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The book is organized as follows:
In Chapter 1, we introduce the basic concepts, definitions and practice
in financial markets. The main objects of study of mathematical finance
are defined, namely stocks, bonds and options.
In Chapter 2, we outline the mathematics that we need and explain
hypermodel approaches to modelling.
In Chapter 3, the absence of arbitrage, the main assumption behind
mathematical finance, is developed through the use of hypermodels, from
it the Black-Scholes type equations for options can be derived.
In Chapter 4, explicit solution to European option pricing and that of
European barrier option are derived.
In Chapter 5, the binary tree hypermodel approach, based on the Cox-
Ross-Rubinstein theory is developed, and pricing formulas are derived. Numerical
examples for various options are given.
In Chapter 6, further applications to the Greeks and the term structure
of interest rates are given. Of particular interest is the simple derivation of
the Malliavin weight formula from the hypermodel.
Chapter 7 is an independent unit that gives more complete coverage
of the mathematics behind hypermodels, i.e. infinitesimal analysis. This
chapter is intended for readers who are mathematically matured and interested
in knowing more the mathematical background.
Chapter 8 contains various kind of MATHEMATICA programs that practitioners
may easily adapt for their own purpose.
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