The Mathematics of Derivatives Securities with Applications in MATLAB (PDF)

Quantitative Finance is expanding rapidly. One of the aspects of
the recent financial crisis is that, given the complexity of
financial products, the demand for people with high numeracy skills
is likely to grow and this means more recognition will be given to
Quantitative Finance in existing and new course structures
worldwide. Evidence has suggested that many holders of complex
financial securities before the financial crisis did not have
in-house experts or rely on a third-party in order to assess the
risk exposure of their investments. Therefore, this experience
shows the need for better understanding of risk associate with
complex financial securities in the future.

The Mathematics of Derivative Securities with Applications in
MATLAB provides readers with an introduction to probability theory,
stochastic calculus and stochastic processes, followed by
discussion on the application of that knowledge to solve complex
financial problems such as pricing and hedging exotic options,
pricing American derivatives, pricing and hedging under stochastic
volatility and an introduction to interest rates modelling.

The book begins with an overview of MATLAB and the various
components that will be used alongside it throughout the textbook.
Following this, the first part of the book is an in depth
introduction to Probability theory, Stochastic Processes and Ito
Calculus and Ito Integral. This is essential to fully understand
some of the mathematical concepts used in the following part of the
book. The second part focuses on financial engineering and guides
the reader through the fundamental theorem of asset pricing using
the Black and Scholes Economy and Formula, Options Pricing through
European and American style options, summaries of Exotic Options,
Stochastic Volatility Models and Interest rate Modelling. Topics
covered in this part are explained using MATLAB codes showing how
the theoretical models are used practically.

Authored from an academic's perspective, the book discusses
complex analytical issues and intricate financial instruments in a
way that it is accessible to postgraduate students with or without
a previous background in probability theory and finance. It is
written to be the ideal primary reference book or a perfect
companion to other related works. The book uses clear and detailed
mathematical explanation accompanied by examples involving real
case scenarios throughout and provides MATLAB codes for a variety
of topics.