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The Mathematics of Derivatives Securities with Applications in MATLAB

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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.

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