Cerrato The Mathematics of Derivatives Securities with Applications in MATLAB

1. Auflage 2012
ISBN: 978-1-119-97341-6
Verlag: John Wiley & Sons
Format: EPUB
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 248 Seiten, E-Book

Reihe: Wiley Finance Series

Quantitative Finance is expanding rapidly. One of the aspects ofthe recent financial crisis is that, given the complexity offinancial products, the demand for people with high numeracy skillsis likely to grow and this means more recognition will be given toQuantitative Finance in existing and new course structuresworldwide. Evidence has suggested that many holders of complexfinancial securities before the financial crisis did not havein-house experts or rely on a third-party in order to assess therisk exposure of their investments. Therefore, this experienceshows the need for better understanding of risk associate withcomplex financial securities in the future.
The Mathematics of Derivative Securities with Applications inMATLAB provides readers with an introduction to probability theory,stochastic calculus and stochastic processes, followed bydiscussion on the application of that knowledge to solve complexfinancial problems such as pricing and hedging exotic options,pricing American derivatives, pricing and hedging under stochasticvolatility and an introduction to interest rates modelling.
The book begins with an overview of MATLAB and the variouscomponents that will be used alongside it throughout the textbook.Following this, the first part of the book is an in depthintroduction to Probability theory, Stochastic Processes and ItoCalculus and Ito Integral. This is essential to fully understandsome of the mathematical concepts used in the following part of thebook. The second part focuses on financial engineering and guidesthe reader through the fundamental theorem of asset pricing usingthe Black and Scholes Economy and Formula, Options Pricing throughEuropean and American style options, summaries of Exotic Options,Stochastic Volatility Models and Interest rate Modelling. Topicscovered in this part are explained using MATLAB codes showing howthe theoretical models are used practically.
Authored from an academic's perspective, the book discussescomplex analytical issues and intricate financial instruments in away that it is accessible to postgraduate students with or withouta previous background in probability theory and finance. It iswritten to be the ideal primary reference book or a perfectcompanion to other related works. The book uses clear and detailedmathematical explanation accompanied by examples involving realcase scenarios throughout and provides MATLAB codes for a varietyof topics.

Autoren/Hrsg.

Cerrato, Mario

Inhaltsverzeichnis

Chapter 1 Introduction.
Overview of MatLab.
Using various MatLab's toolboxes.
Mathematics with MatLab.
Statistics with MatLab.
Programming in MatLab.
Part 1.
Chapter 2 Probability Theory.
Set and sample space.
Sigma 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.
Appendix 1: Bernoulli law of large numbers.
Appendix 2: Conditional expectations.
Appendix 3: Hilbert spaces.
Chapter 3 Stochastic Processes.
Martingales processes.
Stopping times.
The optional stopping theorem.
Local martingales and semi-martingales.
Brownian motions.
Brownian motions and reflection principle.
Martingales separation theorem of Brownian motions.
Appendix 1: Working with Brownian motions.
Chapter 4 Ito Calculus and Ito Integral.
Quadratic variation of Brownian motions.
The construction of Ito integral with elementary process.
The general Ito integral.
Construction of the Ito integral with respect to semi-martingales integrators.
Quadratic variation and general bounded martingales.
Ito lemma and Ito formula.
Appendix 1: Ito Integral and Riemann-Stieljes integral.
Part 2.
Chapter 5 The Black and Scholes Economy and Black and Scholes Formula.
The fundamental theorem of asset pricing.
Martingales measures.
The Girsanov Theorem.
The Randon-Nikodym.
The Black and Scholes Model.
The Black and Scholes formula.
The Black and Scholes in practice.
The Feyman-Kac formula.
Appendix 1: The Kolmogorov Backword equation.
Appendix 2: Change of numeraire.
Chapter 6 Monte Carlo Methods for Options Pricing.
Basic concepts and pricing European style options.
Variance reduction techniques.
Pricing path dependent options.
Projections methods in finance.
Estimations of Greeks by Monte Carlo methods.
Chapter 7 American Option Pricing.
A review of the literature on pricing American put options.
Optimal stopping times and American put options.
A dynamic programming approach to price American options.
The Losgstaff and Schwartz (2001) approach.
The Glasserman and Yu (2004) approach.
Estimation of the upper bound.
Cerrato (2008) approach to compute upper bounds.
Chapter 8 Exotic Options.
Digital and binary.
Asian options.
Forward start options.
Barrier options.
Hedging barrier options.
Chapter 9 Stochastic Volatility Models.
Square root diffusion models.
The Heston Model.
Processes with jumps.
Monte Carlo methods to price derivatives under stochastic volatility.
Euler methods and stochastic differential equations.
Exact simulation of Greeks under stochastic volatility.
Computing Greeks for exotics using simulations.
Chapter 10 Interest Rate Modeling.
A general framework.
Affine models.
The Vasicek model.
The Cox, Ingersoll & Ross Model.
The Hull and White (HW) Model.
Bond options.

Über Autor(innen)

Mario Cerrato is a Senior Lecturer (Associate Professor)in Financial Economics at the University of Glasgow BusinessSchool. He holds a PhD in Financial Econometrics and an MSc inEconomics from London Metropolitan University, and a first degreein Economics from the University of Salerno. Mario's researchinterests are in the area of financial derivatives, security designand financial market microstructures. He has published in leadingfinance journals such as Journey of Money Credit and Banking,Journal of Banking and Finance, International Journal ofTheoretical and Applied Finance, and many others. He isgenerally involved in research collaboration with leading financialfirms in the City of London and Wall Street.