Book description
Presents a multitude of topics relevant to the quantitative finance community by combining the best of the theory with the usefulness of applications
Written by accomplished teachers and researchers in the field, this book presents quantitative finance theory through applications to specific practical problems and comes with accompanying coding techniques in R and MATLAB, and some generic pseudoalgorithms to modern finance. It also offers over 300 examples and exercises that are appropriate for the beginning student as well as the practitioner in the field.
The Quantitative Finance book is divided into four parts. Part One begins by providing readers with the theoretical backdrop needed from probability and stochastic processes. We also present some useful finance concepts used throughout the book. In part two of the book we present the classical BlackScholesMerton model in a uniquely accessible and understandable way. Implied volatility as well as local volatility surfaces are also discussed. Next, solutions to Partial Differential Equations (PDE), wavelets and Fourier transforms are presented. Several methodologies for pricing options namely, tree methods, finite difference method and Monte Carlo simulation methods are also discussed. We conclude this part with a discussion on stochastic differential equations (SDE’s). In the third part of this book, several new and advanced models from current literature such as general Lvy processes, nonlinear PDE's for stochastic volatility models in a transaction fee market, PDE's in a jumpdiffusion with stochastic volatility models and factor and copulas models are discussed. In part four of the book, we conclude with a solid presentation of the typical topics in fixed income securities and derivatives. We discuss models for pricing bonds market, marketable securities, credit default swaps (CDS) and securitizations.
 Classroomtested over a threeyear period with the input of students and experienced practitioners
 Emphasizes the volatility of financial analyses and interpretations
 Weaves theory with application throughout the book
 Utilizes R and MATLAB software programs
 Presents pseudoalgorithms for readers who do not have access to any particular programming system
 Supplemented with extensive authormaintained web site that includes helpful teaching hints, data sets, software programs, and additional content
Quantitative Finance is an ideal textbook for upperundergraduate and beginning graduate students in statistics, financial engineering, quantitative finance, and mathematical finance programs. It will also appeal to practitioners in the same fields.
Table of contents
 Cover
 List of Figures
 List of Tables

Part I: Stochastic Processes and Finance

1 Stochastic Processes
 1.1 Introduction
 1.2 General Characteristics of Stochastic Processes
 1.3 Variation and Quadratic Variation of Stochastic Processes
 1.4 Other More Specific Properties
 1.5 Examples of Stochastic Processes
 1.6 Borel—Cantelli Lemmas
 1.7 Central Limit Theorem
 1.8 Stochastic Differential Equation
 1.9 Stochastic Integral
 1.10 Maximization and Parameter Calibration of Stochastic Processes
 1.11 Quadrature Methods
 1.12 Problems
 2 Basics of Finance

1 Stochastic Processes

Part II: Quantitative Finance in Practice

3 Some Models Used in Quantitative Finance
 3.1 Introduction
 3.2 Assumptions for the Black–Scholes–Merton Derivation
 3.3 The B‐S Model
 3.4 Some Remarks on the B‐S Model
 3.5 Heston Model
 3.6 The Cox–Ingersoll–Ross (CIR) Model
 3.7 Stochastic (SABR) Model
 3.8 Methods for Finding Roots of Functions: Implied Volatility
 3.9 Some Remarks of Implied Volatility (Put–Call Parity)
 3.10 Hedging Using Volatility
 3.11 Functional Approximation Methods
 3.12 Problems
 4 Solving Partial Differential Equations
 5 Wavelets and Fourier Transforms

6 Tree Methods
 6.1 Introduction
 6.2 Tree Methods: the Binomial Tree
 6.3 Tree Methods for Dividend‐Paying Assets
 6.4 Pricing Path‐Dependent Options: Barrier Options
 6.5 Trinomial Tree Method and Other Considerations
 6.6 Markov Process
 6.7 Basic Elements of Operators and Semigroup Theory
 6.8 General Diffusion Process
 6.9 A General Diffusion Approximation Method
 6.10 Particle Filter Construction
 6.11 Quadrinomial Tree Approximation
 6.12 Problems

7 Approximating PDEs
 7.1 Introduction
 7.2 The Explicit Finite Difference Method
 7.3 The Implicit Finite Difference Method
 7.4 The Crank–Nicolson Finite Difference Method
 7.5 A Discussion About the Necessary Number of Nodes in the Schemes
 7.6 Solution of a Tridiagonal System
 7.7 Heston PDE
 7.8 Methods for Free Boundary Problems
 7.9 Methods for Pricing American Options
 7.10 Problems

8 Approximating Stochastic Processes
 8.1 Introduction
 8.2 Plain Vanilla Monte Carlo Method
 8.3 Approximation of Integrals Using the Monte Carlo Method
 8.4 Variance Reduction
 8.5 American Option Pricing with Monte Carlo Simulation
 8.6 Nonstandard Monte Carlo Methods
 8.7 Generating One‐Dimensional Random Variables by Inverting the cdf
 8.8 Generating One‐Dimensional Normal Random Variables
 8.9 Generating Random Variables: Rejection Sampling Method
 8.10 Generating Random Variables: Importance Sampling
 8.11 Problems

9 Stochastic Differential Equations
 9.1 Introduction
 9.2 The Construction of the Stochastic Integral
 9.3 Properties of the Stochastic Integral
 9.4 Itô Lemma
 9.5 Stochastic Differential Equations (SDEs)
 9.6 Examples of Stochastic Differential Equations
 9.7 Linear Systems of SDEs
 9.8 Some Relationship Between SDEs and Partial Differential Equations (PDEs)
 9.9 Euler Method for Approximating SDEs
 9.10 Random Vectors: Moments and Distributions
 9.11 Generating Multivariate (Gaussian) Distributions with Prescribed Covariance Structure
 9.12 Problems

3 Some Models Used in Quantitative Finance

Part III: Advanced Models for Underlying Assets
 10 Stochastic Volatility Models
 11 Jump Diffusion Models
 12 General Lévy Processes
 13 Generalized Lévy Processes, Long Range Correlations, and Memory Effects
 14 Approximating General Derivative Prices

15 Solutions to Complex Models Arising in the Pricing of Financial Options
 15.1 Introduction
 15.2 Option Pricing with Transaction Costs and Stochastic Volatility
 15.3 Option Price Valuation in the Geometric Brownian Motion Case with Transaction Costs
 15.4 Stochastic Volatility Model with Transaction Costs
 15.5 The PDE Derivation When the Volatility is a Traded Asset
 15.6 Problems
 16 Factor and Copulas Models
 Part IV: Fixed Income Securities and Derivatives
 Bibliography
 Index
 End User License Agreement
Product information
 Title: Quantitative Finance
 Author(s):
 Release date: December 2019
 Publisher(s): Wiley
 ISBN: 9781118629956
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