Book Content
Chapter 1 Elementary Financial Calculus
1.1 Motivating Examples
1.2 Cashflows, Interest Rates, Prices and Returns
1.3 Elementary Statistical Analysis of Returns
1.4 Financial Instruments
1.5 A Primer on Option Pricing
Chapter 2 Arbitrage Theory for the One-Period Model
2.1 Definitions and Preliminaries
2.2 Linear Pricing Measure
2.3 More on Arbitrage
2.4 Separation Theorems
2.5 No-Arbitrage and Martingale Measures
2.6 Arbitrage-Free Pricing of Contingent Claims
2.7 Construction of Martingale Measures: General Case
2.8 Complete Financial Markets
2.9 Notes and Further Reading
Chapter 3 Financial Models in Discrete Time
3.1 Adapted Stochastic Processes in Discrete Time
3.2 Martingales and Martingale Differences
3.3 Stationarity
3.4 Linear Processes and ARMA Models
3.5 The Frequency Domain
3.6 Estimation of ARMA Processes
3.7 (G)ARCH Models
3.8 Long-Memory Series
3.9 Notes and Further Reading
Chapter 4 Arbitrage Theory for the Multiperiod Model
4.1 Definitions and Preliminaries
4.2 Self-Financing Trading Strategies
4.3 No-Arbitrage and Martingale Measures
4.4 European Claims on Arbitrage-Free Markets
4.5 The Martingales Representation Theorem in Discrete Time
4.6 The Cox-Ross-Rubinstein Binomial Model
4.7 The Black-Scholes Formula
4.8 American Options and Contingent Claims
4.9 Notes and Further Reading
Chapter 5 Brownian Motion and Related Processes in Continuous Time
5.1 Preliminiaries
5.2 Brownian Motion
5.3 Continuity and Differentiability
5.4 Self-Similarity and Fractional Brownian Motion
5.5 Counting Processes
5.6 Levy Processes
5.7 Notes and Further Reading
Chapter 6 Itô Calculus
6.1 Total and Quadratic Variation
6.2 Stochastic Stieltjes Integration
6.3 The Itô Integral
6.4 Quadratic Covariation
6.5 Itô's Formula
6.6 Itô Processes
6.7 Diffusion Processes and Ergodicity
6.8 Numerical Approximations and Statistical Estimation
6.9 Notes and Further Reading
Chapter 7 The Black-Scholes Model
7.1 The Model and First Properties
7.2 Girsanov's Theorem
7.3 Equivalent Martingale Measure
7.4 Arbitrage-Free Pricing and Hedging Claims
7.5 The Delta Hedge
7.6 Time-Dependent Volatility
7.7 The Generalized Black-Scholes Model
7.8 Notes and Further Reading
Chapter 8
8.1 Limit Theory for Correlated Time Series
8.2 A Regression Model for Financial Time Series
8.3 Limit Theorems for Martingale Differences
8.4 Asymptotics
8.5 Density Estimation and Nonparametric Regression
8.6 The CLT for Linear Processes
8.7 Mixing Processes
8.8 Limit Theorems for Mixing Processes
8.9 Notes and Further Reading
Chapter 9 Special Topics
9.1 Copulas - and the 2008 Financial Crisis
9.2 Local Linear Nonparametric Regression
9.3 Change-Point Detection and Monitoring
9.4 Unit Roots and Random Walk
9.5 Notes and Further Reading