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Statistical Methods for Financial Engineering




ISBN 9781439856949
Published April 5, 2013 by Chapman and Hall/CRC
496 Pages 61 B/W Illustrations

 
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Book Description

While many financial engineering books are available, the statistical aspects behind the implementation of stochastic models used in the field are often overlooked or restricted to a few well-known cases. Statistical Methods for Financial Engineering guides current and future practitioners on implementing the most useful stochastic models used in financial engineering.

After introducing properties of univariate and multivariate models for asset dynamics as well as estimation techniques, the book discusses limits of the Black-Scholes model, statistical tests to verify some of its assumptions, and the challenges of dynamic hedging in discrete time. It then covers the estimation of risk and performance measures, the foundations of spot interest rate modeling, Lévy processes and their financial applications, the properties and parameter estimation of GARCH models, and the importance of dependence models in hedge fund replication and other applications. It concludes with the topic of filtering and its financial applications.

This self-contained book offers a basic presentation of stochastic models and addresses issues related to their implementation in the financial industry. Each chapter introduces powerful and practical statistical tools necessary to implement the models. The author not only shows how to estimate parameters efficiently, but he also demonstrates, whenever possible, how to test the validity of the proposed models. Throughout the text, examples using MATLAB® illustrate the application of the techniques to solve real-world financial problems. MATLAB and R programs are available on the author’s website.

Table of Contents

Black-Scholes Model
The Black-Scholes Model
Dynamic Model for an Asset
Estimation of Parameters
Estimation Errors
Black-Scholes Formula
Greeks
Estimation of Greeks using the Broadie-Glasserman Methodologies

Multivariate Black-Scholes Model
Black-Scholes Model for Several Assets
Estimation of Parameters
Estimation Errors
Evaluation of Options on Several Assets
Greeks

Discussion of the Black-Scholes Model
Critiques of the Model
Some Extensions of the Black-Scholes Model
Discrete Time Hedging
Optimal Quadratic Mean Hedging

Measures of Risk and Performance
Measures of Risk
Estimation of Measures of Risk by Monte Carlo Methods
Measures of Risk and the Delta-Gamma Approximation
Performance Measures

Modeling Interest Rates
Introduction
Vasicek Model
Cox-Ingersoll-Ross (CIR) Model
Other Models for the Spot Rates

Lévy Models
Complete Models
Stochastic Processes with Jumps
Lévy Processes
Examples of Lévy Processes
Change of Distribution
Model Implementation and Estimation of Parameters

Stochastic Volatility Models
GARCH Models
Estimation of Parameters
Duan Methodology of Option Pricing
Stochastic Volatility Model of Hull-White
Stochastic Volatility Model of Heston

Copulas and Applications
Weak Replication of Hedge Funds
Default Risk
Modeling Dependence
Bivariate Copulas
Measures of Dependence
Multivariate Copulas
Families of Copulas
Estimation of the Parameters of Copula Models
Tests of Independence
Tests of Goodness-of-Fit
Example of Implementation of a Copula Model

Filtering
Description of the Filtering Problem
Kalman Filter
IMM Filter
General Filtering Problem
Computation of the Conditional Densities
Particle Filters

Applications of Filtering
Estimation of ARMA Models
Regime-Switching Markov Models
Replication of Hedge Funds

Appendix A: Probability Distributions
Appendix B: Estimation of Parameters

Index

Suggested Reading, Exercises, Assignment Questions, Appendices, and References appear at the end of each chapter.

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Reviews

"… an interesting book with many features that are not easily found elsewhere. … libraries will certainly want to acquire a copy. … there are plenty of points at which even experts will pick up new ideas."
—J. Michael Steele, Journal of the American Statistical Association, September 2014, Vol. 109

"… a successful attempt to cover the main statistical tools and methods used for practical purposes in financial engineering. In contrast to those few existing books on the implementation of stochastic models in financial markets, this monograph covers a vast number of topics from mathematical finance … can be used by practitioners as a reference book, but also it can serve as an excellent textbook for training quantitative analysts …"
Mathematical Reviews, September 2014