Contents
1. Introduction
2. Financial Markets
2.1 Market price formation
2.2 Returns and dividends
2.2.1 Simple and compounded returns
2.2.2 Dividend effects
2.3 Market Efficiency
2.3.1 Arbitrage
2.3.2 Efficient market hypothesis
2.3.2.1 The idea
2.3.2.2 The critique
2.4 Pathways for further reading
2.5 Exercises
3. Probability distributions
3.1 Basic definitions
3.2 Some important distributions
3.3 Stable distributions and scale invariance
3.4 References for further reading
3.5 Exercises
4. Stochastic processes
4.1 Markov process
4.2 Brownian motion
4.3 Stochastic differential equation. Ito’s lemma
4.4 Stochastic integral
4.5 Martingales
4.6 References for further reading
4.7 Exercises
5. Time series analysis
5.1 Autoregressive and moving average models
5.2 Trends and seasonality
5.3 Conditional heteroskedascisity
5.4 Multivariate time series
5.5 References for further reading and econometric software
5.6 Exercises
6. Fractals
6.1 Basic definitions
6.2 Multifractals
6.3 References for further reading
6.4 Exercises
7. Nonlinear dynamical systems
7.1 Motivation
7.2 Discrete systems: Logistic map
7.3 Continuous systems
7.4 Lorenz model
7.5 Pathways to chaos
7.6 Measuring chaos
7.7 References for further reading
7.8 Exercises
8. Scaling in financial time series
8.1 Introduction
8.2 Power laws in financial data
8.3 New developments
8.4 References for further reading
8.5 Exercises
9. Option Pricing
9.1 Financial derivatives
9.2 General properties of options
9.3 Binomial trees
9.4 Black-Scholes theory
9.5 References for further reading
9.6 Appendix. The invariant of the arbitrage-free portfolio
9.7 Exercises
10. Portfolio management
10.1 Portfolio selection
10.2 Capital asset pricing model
10.3 Arbitrage pricing theory
10.4 Arbitrage trading strategies
10.5 References for further reading
10.6 Exercises
11. Market risk measurement
11.1 Risk measures
11.2 Calculating risk
11.3 References for further reading
11.4 Exercises
12. Agent-based modeling of financial markets
12.1 Introduction
12.2 Adaptive equilibrium models
12.3 Non-equilibrium price models
12.4 Modeling of observable variables
12.5 References for further reading
12.6 Exercises