Statistical Methods for Financial Engineering (Hardback) book cover

Statistical Methods for Financial Engineering

By Bruno Remillard

© 2013 – Chapman and Hall/CRC

496 pages | 61 B/W Illus.

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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.


"… 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

Table of Contents

Black-Scholes Model

The Black-Scholes Model

Dynamic Model for an Asset

Estimation of Parameters

Estimation Errors

Black-Scholes Formula


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


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


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


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


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

Subject Categories

BISAC Subject Codes/Headings:
MATHEMATICS / Probability & Statistics / General