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1st Edition

Statistics for Finance




ISBN 9781482228991
Published April 16, 2015 by Chapman and Hall/CRC
384 Pages 63 B/W Illustrations

 
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Book Description

Statistics for Finance develops students’ professional skills in statistics with applications in finance. Developed from the authors’ courses at the Technical University of Denmark and Lund University, the text bridges the gap between classical, rigorous treatments of financial mathematics that rarely connect concepts to data and books on econometrics and time series analysis that do not cover specific problems related to option valuation.

The book discusses applications of financial derivatives pertaining to risk assessment and elimination. The authors cover various statistical and mathematical techniques, including linear and nonlinear time series analysis, stochastic calculus models, stochastic differential equations, Itō’s formula, the Black–Scholes model, the generalized method-of-moments, and the Kalman filter. They explain how these tools are used to price financial derivatives, identify interest rate models, value bonds, estimate parameters, and much more.

This textbook will help students understand and manage empirical research in financial engineering. It includes examples of how the statistical tools can be used to improve value-at-risk calculations and other issues. In addition, end-of-chapter exercises develop students’ financial reasoning skills.

Table of Contents

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

Problems appear at the end of each chapter.

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Author(s)

Biography

Erik Lindström is an associate professor in the Centre for Mathematical Sciences at Lund University. His research ranges from statistical methodology (primarily time series analysis in discrete and continuous time) to financial mathematics as well as problems related to energy markets. He earned a PhD in mathematical statistics from Lund Institute of Technology/Lund University.

Henrik Madsen is a professor and head of the Section for Dynamical Systems in the Department for Applied Mathematics and Computer Sciences at the Technical University of Denmark. An elected member of the ISI and IEEE, he has authored or co-authored 480 papers and 11 books in areas including mathematical statistics, time series analysis, and the integration of renewables in electricity markets. He earned a PhD in statistics from the Technical University of Denmark.

Jan Nygaard Nielsen is a principal architect at Netcompany, a Danish IT and business consulting firm. He earned a PhD from the Technical University of Denmark.

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