6.5 Cross-Correlations in Stock Markets

161

(12)

6. Turbulence and Foreign Exchange Markets

173

(24)

6.1 Important Questions

173

(1)

6.2 Turbulent Flows

173

(9)

6.2.1 Phenomenology

174

(4)

6.2.2 Statistical Description of Turbulence

178

(3)

6.2.3 Relation to Non-extensive Statistical Mechanics

181

(1)

6.3 Foreign Exchange Markets

182

(15)

6.3.1 Why Foreign Exchange Markets?

182

(1)

6.3.2 Empirical Results

183

(6)

6.3.3 Stochastic Cascade Models

189

(2)

6.3.4 The Multifract al Interpretation

191

(6)

7. Derivative Pricing Beyond Black—Scholes

197

(24)

7.1 Important Questions

197

(1)

7.2 An Integral Framework for Derivative Pricing

197

(2)

7.3 Application to Forward Contracts

199

(1)

7.4 Option Pricing (European Calls)

200

(4)

7.5 Monte Carlo Simulations

204

(4)

7.6 Option Pricing in a Tsallis World

208

(2)

7.7 Path Integrals: Integrating the Fat Tails into Option Pricing

210

(6)

7.8 Path Integrals: Integrating Path Dependence into Option Pricing

216

(5)

8. Microscopic Market Models

221

(38)

8.1 Important Questions

221

(1)

8.2 Are Markets Efficient?

222

(4)

8.3 Computer Simulation of Market Models

226

(20)

8.3.1 Two Classical Examples

226

(1)

8.3.2 Recent Models

227

(19)

8.4 The Minority Game

246

(13)

8.4.1 The Basic Minority Game

247

(2)

8.4.2 A Phase Transition in the Minority Game

249

(1)

8.4.3 Relation to Financial Markets

250

(2)

8.4.4 Spin Glasses and an Exact Solution

252

(3)

8.4.5 Extensions of the Minority Game

255

(4)

9. Theory of Stock Exchange Crashes

259

(30)

9.1 Important Questions

259

(1)

9.2 Examples

260

(4)

9.3 Earthquakes and Material Failure

264

(6)

9.4 Stock Exchange Crashes

270

(6)

9.5 What Causes Crashes?

276

(2)

9.6 Are Crashes Rational?

278

(1)

9.7 What Happens After a Crash?

279

(6)

9.8 A Richter Scale for Financial Markets

285

(4)

10. Risk Management

289

(36)

10.1 Important Questions

289

(1)

10.2 What is Risk?

290

(1)

10.3 Measures of Risk

291

(17)

10.3.1 Volatility

292

(1)

10.3.2 Generalizations of Volatility and Moments

293

(2)

10.3.3 Statistics of Extremal Events

295

(2)

10.3.4 Value at Risk

297

(6)

10.3.5 Coherent Measures of Risk

303

(3)

10.3.6 Expected Shortfall

306

(2)

10.4 Types of Risk

308

(6)

10.4.1 Market Risk

308

(1)

10.4.2 Credit Risk

308

(3)

10.4.3 Operational Risk

311

(3)

10.4.4 Liquidity Risk

314

(1)

10.5 Risk Management

314

(11)

10.5.1 Risk Management Requires a Strategy

314

(1)

10.5.2 Limit Systems

315

(1)

10.5.3 Hedging

316

(1)

10.5.4 Portfolio Insurance

317

(1)

10.5.5 Diversification

318

(5)

10.5.6 Strategic Risk Management

323

(2)

11. Economic and Regulatory Capital for Financial Institutions

325

(34)

11.1 Important Questions

325

(1)

11.2 Economic Capital

326

(7)

11.2.1 What Determines Economic Capital?

326

(1)

11.2.2 How Calculate Economic Capital?

327

(1)

11.2.3 How Allocate Economic Capital?

328

(3)

11.2.4 Economic Capital as a Management Tool

331

(2)

11.3 The Regulatory Framework

333

(26)

11.3.1 Why Banking Regulation?

333

(1)

11.3.2 Risk-Based Capital Requirements

334

(2)

11.3.3 Basel I: Regulation of Credit Risk

336

(2)

11.3.4 Internal Models

338

(3)

11.3.5 Basel II: The New International Capital Adequacy Framework

341

(17)

11.3.6 Outlook: Basel III and Basel IV

358

(1)

Appendix

359

(5)

Notes and References

364

(11)

Index

375

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The Statistical Mechanics of Financial Markets

Summary

Table of Contents

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