Mathematical Finance is a reference text encompassing a variety of topics in finance. These topics are divided into deterministic and stochastic. The deterministic part talks about our general perception of finance, trying to help us understand the universal financial laws, while the second, stochastic, part discusses the dynamics of these financial laws and how to measure and manage them.
After a bit of an introduction of what is an object of mathematical finance, the first part of the book discusses financial laws, financial operations, annuities, amortization and funding for loans as well as term structures and time and variability indicators. The discussion is purely mathematical, leaving very little space for general intuition. This is acceptable, since after all this is a reference book. The authors go into detail describing the actual computation behind the mathematics. This is done by mimicking Excel, i.e. writing steps to be performed in Excel. It does serve the purpose, as it provides a way to really understand the written theory.
The second part of the book is about stochastic models. Naturally, the section starts by introducing the needed probability theory: Markov chains, semi-Markov processes and stochastic calculus are introduced prior to starting the applied section. As the titles suggest this is a strictly theoretical presentation of the topics. The rest of the book mainly deals with option theory and credit risk. The mathematical presentation is again fully supported with numerical examples and illustrations. Credit risk is mainly concentrated on Merton’s model and the construction of ratings.
Being a reference book, Mathematical Finance is very technical and requires a reasonable level of knowledge in the area of finance, mathematics, probability and statistics. Computationally, it is not demanding as the Excel computations can be easily performed while reading the book.
Ita Cirovic Donev holds a Masters degree in statistics from Rice University. Her main research areas are in mathematical finance; more precisely, statistical methods for credit and market risk. Apart from the academic work she does statistical consulting work for financial institutions in the area of risk management.