Written in a rigorous yet logical and easy to use style, spanning a range of disciplines, including business, mathematics, finance and economics, this comprehensive textbook offers a systematic, self-sufficient yet concise presentation of the main topics and related parts of stochastic analysis and statistical finance that are covered in the majority of university programmes.
Providing all explanations of basic concepts and results with proofs and numerous examples and problems, it includes:
- an introduction to probability theory
- a detailed study of discrete and continuous time market models
- a comprehensive review of Ito calculus and statistical methods as a basis for statistical estimation of models for pricing
- a detailed discussion of options and their pricing, including American options in a continuous time setting.
An excellent introduction to the topic, this textbook is an essential resource for all students on undergraduate and postgraduate courses and advanced degree programs in econometrics, finance, applied mathematics and mathematical modelling as well as academics and practitioners.
Table of Contents
1. Review of Probability Theory 2. Basics of Stochastic Theory 3. Discrete Time Market Models 4. Basics of Ito Calculus and Stochastic Analysis 5. Continuous Time Market Models 6. American Options and Binomial Trees 7. Implied and Historical Volatility 8. Review of Statistical Estimation 9. Estimation of Models for Stock Prices
Nikolai Dokuchaev is Associate Professor in the Department of Mathematics, Trent University, Ontario, Canada.
"The book provides a systematic, self-sufficient, and yet short presentation of the main topics of mathematical finance. …The book is suitable for undergraduate and graduate courses in mathematics, statistics, finance, and economics. It also provides fundamentals for further research and study in these fields."
—Pavel Stoynov, Zentralblatt MATH 1173