This book introduces physics students to concepts and methods of finance. Despite being perceived as quite distant from physics, finance shares a number of common methods and ideas, usually related to noise and uncertainties. Juxtaposing the key methods to applications in both physics and finance articulates both differences and common features, this gives students a deeper understanding of the underlying ideas. Moreover, they acquire a number of useful mathematical and computational tools, such as stochastic differential equations, path integrals, Monte-Carlo methods, and basic cryptology. Each chapter ends with a set of carefully designed exercises enabling readers to test their comprehension.
Author(s): Volker Ziemann
Series: Undergraduate Lecture Notes in Physics
Publisher: Springer
Year: 2021
Language: English
Pages: x+286
Preface
Contents
1 Introduction
References
2 Concepts of Finance
2.1 Stocks and Other Tradeable Goods
2.2 Hedging and Shorting
2.3 Derivatives
2.4 Money
2.5 Discounting and Liquidity
2.6 Efficient Market Hypothesis
2.7 Theoretical Markets
2.8 Market Participants
3 Portfolio Theory and CAPM
3.1 Variational Calculus and Lagrange Multipliers
3.2 Portfolio with Risky Assets Only
3.3 Portfolio with a Risk-Free Asset
3.4 Capital Market Line and Sharpe Ratio
3.5 Capital Asset Pricing Model
3.6 Valuation
Exercises
References
4 Stochastic Processes
4.1 Binomial Trees
4.2 Wiener Process
4.3 Diffusion Processes and Green's Functions
4.4 Stochastic Integrals and Ito's Lemma
4.5 Master and Fokker-Planck Equations
4.6 A First Look at Option Pricing
4.7 Digression on Expectation Values
References
5 Black-Scholes Differential Equation
5.1 Derivation
5.2 The Solution
5.3 Risk-Neutrality and Martingales
5.4 Dynamic Hedging
5.5 Other Examples
References
6 The Greeks and Risk Management
6.1 The Greeks
6.2 Volatility Smile
6.3 Value at Risk
6.4 Tailoring Risk to One's Desire
References
7 Regression Models and Hypothesis Testing
7.1 Regression and Linear Fitting
7.2 Examples
7.3 Goodness-of-Fit R2
7.4 χ2-Distribution
7.5 Student's t-Distribution
7.6 Hypothesis Testing and p-Values
7.7 F-Test
7.8 Parsimony
References
8 Time Series
8.1 Trend and Seasonality
8.2 MA, AR, and ARMA
8.3 Auto-Covariance and Autocorrelation
8.4 Partial Autocorrelation Function
8.5 Determining the Model Coefficients
8.6 Box-Jenkins
8.7 Forecasting
8.8 Zoo of Models
References
9 Bubbles, Crashes, Fat Tails and Lévy-Stable Distributions
9.1 Historical Bubbles and Crashes
9.2 Bubble-Crash Mechanisms
9.3 Behavioral Economics
9.4 Fat-Tailed Distributions
9.5 Power Laws
9.6 Fractals
9.7 Sums of Random Numbers
9.8 Lévy-Stable Distributions
9.9 Extreme-Value Theory
9.10 Finite-Time Divergence and Log-Periodic Oscillations
References
10 Quantum Finance and Path Integrals
10.1 Quantum Mechanics
10.2 Black-Scholes Hamiltonian
10.3 Pricing Kernel
10.4 Barrier Options
10.5 Path Integrals in Quantum Mechanics
10.6 Path Integrals in Finance
10.7 Monte-Carlo Integration
10.8 Numerical Evaluation of Path Integrals
References
11 Optimal Control Theory
11.1 Macroeconomic Models
11.2 Control and Feedback
11.3 Hamiltonian Mechanics
11.4 Hamiltonians for Optimal Control
11.5 Donkey Revisited
11.6 Linear Quadratic Regulators
11.7 Controlling the Robinson-Crusoe Economy
References
12 Cryptocurrencies
12.1 Information, Probabilities, and Codes
12.2 Relation to the Thermodynamic Entropy
12.3 Moving Information Through Discrete Channels
12.4 Continuous Information Channels
12.5 Cryptography Fundamentals
12.6 Early Public-Key Systems
12.7 Elliptic Curve Cryptography
12.8 Bitcoins and Blockchains
12.9 Ethereum and Smart Contracts
12.10 Quantum Computing
References
13 Solutions for Selected Exercises
Appendix A On the Independence of Certain Random Variables
Appendix B Software
B.1 Markowitz Simulation
B.2 Functions for Call and Put Options
B.3 Dynamic Hedging Simulation
B.4 Cantor, Koch, and Mandelbrot
B.5 Metropolis-Hastings Algorithm
B.6 Numerical Path Integrals
B.7 Macroeconomic Models
B.8 The Donkey's Solution
B.9 Character Frequency in the King James Bible
B.10 Entropy of Audio Files
B.11 Elliptic Curves
B.12 Ethereum Contract Test Environment
Index
