Statistical Methods for Financial Engineering

Statistical Methods for Financial Engineering

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Features

  • Explains how to use numerous statistical techniques, such as Monte Carlo methods, nonparametric estimation, maximum likelihood techniques, and particle filters, to address financial questions, including hedging, interest rate modeling, option pricing, and credit risk modeling
  • Describes the validation of stochastic models
  • Requires no prior financial or stochastic calculus background
  • Offers material suitable for a graduate-level course on statistical methods in finance or financial engineering
  • Provides proofs and advanced topics, such as probability distributions and parameter estimation, in the appendices
  • Includes MATLAB and R programs on the author’s website, enabling practitioners to use the techniques in the context of real-life financial problems

Summary

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.