Quantitative Finance for Physicists

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