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Mathematics of Derivatives Securities with Applications in MATLAB

ISBN-10: 0470683694

ISBN-13: 9780470683699

Edition: 2012

Authors: Mario Cerrato

List price: $42.50
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Description:

The book is divided into two parts the first part introduces probability theory, stochastic calculus and stochastic processes before moving on to the second part which instructs readers on how to apply the content learnt in part one to solve complex financial problems such as pricing and hedging exotic options, pricing American derivatives, pricing and hedging under stochastic volatility, and interest rate modelling. Each chapter provides a thorough discussion of the topics covered with practical examples in MATLAB so that readers will build up to an analysis of modern cutting edge research in finance, combining probabilistic models and cutting edge finance illustrated by MATLAB applications.Most books currently available on the subject require the reader to have some knowledge of the subject area and rarely consider computational applications such as MATLAB. This book stands apart from the rest as it covers complex analytical issues and complex financial instruments in a way that is accessible to those without a background in probability theory and finance, as well as providing detailed mathematical explanations with MATLAB code for a variety of topics and real world case examples. Contents: Chapter 1 IntroductionOverview of MatLabUsing various MatLab 's toolboxesMathematics with MatLabStatistics with MatLabProgramming in MatLab Part 1 Chapter 2 Probability Theory Set and sample spaceSigma algebra, probability measure and probability space Discrete and continuous random variables Measurable mapping Joint, conditional and marginal distributions Expected values and moment of a distribution 
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Book details

List price: $42.50
Copyright year: 2012
Publisher: John Wiley & Sons, Limited
Publication date: 2/20/2012
Binding: Hardcover
Pages: 248
Size: 6.25" wide x 9.00" long x 1.00" tall
Weight: 1.100
Language: English

Preface
An Introduction to Probability Theory
The Notion of a Set and a Sample Space
Sigma Algebras or Field
Probability Measure and Probability Space
Measurable Mapping
Cumulative Distribution Functions
Convergence in Distribution
Random Variables
Discrete Random Variables
Example of Discrete Random Variables: The Binomial Distribution
Hypergeometric Distribution
Poisson Distribution
Continuous Random Variables
Uniform Distribution
The Normal Distribution
Change of Variable
Exponential Distribution
Gamma Distribution
Measurable Function
Cumulative Distribution Function and Probability Density Function
Joint, Conditional and Marginal Distributions
Expected Values of Random Variables and Moments of a Distribution
The Bernoulli Law of Large Numbers
Conditional Expectations
Stochastic Processes
Stochastic Processes
Martingales Processes
Brownian Motions
Brownian Motion and the Reflection Principle
Geometric Brownian Motions
An Application of Brownian Motions
Ito Calculus and Ito Integral
Total Variation and Quadratic Variation of Differentiable Functions
Quadratic Variation of Brownian Motions
The Construction of the Ito Integral
Properties of the Ito Integral
The General Ito Stochastic Integral
Properties of the General Ito Integral
Construction of the Ito Integral with Respect to Semi-Martingale Integrators
Quadratic Variation of a General Bounded Martingale
Quadratic Variation of a General Bounded Martingale
Ito Lemma and Ito Formula
The Riemann-Stieljes Integral
The Black and Scholes Economy
Introduction
Trading Strategies and Martingale Processes
The Fundamental Theorem of Asset Pricing
Martingale Measures
Girsanov Theorem
Risk-Neutral Measures
The Randon-Nikodym Condition
Geometric Brownian Motion
The Black and Scholes Model
Introduction
The Black and Scholes Model
The Black and Scholes Formula
Black and Scholes in Practice
The Feynman-Kac Formula
The Kolmogorov Backward Equation
Change of Numeraire
Black and Scholes and the Greeks
Monte Carlo Methods
Introduction
The Data Generating Process (DGP) and the Model
Pricing European Options
Variance Reduction Techniques
Antithetic Variate Methods
Control Variate Methods
Common Random Numbers
Importance Sampling
Monte Carlo European Options
Variance Reduction Techniques - First Part
Monte Carlo 1
Monte Carlo 2
Monte Carlo Methods and American Options
Introduction
Pricing American Options
Dynamic Programming Approach and American Option Pricing
The Longstaff and Schwartz Least Squares Method
The Glasserman and Yu Regression Later Method
Upper and Lower Bounds and American Options
Multiassets Simulation
Pricing a Basket Option Using the Regression Methods
American Option Pricing: The Dual Approach
Introduction
A General Framework for American Option Pricing
A Simple Approach to Designing Optimal Martingales
Optimal Martingales and American Option Pricing
A Simple Algorithm for American Option Pricing
Empirical Results
Computing Upper Bounds
Empirical Results
Estimation of Greeks using Monte Carlo Methods
Finite Difference Approximations
Pathwise Derivatives Estimation
Likelihood Ratio Method
Discussion
Pathwise Greeks using Monte Carlo
Exotic Options
Introduction
Digital Options
Asian Options
Forward Start Options
Barrier Options
Hedging Barrier Options
Digital Options
Pricing and Hedging Exotic Options
Introduction
Monte Carlo Simulations and Asian Options
Simulation of Greeks for Exotic Options
Monte Carlo Simulations and Forward Start Options
Simulation of the Greeks for Exotic Options
Monte Carlo Simulations and Barrier Options
The Price and the Delta of Forward Start Options
The Price of Barrier Options Using Importance Sampling
Stochastic Volatility Models
Introduction
The Model
Square Root Diffusion Process
The Heston Stochastic Volatility Model (HSVM)
Processes with Jumps
Application of the Euler Method to Solve SDEs
Exact Simulation Under SV
Exact Simulation of Greeks Under SV
Stochastic Volatility Using the Heston Model
Implied Volatility Models
Introduction
Modelling Implied Volatility
Examples
Local Volatility Models
An Overview
The Model
Numerical Methods
An Introduction to Interest Rate Modelling
A General Framework
Affine Models (AMs)
The Vasicek Model
The Cox, Ingersoll and Ross (CIR) Model
The Hull and White (HW) Model
The Black Formula and Bond Options
Interest Rate Modelling
Some Preliminary Definitions
Interest Rate Caplets and Floorlets
Forward Rates and Numeraire
Libor Futures Contracts
Martingale Measure
Binomial and Finite Difference Methods
The Binomial Model
Expected Value and Variance in the Black and Scholes and Binomial Models
The Cox-Ross-Rubinstein Model
Finite Difference Methods
The Binomial Method
An Introduction to MATLAB
What is MATLAB?
Starting MATLAB
Main Operations in MATLAB
Vectors and Matrices
Basic Matrix Operations
Linear Algebra
Basics of Polynomial Evaluations
Graphing in MATLAB
Several Graphs on One Plot
Programming in MATLAB: Basic Loops
M-File Functions
MATLAB Applications in Risk Management
MATLAB Programming: Application in Financial Economics
Mortgage Backed Securities
Introduction
The Mortgage Industry
The Mortgage Backed Security (MBS) Model
The Term Structure Model
Preliminary Numerical Example
Dynamic Option Adjusted Spread
Numerical Example
Practical Numerical Examples
Empirical Results
The Pre-Payment Model
Value at Risk
Introduction
Value at Risk (VaR)
The Main Parameters of a VaR
VaR Methodology
Historical Simulations
Variance-Covariance Method
Monte Carlo Method
Empirical Applications
Historical Simulations
Variance-Covariance Method
Fat Tails and VaR
Generalized Extreme Value and the Pareto Distribution
Bibliography
References
Index