Mathematical finance requires the use of advanced mathematical techniques drawn from the theory of probability, stochastic processes and stochastic differential equations. These areas are generally introduced and developed at an abstract level, making it problematic applying these techniques to practical issues in finance.
Problems and Solutions in Mathematical Finance Volume I: Stochastic Calculus is the first of a four-volume set of books focusing on problems and solutions in mathematical finance.
This volume introduces the reader to the basic stochastic calculus concepts required for the study of this important subject, providing a large number of worked examples which enable the reader to build the necessary foundation for more practical orientated problems in the later volumes. Through this application and by working through the numerous examples, the reader will properly understand and appreciate the fundamentals that underpin mathematical finance.
This book takes a dual approach using stochastic calculus to develop partial differentiation equations for pricing options and also constructs probability measures via martingale theory so that option prices can be expressed as expectations. Each chapter begins with an introduction to the fundamentals and the essential definitions and explanations needed to solve the subsequent problems.
Written mainly for students, industry practitioners and those involved in teaching in this field of study, Stochastic Calculus provides a valuable reference book to complement one’s further understanding of mathematical finance.
Eric Chin is a quantitative analyst at an investment bank in the City of London where he is involved in providing guidance on price testing methodologies and their implementation, formulating model calibration and model appropriateness on commodity and credit products. Prior to joining the banking industry he worked as a senior researcher at British Telecom investigating radio spectrum trading and risk management within the telecommunications sector. Eric Chin holds an MSc in Applied Statistics and an MSc in Mathematical Finance both from University of Oxford. He also holds a PhD in Mathematics from University of Dundee.
Dian Nel has more than 10 years of experience in the commodities sector. He currently works in the City of London where he specialises in oil and gas markets. He holds a BEng in Electrical and Electronic Engineering from StellenboschUniversity and an MSc in Mathematical Finance from ChristChurch, OxfordUniversity. He is a Chartered Engineer registered with the Engineering Council UK.
Sverrir Olafsson is Professor of Financial Mathematics at Reykjavik University; a Visiting Professor at QueenMaryUniversity, London and a director of Riskcon Ltd, a UK based risk management consultancy. Previously he was a Chief Researcher at BT Research and held academic positions at The Mathematical Departments of Kings College, London; UMIST Manchester and The University of Southampton. Dr Olafsson is the author of over 95 refereed academic papers and has been a key note speaker at numerous international conferences and seminars. He is on the editorial board of three international journals. He has provided an extensive consultancy on financial risk management and given numerous specialist seminars to finance specialists. In the last five years his main teaching has been MSc courses on Risk Management, Fixed Income, and Mathematical Finance.
Dr Olafsson has an MSc and PhD in mathematical physics from the Universities of Tübingen and Karlsruhe respectively.
1 General Probability and Statistical Theory
11 Introduction
12 Problems and Solutions
121 Probability Spaces
122 Discrete and Continuous Random Variables
123 Properties of Expectations
2 General Statistical Theory
21 Introduction
22 Problems and Solutions
221 Parameter Estimation
222 Hypotheses Testing
223 Goodness of Fit Analysis
224 Regression Analysis
3 Wiener Process
31 Introduction
32 Problems and Solutions
321 Random Walks
322 Examples of Wiener Process
323 Markov Property
324 Martingale Property
325 First Passage Time
326 Reflection Principle
327 Quadratic Variation
4 Stochastic Differential Equations
41 Introduction
42 Problems and Solutions
421 Ito Calculus
422 One-Dimension Diffusion Process
423 Multi-Dimensional Diffusion Process
5 Change of Measure
51 Introduction
52 Problems and Solutions
521 Martingale Representation Theorem
522 Girsanov's Theorem
523 Risk Neutral Measure
6 Poisson Process
61 Introduction
62 Problems and Solutions
621 Properties of Poisson Process
622 Jump Diffusion Process
623 Change of Measure
Appendix A Mathematics Formulae
Appendix B Probability Theory Formulae
Appendix C Statistical Theory Formulae
Appendix D Differential Equations Formulae
