The Mathematics of Derivatives Securities with Applications in MATLAB
(Sprache: Englisch)
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...
Leider schon ausverkauft
versandkostenfrei
Buch (Kartoniert)
51.90 €
25 DeutschlandCard Punkte
sammeln
- Lastschrift, Kreditkarte, Paypal, Rechnung
- Kostenlose Rücksendung
- Ratenzahlung möglich
Produktdetails
Produktinformationen zu „The Mathematics of Derivatives Securities with Applications in MATLAB “
Klappentext zu „The Mathematics of Derivatives Securities with Applications in MATLAB “
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.
Inhaltsverzeichnis zu „The Mathematics of Derivatives Securities with Applications in MATLAB “
Preface xi1 An Introduction to Probability Theory 1
1.1 The Notion of a Set and a Sample Space 1
1.2 Sigma Algebras or Field 2
1.3 Probability Measure and Probability Space 2
1.4 Measurable Mapping 3
1.5 Cumulative Distribution Functions 4
1.6 Convergence in Distribution 5
1.7 Random Variables 5
1.8 Discrete Random Variables 6
1.9 Example of Discrete Random Variables: The Binomial Distribution 6
1.10 Hypergeometric Distribution 7
1.11 Poisson Distribution 8
1.12 Continuous Random Variables 9
1.13 Uniform Distribution 9
1.14 The Normal Distribution 9
1.15 Change of Variable 11
1.16 Exponential Distribution 12
1.17 Gamma Distribution 12
1.18 Measurable Function 13
1.19 Cumulative Distribution Function and Probability Density Function 13
1.20 Joint, Conditional and Marginal Distributions 17
1.21 Expected Values of Random Variables and Moments of a Distribution 19
2 Stochastic Processes 25
2.1 Stochastic Processes 25
2.2 Martingales Processes 26
2.3 Brownian Motions 29
2.4 Brownian Motion and the Reflection Principle 32
2.5 Geometric Brownian Motions 35
3 Ito Calculus and Ito Integral 37
3.1 Total Variation and Quadratic Variation of Differentiable Functions 37
3.2 Quadratic Variation of Brownian Motions 39
3.3 The Construction of the Ito Integral 40
3.4 Properties of the Ito Integral 41
3.5 The General Ito Stochastic Integral 42
3.6 Properties of the General Ito Integral 43
3.7 Construction of the Ito Integral with Respect to Semi-Martingale Integrators 44
3.8 Quadratic Variation of a General Bounded Martingale 46
4 The Black and Scholes Economy 55
4.1 Introduction 55
4.2 Trading Strategies and Martingale Processes
... mehr
55
4.3 The Fundamental Theorem of Asset Pricing 56
4.4 Martingale Measures 58
4.5 Girsanov Theorem 59
4.6 Risk-Neutral Measures 62
5 The Black and Scholes Model 67
5.1 Introduction 67
5.2 The Black and Scholes Model 67
5.3 The Black and Scholes Formula 68
5.4 Black and Scholes in Practice 70
5.5 The Feynman-Kac Formula 71
6 Monte Carlo Methods 79
6.1 Introduction 79
6.2 The Data Generating Process (DGP) and the Model 79
6.3 Pricing European Options 80
6.4 Variance Reduction Techniques 81
7 Monte Carlo Methods and American Options 91
7.1 Introduction 91
7.2 Pricing American Options 91
7.3 Dynamic Programming Approach and American Option Pricing 92
7.4 The Longstaff and Schwartz Least Squares Method 93
7.5 The Glasserman and Yu Regression Later Method 95
7.6 Upper and Lower Bounds and American Options 96
8 American Option Pricing: The Dual Approach 101
8.1 Introduction 101
8.2 A General Framework for American Option Pricing 101
8.3 A Simple Approach to Designing Optimal Martingales 104
8.4 Optimal Martingales and American Option Pricing 104
8.5 A Simple Algorithm for American Option Pricing 105
8.6 Empirical Results 106
8.7 Computing Upper Bounds 107
8.8 Empirical Results 109
9 Estimation of Greeks using Monte Carlo Methods 113
9.1 Finite Difference Approximations 113
9.2 Pathwise Derivatives Estimation 114
9.3 Likelihood Ratio Method 116
9.4 Discussi
4.3 The Fundamental Theorem of Asset Pricing 56
4.4 Martingale Measures 58
4.5 Girsanov Theorem 59
4.6 Risk-Neutral Measures 62
5 The Black and Scholes Model 67
5.1 Introduction 67
5.2 The Black and Scholes Model 67
5.3 The Black and Scholes Formula 68
5.4 Black and Scholes in Practice 70
5.5 The Feynman-Kac Formula 71
6 Monte Carlo Methods 79
6.1 Introduction 79
6.2 The Data Generating Process (DGP) and the Model 79
6.3 Pricing European Options 80
6.4 Variance Reduction Techniques 81
7 Monte Carlo Methods and American Options 91
7.1 Introduction 91
7.2 Pricing American Options 91
7.3 Dynamic Programming Approach and American Option Pricing 92
7.4 The Longstaff and Schwartz Least Squares Method 93
7.5 The Glasserman and Yu Regression Later Method 95
7.6 Upper and Lower Bounds and American Options 96
8 American Option Pricing: The Dual Approach 101
8.1 Introduction 101
8.2 A General Framework for American Option Pricing 101
8.3 A Simple Approach to Designing Optimal Martingales 104
8.4 Optimal Martingales and American Option Pricing 104
8.5 A Simple Algorithm for American Option Pricing 105
8.6 Empirical Results 106
8.7 Computing Upper Bounds 107
8.8 Empirical Results 109
9 Estimation of Greeks using Monte Carlo Methods 113
9.1 Finite Difference Approximations 113
9.2 Pathwise Derivatives Estimation 114
9.3 Likelihood Ratio Method 116
9.4 Discussi
... weniger
Autoren-Porträt von Mario Cerrato
Mario Cerrato, Glasgow, Scotland is a Lecturer in Economics at the University of Glasgow, Department of Economics. He previously held posts at London Metropolitan University, Banca del Salento and Expedia Capital Management Ltd. He has been actively involved in various consultancies in the area of financial engineering over the last five years. He has published numerous articles in the area of financial econometrics and financial derivatives in international journals like the International Journal of Finance & Economics, International Journal of Theoretical and Applied Finance, Computational Statistics and Data Analysis.
Bibliographische Angaben
- Autor: Mario Cerrato
- 2011, 1. Auflage, 512 Seiten, Maße: 15,8 x 23,1 cm, Kartoniert (TB), Englisch
- Verlag: Wiley & Sons
- ISBN-10: 0470683694
- ISBN-13: 9780470683699
Sprache:
Englisch
Pressezitat
"The book can be warmly recommended to readers who wish to learn the main methods of quantitative finance without delving into its mathematical foundations." ( Zentralblatt MATH , 1 December 2012)Kommentar zu "The Mathematics of Derivatives Securities with Applications in MATLAB"
0 Gebrauchte Artikel zu „The Mathematics of Derivatives Securities with Applications in MATLAB“
| Zustand | Preis | Porto | Zahlung | Verkäufer | Rating |
|---|
Schreiben Sie einen Kommentar zu "The Mathematics of Derivatives Securities with Applications in MATLAB".
Kommentar verfassen