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 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

With more and more physicists and physics students exploring the possibility of utilizing their advanced math skills for a career in the finance industry, this much-needed book quickly introduces them to fundamental and advanced finance principles and methods.

Quantitative Finance for Physicists provides a short, straightforward introduction for those who already have a background in physics. Find out how fractals, scaling, chaos, and other physics concepts are useful in analyzing financial time series. Learn about key topics in quantitative finance such as option pricing, portfolio management, and risk measurement. This book provides the basic knowledge in finance required to enable readers with physics backgrounds to move successfully into the financial industry.

• Short, self-contained book for physicists to master basic concepts and quantitative methods of finance
• Growing field—many physicists are moving into finance positions because of the high-level math required
• Draws on the author's own experience as a physicist who moved into a financial analyst position

Physics students following a course on finance worldwide, students in econophysics and quantitative finance, physicists interested in moving into professional finance positions.