Home Page Icon
Home Page
Table of Contents for
Statistics for Finance
Close
Statistics for Finance
by Erik Lindström, Henrik Madsen, Jan Nygaard Nielsen
Statistics for Finance
Preliminaries
Preface
Author biographies
Erik Lindström
Henrik Madsen
Jan Nygaard Nielsen
Chapter 1 Introduction
1.1 Introduction to financial derivatives
1.2 Financial derivatives—what's the big deal?
1.3 Stylized facts
1.3.1 No autocorrelation in returns
1.3.2 Unconditional heavy tails
1.3.3 Gain/loss asymmetry
1.3.4 Aggregational Gaussianity
1.3.5 Volatility clustering
1.3.6 Conditional heavy tails
1.3.7 Significant autocorrelation for absolute returns
1.3.8 Leverage effects
1.4 Overview
Figure 1.1
Figure 1.1
Figure 1.2
Figure 1.3
Figure 1.4
Figure 1.5
Figure 1.6
Figure 1.7
Figure 1.8
Table 1.1
Table 1.1
Chapter 2 Fundamentals
2.1 Interest rates
2.1.1 Future and present value of a single payment
2.1.2 Annuities
2.1.3 Future value of an annuity
2.1.4 Present value of a unit annuity
2.2 Cash flows
2.3 Continuously compounded interest rates
2.4 Interest rate options: caps and floors
2.5 Notes
2.6 Problems
Figure 2.1
Figure 2.1
Figure 2.2
Figure 2.3
Figure 2.4
Figure 2.5
Table 2.1
Table 2.1
Chapter 3 Discrete time finance
3.1 The binomial one-period model
3.2 One-period model
3.2.1 Risk-neutral probabilities
3.2.2 Complete and incomplete markets
3.3 Multiperiod model
3.3.1 σ-algebras and information sets
3.3.2 Financial multiperiod markets
3.3.3 Martingale measures
3.4 Notes
3.5 Problems
Figure 3.1
Figure 3.1
Figure 3.2
Figure 3.3
Figure 3.4
Figure 3.5
Chapter 4 Linear time series models
4.1 Introduction
4.2 Linear systems in the time domain
4.3 Linear stochastic processes
4.4 Linear processes with a rational transfer function
4.4.1 ARMA process
4.4.2 ARIMA process
4.4.3 Seasonal models
4.5 Autocovariance functions
4.5.1 Autocovariance function for ARMA processes
4.6 Prediction in linear processes
4.7 Problems
Figure 4.1
Figure 4.1
Figure 4.2
Chapter 5 Nonlinear time series models
5.1 Introduction
5.2 Aim of model building
5.3 Qualitative properties of the models
5.3.1 Volterra series expansion
5.3.2 Generalized transfer functions
5.4 Parameter estimation
5.4.1 Maximum likelihood estimation
5.4.1.1 Cramér-Rao bound
5.4.1.2 The likelihood ratio test
5.4.2 Quasi-maximum likelihood
5.4.3 Generalized method of moments
5.4.3.1 GMM and moment restrictions
5.4.3.2 Standard error of the estimates
5.4.3.3 Estimation of the weight matrix
5.4.3.4 Nested tests for model reduction
5.5 Parametric models
5.5.1 Threshold and regime models
5.5.1.1 Self-exciting threshold AR (SETAR)
5.5.1.2 Self-exciting threshold ARMA (SETARMA)
5.5.1.3 Open loop threshold AR (TARSO)
5.5.1.4 Smooth threshold AR (STAR)
5.5.1.5 Hidden Markov models and related models
5.5.2 Models with conditional heteroscedasticity (ARCH)
5.5.2.1 ARCH regression model
5.5.2.2 GARCH model
5.5.2.3 EGARCH model
5.5.2.4 FIGARCH model
5.5.2.5 ARCH-M model
5.5.2.6 SW-ARCH model
5.5.2.7 General remarks on ARCH models
5.5.2.8 Multivariate GARCH models
5.5.3 Stochastic volatility models
5.6 Model identification
5.7 Prediction in nonlinear models
5.8 Applications of nonlinear models
5.8.1 Electricity spot prices
5.8.2 Comparing ARCH models
5.9 Problems
Figure 5.1
Figure 5.1
Figure 5.2
Figure 5.3
Figure 5.4
Chapter 6 Kernel estimators in time series analysis
