#Introduction
Introduction to financial derivatives
Financial derivatives—what’s the big deal?
Stylized facts
Overview
#Fundamentals
Interest rates
Cash flows
Continuously compounded interest rates
Interest rate options: caps and floors
#Discrete-Time Finance
The binomial one period model
The one period model
The multi period model
#Linear Time Series Models
Introduction
Linear systems in the time domain
Linear stochastic processes
Linear processes with a rational transfer function
Autocovariance functions
Prediction in linear processes
#Non-Linear Time Series Models
Introduction
The aim of model building
Qualitative properties of the models
Parameter estimation
Parametric models
Model identification
Prediction in non-linear models
Applications of non-linear models
#Kernel Estimators in Time Series Analysis
Non-parametric estimation
Kernel estimators for time series
Kernel estimation for regression
Applications of kernel estimators
#Stochastic Calculus
Dynamical systems
The Wiener process
Stochastic Integrals
Itō stochastic calculus
Extensions to jump processes
#Stochastic Differential Equations
Stochastic differential equations
Analytical solution methods
Feynman–Kac representation
Girsanov measure transformation
#Continuous-Time Security Markets
From discrete to continuous time
Classical arbitrage theory
Modern approach using martingale measures
Pricing
Model extensions
Computational methods
#Stochastic Interest Rate Models
Gaussian one-factor models
A general class of one-factor models
Time-dependent models
Multifactor and stochastic volatility models
#The Term Structure of Interest Rates
Basic concepts
The classical approach
The term structure for specific models
Heath–Jarrow–Morton framework
Credit models
Estimation of the term structure—curve-fitting
#Discrete-Time Approximations
Stochastic Taylor expansion
Convergence
Discretization schemes
Multilevel Monte Carlo
Simulation of SDEs
#Parameter Estimation in Discretely Observed SDEs
Introduction
High frequency methods
Approximate methods for linear and non-linear models
State dependent diffusion term
MLE for non-linear diffusions
Generalized method of moments (GMM)
Model validation for discretely observed SDEs
#Inference in Partially Observed Processes
Introduction
The model
Exact filtering
Conditional moment estimators
Kalman filter
Approximate filters
State filtering and prediction
The unscented Kalman filter
A maximum likelihood method
Sequential Monte Carlo filters
Application of non-linear filters
Appendix A: Projections in Hilbert Spaces
Appendix B: Probability Theory
Bibliography
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