Description
This book is intended for students at the advanced undergraduate level or PhD level who want to develop professional skills in statistics with applications towards finance. The basis for this book is lecture notes written for a course “Statistics in Finance” at the Technical University of Denmark (DTU). Those notes were also used later in a related course at Lund University, now as a part of larger package of courses covering financial economics, risk management and financial mathematics.
The purpose of this book is to bridge the gap between on one hand classical books on financial mathematics that typically provide a rigorous treatment of the topic, but rarely connects the data, and on the other hand books on econometrics or time series analysis that do not cover the specific problems related to option valuation. We also include examples on how the statistical tools can be used to improve, e.g., Value at Risk calculations.
There is of course a risk that a book trying to cover several fields will become a “Jack of all trades, master of none”, but our intention has been not only to cover different fields, but also to integrate them through examples, case studies and cross references throughout the book, thereby adding value beyond each part. In fact, the extended version of that quote is
Jack of all trades, master of none
Often times better than a master of one
A consequence of this design choice is that complete formal proofs seldom are presented. Instead, we either provide a reference to a source where the full proof can be found or try to make it plausible by presenting the main ideas of the proof, but skipping the technical details.
The book can be used for several different courses. It can be used for a course on financial econometrics, starting with a brief introduction of stylized facts in finance (Chapter 1), followed by statistical methods in discrete time (Chapters 4, 5 and 6), continuous time (Chapters 12, 13) and, finally, partially observed models in discrete and continuous time (Chapter 14).
It can also form the basis for a course on financial mathematics with an introduction to the problems (Chapters 1, 2 and 3) and then move over to continuous time problems using Brownian motions or jump process (Chapters 7 and 8), followed by applications in security markets (Chapter 9) and interest rate markets (Chapters 10 and 11). It would also be possible to include the numerical schemes in Chapter 12 if that course also has some computational elements. Chapter 14 also presents some cases on how options or bonds can be calibrated to market data.
We still believe, however, that the book as a whole contains values that are lost when using only a subset of the content. The integration of different topics leads to new insights and will ideally inspire new research. For example additional complexity in option valuation models can easily be motivated by statistical findings in Chapter 1, while advanced option valuation models are partly responsible for sparking an interest in statistics for partially observed models in Chapter 14.
Many people have helped with the development of the text over the years, Former students taking the course have been an especially excellent source of constructive feedback. The text has also been improved on by suggestions and feedback from former and current colleagues, where we especially would like to thank (in alphabetical order) Stefan I. Adalbjörnsson, Carl Åkerlindh, Mikkel Baadsgaard, Jan-Emil Banning Iversen, Jingyi Guo, Jan Holst, Josef Höök, Michael Preisel, Johan Svärd, and Magnus Wiktorsson. Without their help, the text would not have been what it is today!