1. Introduction
1.1 Motivation
1.2 Why Physicists? Why Models of Physics?
1.3 Physics and Finance - Historical
1.4 Aims of this Book
2. Basic Information on Capital Markets
2.1 Risk
2.2 Assets
2.3 Three Important Derivatives
2.3.1 Forward Contracts
2.3.2 Futures Contract
2.3.3 Options
2.4 Derivative Positions
2.5 Market Actors
2.6 Price Formation at Organized Exchanges
2.6.1 Order Types
2.6.2 Price Formation by Auction
2.6.3 Continuous Trading: The XETRA Computer Trading System
3. Random Walks in Finance and Physics
3.1 Important Questions
3.2 Bachelier's "Theorie de la Speculation"
3.2.1 Preliminaries
3.2.2 Probabilities in Stock Market Operations
3.2.3 Empirical Data on Successful Operations in Stock Markets
3.2.4 Biographical Information on Louis Bachelier (1870-1946)
3.3 Einstein's Theory of Brownian Motion
3.3.1 Osmotic Pressure and Diffusion in Suspensions
3.3.2 Brownian Motion
3.4 Experimental Situation
3.4.1 Financial Data
3.4.2 Perrin's Observations of Brownian Motion
3.4.3 One-Dimensional Motion of Electronic Spins
4. The Black-Scholes Theory of Option Prices
4.1 Important Questions
4.2 Assumptions and Notation
4.2.1 Assumptions
4.2.2 Notation
4.3 Prices for Derivatives
4.3.1 Forward Price
4.3.2 Futures Price
4.3.3 Limits on Option Prices
4.4 Modeling Fluctuations of Financial Assets
4.4.1 Stochastic Processes
4.4.2 The Standard Model of Stock Prices
4.4.3 The It6 Lemma
4.4.4 Log-normal Distributions for Stock Prices
4.5 Option Pricing
4.5.1 The Black-Scholes Differential Equation
4.5.2 Solution of the Black-Scholes Equation
4.5.3 Risk-Neutral Valuation
4.5.4 American Options
4.5.5 The Greeks
4.5.6 Synthetic Replication of Options
4.5.7 Implied Volatility
4.5.8 Volatility Indices
5. Scaling in Financial Data and in Physics
5.1 Important Questions
5.2 Stationarity of Financial Markets
5.3 Geometric Brownian Motion
5.3.1 Price Histories
5.3.2 Statistical Independence of Price Fluctuations
5.3.3 Statistics of Price Changes of Financial Assets
5.4 Pareto Laws and Levy Flights
5.4.1 Definitions
5.4.2 The Gaussian Distribution and the Central Limit Theorem
5.4.3 Levy Distributions
5.4.4 Non-stable Distributions with Power Laws
5.5 Scaling, Levy Distributions, and Levy Flights in Nature
5.5.1 Criticality and Self-Organized Criticality, Diffusion and Superdiffusion
5.5.2 Micelles
5.5.3 Fluid Dynamics
5.5.4 The Dynamics of the Human Heart
5.5.5 Amorphous Semiconductors and Glasses
5.5.6 Superposition of Chaotic Processes
5.5.7 Tsallis Statistics
5.6 New Developments: Non-stable Scaling, Temporal and Interasset Correlations in Financial Markets
5.6.1 Non-stable Scaling in Financial Asset Returns
5.6.2 The Breadth of the Market
5.6.3 Non-linear Temporal Correlations
5.6.4 Stochastic Volatility Models
5.6.5 Cross-Correlations in Stock Markets
6. Turbulence and Foreign Exchange Markets
6.1 Important Questions
6.2 Turbulent Flows
6.2.1 Phenomenology
6.2.2 Statistical Description of Turbulence
6.2.3 Relation to Non-extensive Statistical Mechanics
6.3 Foreign Exchange Markets
6.3.1 Why Foreign Exchange Markets?
6.3.2 Empirical Results
6.3.3 Stochastic Cascade Models
6.3.4 The Multifractal Interpretation
7. Derivative Pricing Beyond Blaek-Scholes
7.1 Important Questions
7.2 An Integral Framework for Derivative Pricing
7.3 Application to Forward Contracts
7.4 Option Pricing (European Calls)
7.5 Monte Carlo Simulations
7.6 Option Pricing in a Tsallis World
7.7 Path Integrals: Integrating the Fat Tails into Option Pricing
7.8 Path Integrals: Integrating Path Dependence into Option Pricing
8. Microscopic Market Models
8.1 Important Questions
8.2 Are Markets Efficient?
8.3 Computer Simulation of Market Models
8.3.1 Two Classical Examples
8.3.2 Recent Models
8.4 The Minority Game
8.4.1 The Basic Minority Game
8.4.2 A Phase Transition in the Minority Game
8.4.3 Relation to Financial Markets
8.4.4 Spin Glasses and an Exact Solution
8.4.5 Extensions of the Minority Game
9. Theory of Stock Exchange Crashes
9.1 Important Questions
9.2 Examples
9.3 Earthquakes and Material Failure
9.4 Stock Exchange Crashes
9.5 What Causes Crashes?
9.6 Are Crashes Rational?
9.7 What Happens After a Crash?
9.8 A Richter Scale for Financial Markets
10. Risk Management
10.1 Important Questions
10.2 What is Risk?
10.3 Measures of Risk
10.3.1 Volatility
10.3.2 Generalizations of Volatility and Moments
10.3.3 Statistics of Extremal Events
10.3.4 Value at Risk
10.3.5 Coherent Measures of Risk
10.3.6 Expected Shortfall
10.4 Types of Risk
10.4.1 Market Risk
10.4.2 Credit Risk
10.4.3 Operational Risk
10.4.4 Liquidity Risk
10.5 Risk Management
10.5.1 Risk Management Requires a Strategy
10.5.2 Limit Systems
10.5.3 Hedging
10.5.4 Portfolio Insurance
10.5.5 Diversification
10.5.6 Strategic Risk Management
11. Economic and Regulatory Capital for Financial Institutions
11.1 Important Questions
11.2 Economic Capital
11.2.1 What Determines Economic Capital?
11.2.2 How Calculate Economic Capital?
11.2.3 How Allocate Economic Capital?
11.2.4 Economic Capital as a Management Tool
11.3 The Regulatory Framework
11.3.1 Why Banking Regulation?
11.3.2 Risk-Based Capital Requirements
11.3.3 Basel Ⅰ: Regulation of Credit Risk
11.3.4 Internal Models
11.3.5 Basel Ⅱ: The New International Capital Adequacy Framework
11.3.6 Outlook: Basel Ⅲ and Basel Ⅳ
Appendix
Notes and References
Index
