| Introduction | p. 1 |
| Motivation | p. 1 |
| Why Physicists? Why Models of Physics? | p. 4 |
| Physics and Finance - Historical | p. 6 |
| Aims of this Book | p. 8 |
| Basic Information on Capital Markets | p. 13 |
| Risk | p. 13 |
| Assets | p. 13 |
| Three Important Derivatives | p. 15 |
| Forward Contracts | p. 16 |
| Futures Contract | p. 16 |
| Options | p. 17 |
| Derivative Positions | p. 19 |
| Market Actors | p. 20 |
| Price Formation at Organized Exchanges | p. 21 |
| Order Types | p. 21 |
| Price Formation by Auction | p. 22 |
| Continuous Trading: The XETRA Computer Trading System | p. 23 |
| Random Walks in Finance and Physics | p. 27 |
| Important Questions | p. 27 |
| Bachelier's "Theorie de la Speculation" | p. 28 |
| Preliminaries | p. 28 |
| Probabilities in Stock Market Operations | p. 32 |
| Empirical Data on Successful Operations in Stock Markets | p. 39 |
| Biographical Information on Louis Bachelier (1870-1946) | p. 40 |
| Einstein's Theory of Brownian Motion | p. 41 |
| Osmotic Pressure and Diffusion in Suspensions | p. 41 |
| Brownian Motion | p. 43 |
| Experimental Situation | p. 44 |
| Financial Data | p. 44 |
| Perrin's Observations of Brownian Motion | p. 46 |
| One-Dimensional Motion of Electronic Spins | p. 47 |
| The Black-Scholes Theory of Option Prices | p. 51 |
| Important Questions | p. 51 |
| Assumptions and Notation | p. 52 |
| Assumptions | p. 52 |
| Notation | p. 53 |
| Prices for Derivatives | p. 53 |
| Forward Price | p. 54 |
| Futures Price | p. 55 |
| Limits on Option Prices | p. 56 |
| Modeling Fluctuations of Financial Assets | p. 58 |
| Stochastic Processes | p. 59 |
| The Standard Model of Stock Prices | p. 67 |
| The Ito Lemma | p. 68 |
| Log-normal Distributions for Stock Prices | p. 70 |
| Option Pricing | p. 72 |
| The Black-Scholes Differential Equation | p. 72 |
| Solution of the Black-Scholes Equation | p. 75 |
| Risk-Neutral Valuation | p. 80 |
| American Options | p. 81 |
| The Greeks | p. 83 |
| Synthetic Replication of Options | p. 87 |
| Implied Volatility | p. 88 |
| Volatility Indices | p. 93 |
| Scaling in Financial Data and in Physics | p. 101 |
| Important Questions | p. 101 |
| Stationarity of Financial Markets | p. 102 |
| Geometric Brownian Motion | p. 106 |
| Price Histories | p. 106 |
| Statistical Independence of Price Fluctuations | p. 106 |
| Statistics of Price Changes of Financial Assets | p. 111 |
| Pareto Laws and Levy Flights | p. 120 |
| Definitions | p. 121 |
| The Gaussian Distribution and the Central Limit Theorem | p. 123 |
| Levy Distributions | p. 126 |
| Non-stable Distributions with Power Laws | p. 129 |
| Scaling, Levy Distributions, and Levy Flights in Nature | p. 131 |
| Criticality and Self-Organized Criticality, Diffusion and Superdiffusion | p. 131 |
| Micelles | p. 133 |
| Fluid Dynamics | p. 134 |
| The Dynamics of the Human Heart | p. 137 |
| Amorphous Semiconductors and Glasses | p. 138 |
| Superposition of Chaotic Processes | p. 141 |
| Tsallis Statistics | p. 142 |
| New Developments: Non-stable Scaling, Temporal and Interasset Correlations in Financial Markets | p. 146 |
| Non-stable Scaling in Financial Asset Returns | p. 147 |
| The Breadth of the Market | p. 151 |
| Non-linear Temporal Correlations | p. 154 |