6.1 Non-parametric estimation
6.2 Kernel estimators for time series
6.2.1 Introduction
6.2.2 Kernel estimator
6.2.3 Central limit theorems
6.3 Kernel estimation for regression
6.3.1 Estimator for regression
6.3.2 Product kernel
6.3.3 Non-parametric estimation of the pdf
6.3.4 Non-parametric LS
6.3.5 Bandwidth
6.3.6 Selection of bandwidth — cross validation
6.3.7 Variance of the non-parametric estimates
6.4 Applications of kernel estimators
6.4.1 Non-parametric estimation of the conditional mean and variance
6.4.2 Non-parametric estimation of non-stationarity — an example
6.4.3 Non-parametric estimation of dependence on external variables — an example
6.4.4 Non-parametric GARCH models
6.5 Notes
Figure 6.1
Figure 6.1
Figure 6.2
Figure 6.3
Figure 6.4
Figure 6.5
Figure 6.6
Figure 6.7
Figure 6.8
Chapter 7 Stochastic calculus
7.1 Dynamical systems
7.2 The Wiener process
7.3 Stochastic Integrals
7.4 Itō stochastic calculus
7.5 Extensions to jump processes
7.6 Problems
Chapter 8 Stochastic differential equations
8.1 Stochastic Differential Equations
8.1.1 Existence and uniqueness
8.1.2 Itō formula
8.1.3 Multivariate SDEs
8.1.4 Stratonovitch SDE
8.2 Analytical solution methods
8.2.1 Linear, univariate SDEs
8.3 Feynman-Kac representation
8.4 Girsanov measure transformation
8.4.1 Measure theory
8.4.2 Radon–Nikodym theorem
8.4.3 Girsanov transformation
8.4.4 Maximum likelihood estimation for continuously observed diffusions
8.5 Notes
8.6 Problems
Chapter 9 Continuous-time security markets
9.1 From discrete to continuous time
9.2 Classical arbitrage theory
9.2.1 Black-Scholes formula
9.2.2 Hedging strategies
9.2.2.1 Quadratic hedging
9.3 Modern approach using martingale measures
9.4 Pricing
9.5 Model extensions
9.6 Computational methods
9.6.1 Fourier methods
9.7 Problems
Figure 9.1
Figure 9.1
Figure 9.2
Chapter 10 Stochastic interest rate models
10.1 Gaussian one-factor models
10.1.1 Merton model
10.1.2 Vasicek model
10.2 A general class of one-factor models
10.3 Time-dependent models
10.3.1 Ho–Lee
10.3.2 Black–Derman–Toy
10.3.3 Hull–White
10.3.3.1 CIR++model
10.4 Multifactor and stochastic volatility models
10.4.1 Stochastic volatility models
10.4.2 Affine Term Structure models
10.5 Notes
10.6 Problems
Figure 10.1
Figure 10.1
Figure 10.2
Table 10.1
Table 10.1
Chapter 11 Term structure of interest rates
11.1 Basic concepts
11.1.1 Known interest rates
11.1.2 Discrete dividends
11.1.3 Yield curve
11.1.4 Stochastic interest rates
11.2 Classical approach
11.2.1 Exogenous specification of the market price of risk
11.2.2 Illustrative example
11.2.3 Modern approach
11.3 Term structure for specific models
11.3.1 Example 1: The Vasicek model
11.3.2 Example 2: The Ho–Lee model
11.3.3 Example 3: The Cox–Ingersoll–Ross model
11.3.4 Multifactor models
11.4 Heath–Jarrow–Morton framework
11.5 Credit models
11.5.1 Intensity models
11.6 Estimation of the term structure — curve-fitting
11.6.1 Polynomial methods
11.6.2 Decay functions
11.6.3 Nelson–Siegel method
11.7 Notes
11.8 Problems
Figure 11.1
Figure 11.1
Figure 11.2
Figure 11.3
Figure 11.4
Figure 11.5
Table 11.1
Table 11.1
Table 11.2
Chapter 12 Discrete time approximations
12.1 Stochastic Taylor expansion
12.2 Convergence
12.3 Discretization schemes
12.3.1 Strong Taylor approximations
12.3.1.1 Explicit Euler scheme
12.3.1.2 Milstein scheme
12.3.1.3 The order 1.5 strong Taylor scheme
12.3.2 Weak Taylor approximations
12.3.2.1 The order 2.0 weak Taylor scheme
12.3.3 Exponential approximation
12.4 Multilevel Monte Carlo
12.5 Simulation of SDEs
Figure 12.1
Figure 12.1
Figure 12.2
Figure 12.3
Chapter 13 Parameter estimation in discretely observed SDEs
13.1 Introduction
13.2 High frequency methods
13.3 Approximate methods for linear and non-linear models
13.4 State dependent diffusion term
13.4.1 A transformation approach
13.5 MLE for non-linear diffusions
13.5.1 Simulation-based estimators
13.5.1.1 Jump diffusions
13.5.2 Numerical methods for the Fokker-Planck equation 273
13.5.3 Series expansion
13.6 Generalized method of moments
13.6.1 GMM and moment restrictions
13.7 Model validation for discretely observed SDEs
13.7.1 Generalized Gaussian residuals
13.7.1.1 Case study
13.8 Problems
Figure 13.1
Figure 13.1
Figure 13.2
Figure 13.3
Figure 13.4
Figure 13.5
Chapter 14 Inference in partially observed processes
14.1 Introduction
14.2 Model
14.3 Exact filtering
14.3.1 Prediction
14.3.1.1 Scalar case
14.3.1.2 General case
14.3.2 Updating
14.4 Conditional moment estimators
14.4.1 Prediction and updating
14.5 Kalman filter
14.6 Approximate filters
14.6.1 Truncated second order filter
14.6.2 Linearized Kalman filter
14.6.3 Extended Kalman filter
14.6.4 Statistically linearized filter
14.6.5 Non-linear models
14.6.6 Linear time-varying models
14.6.7 Linear time-invariant models
14.6.8 Case: Affine term structure models
14.7 State filtering and prediction
14.7.1 Linear models
14.7.1.1 Linear time-varying models
14.7.1.2 Linear time-invariant models
14.7.2 The system equation in discrete time
14.7.3 Non-linear models
14.8 Unscented Kalman Filter
14.9 A maximum likelihood method
14.10 Sequential Monte Carlo filters
14.10.1 Optimal filtering
14.10.2 Bootstrap filter
14.10.3 Parameter estimation
14.11 Application of non-linear filters
14.11.1 Sequential calibration of options
14.11.2 Computing Value at Risk in a stochastic volatility model
14.11.3 Extended Kalman filtering applied to bonds
Data description
14.11.4 Case 1: A Wiener process
14.11.5 Case 2: The Vasicek model
14.12 Problems
Figure 14.1
Figure 14.1
Figure 14.2
Figure 14.3
Figure 14.4
Figure 14.5
Figure 14.6
Figure 14.7
Figure 14.8
Table 14.1
Table 14.1
Table 14.2
Table 14.3
Appendix A Projections in Hilbert spaces
A.1 Introduction
A.2 Hilbert spaces
A.3 The projection theorem
A.3.1 Prediction equations
A.4 Conditional expectation and linear projections
A.5 Kalman filter
A.6 Projections in ℝn
Figure A.1
Figure A.1
Appendix B Probability theory
B.1 Measures and σ-algebras
B.2 Partitions and information
B.3 Conditional expectation
B.4 Notes
Bibliography
Search in book...
Toggle Font Controls
Playlists
Add To
Create new playlist
Name your new playlist
Playlist description (optional)
Cancel
Create playlist
Sign In
Email address
Password
Forgot Password?
Create account
Login
or
Continue with Facebook
Continue with Google
Sign Up
Full Name
Email address
Confirm Email Address
Password
Login
Create account
or
Continue with Facebook
Continue with Google
Next
Next Chapter
Statistics for Finance
Add Highlight
No Comment
..................Content has been hidden....................
You can't read the all page of ebook, please click
here
login for view all page.
Day Mode
Cloud Mode
Night Mode
Reset