| Stochastic Volatility Models | p. 159 |
| Cross-Correlations in Stock Markets | p. 161 |
| Turbulence and Foreign Exchange Markets | p. 173 |
| Important Questions | p. 173 |
| Turbulent Flows | p. 173 |
| Phenomenology | p. 174 |
| Statistical Description of Turbulence | p. 178 |
| Relation to Non-extensive Statistical Mechanics | p. 181 |
| Foreign Exchange Markets | p. 182 |
| Why Foreign Exchange Markets? | p. 182 |
| Empirical Results | p. 183 |
| Stochastic Cascade Models | p. 189 |
| The Multifractal Interpretation | p. 191 |
| Derivative Pricing Beyond Black-Scholes | p. 197 |
| Important Questions | p. 197 |
| An Integral Framework for Derivative Pricing | p. 197 |
| Application to Forward Contracts | p. 199 |
| Option Pricing (European Calls) | p. 200 |
| Monte Carlo Simulations | p. 204 |
| Option Pricing in a Tsallis World | p. 208 |
| Path Integrals: Integrating the Fat Tails into Option Pricing | p. 210 |
| Path Integrals: Integrating Path Dependence into Option Pricing | p. 216 |
| Microscopic Market Models | p. 221 |
| Important Questions | p. 221 |
| Are Markets Efficient? | p. 222 |
| Computer Simulation of Market Models | p. 226 |
| Two Classical Examples | p. 226 |
| Recent Models | p. 227 |
| The Minority Game | p. 246 |
| The Basic Minority Game | p. 247 |
| A Phase Transition in the Minority Game | p. 249 |
| Relation to Financial Markets | p. 250 |
| Spin Glasses and an Exact Solution | p. 252 |
| Extensions of the Minority Game | p. 255 |
| Theory of Stock Exchange Crashes | p. 259 |
| Important Questions | p. 259 |
| Examples | p. 260 |
| Earthquakes and Material Failure | p. 264 |
| Stock Exchange Crashes | p. 270 |
| What Causes Crashes? | p. 276 |
| Are Crashes Rational? | p. 278 |
| What Happens After a Crash? | p. 279 |
| A Richter Scale for Financial Markets | p. 285 |
| Risk Management | p. 289 |
| Important Questions | p. 289 |
| What is Risk? | p. 290 |
| Measures of Risk | p. 291 |
| Volatility | p. 292 |
| Generalizations of Volatility and Moments | p. 293 |
| Statistics of Extremal Events | p. 295 |
| Value at Risk | p. 297 |
| Coherent Measures of Risk | p. 303 |
| Expected Shortfall | p. 306 |
| Types of Risk | p. 308 |
| Market Risk | p. 308 |
| Credit Risk | p. 308 |
| Operational Risk | p. 311 |
| Liquidity Risk | p. 314 |
| Risk Management | p. 314 |
| Risk Management Requires a Strategy | p. 314 |
| Limit Systems | p. 315 |
| Hedging | p. 316 |
| Portfolio Insurance | p. 317 |
| Diversification | p. 318 |
| Strategic Risk Management | p. 323 |
| Economic and Regulatory Capital for Financial Institutions | p. 325 |
| Important Questions | p. 325 |
| Economic Capital | p. 326 |
| What Determines Economic Capital? | p. 326 |
| How Calculate Economic Capital? | p. 327 |
| How Allocate Economic Capital? | p. 328 |
| Economic Capital as a Management Tool | p. 331 |
| The Regulatory Framework | p. 333 |
| Why Banking Regulation? | p. 333 |
| Risk-Based Capital Requirements | p. 334 |
| Basel I: Regulation of Credit Risk | p. 336 |
| Internal Models | p. 338 |
| Basel II: The New International Capital Adequacy Framework | p. 341 |
| Outlook: Basel III and Basel IV | p. 358 |
| Appendix | p. 359 |
| Notes and References | p. 364 |
| Index | p. 375 |
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