Description du cours
Intitulé de l'Unité d'Enseignement
Introduction to Financial Mathematics
Code de l'Unité d'Enseignement
2023 - 2024
Nombre de crédits
Objectifs et contribution de l'Unité d'Enseignement au programme
Finance offers a structured framework for making choices, and financial mathematics has become an indispensable tool for operating in a world where finance is taking on an important role. Indeed, the use of financial mathematics allows us to make decisions by arbitrating risk and profitability in an increasingly complex and uncertain context.
This course therefore teaches how to solve problems in order to make choices in a more transparent and value-based manner. But studying finance also means trying to understand the notion of value, much more than just money. Money is only a tool to measure value. Whereas finance is a much more fundamental search for what value is.
You will discover in this course a framework and tools to start evaluating a project, a business, a good idea,... To do so, you will use technology: calculators, excel, computers, etc. But what is most important is your understanding and mastery of the toolbox that we will build together.
The course is based on very practical applications and aims to present the different elements of financial calculation. The following topics will be covered: the different types of interest rates (simple and compound interest, equivalent and proportional interest rates); the difference between discounting and capitalization situations; methods for calculating the future value and the present value of a series of annuities; and the main fields of application of financial calculation. Methods for valuing and modelling financial returns and risks will also be discussed.
At the end of the course, the student should be able to:
• Understand and use basic mathematical tools (Course Form).
• Differentiate between the main financial products used in the course applications.
• Understand and distinguish the concepts of interest rate, return and risk.
• Estimate a return or risk related to a financial asset.
• Understand the time value of money by using the concepts of interest and discounting and by establishing a time line of flows.
• Discount and capitalize a series of flows.
• Evaluate simple financial assets
• To convert rates for periods less than one year.
• Establish a loan repayment plan by annual instalments according to different methods.
• Solve a situation by applying the mathematical tools taught.
• To choose between two investments using the financial selection criteria studied (NPV and IRR)
This course contributes to several Program Competency goals :
- It allows the student to acquire new knowledge and skills in finance (CG1)
- It provides the student with the tools to make responsible and thoughtful decisions (CG2)
Prérequis et corequis
None. However, it is advisable to have taken Mathematics and Statistics courses.
Description du contenu
The course is organized in 8 weeks of learning
Week 1 : Introduction & concept of interest rates
Week 2 : Discounting of a single feed
Week 3 : Discounting of flow sequences
Week 4 : Principle of the ordinary annuity
Week 5 : Perpetuities and other variations of the annuity
Week 6 : Undivided loans and amortization
Week 7 : Criteria for choosing investments (introduction)
Week 8 : Introduction to risky assets (equities) & statistical measures of risk
The course is given in classroom. The course explains the main concepts covered by the subject, applies them through numerous examples and presents several exercises to the student that he will have to solve during the course. Finally, it is composed of complementary exercises and corrected cases allowing the student to test the acquired knowledge.
In addition to the course slides and supporting videos, the book (in French) « Mathématique Financière » Devolder, Fox & Vaguener (2020), publié chez Pearson Education, may be a useful reference.
Formative evaluation: Exercises will be carried out in class to allow the student to directly test his understanding and ability to apply the concepts seen in the course. The student will also be required to complete 8 homework weekly assignments on moodle.
Summative evaluation: The course ends with a written exam organized in person on the date scheduled in the exam schedule established by the academic secretariat. The student will not be provided with any form (list of forms).
The evaluation criteria are based on the following points:
-Understanding of the problem exposed (e.g. drawing a flow timeline and identifying the variable to be estimated)
-Identification of the adequate resolution methods (Choice of formulas)
- Processing of statement data if necessary (e.g. calculating a rate, outstanding balance, ...)
- Use of the models necessary to deal with the given problem (calculation approaches)
- Resolution of the case/exercise (Calculation).
The objective of the evaluation is to test that the student has acquired the knowledge and know-how by having followed all the courses and completed the proposed exercises. During the evaluation and through the type of questions asked, the student will be asked to demonstrate:
1. That he has understood the content of the course, for example by testing the comprehension of the formulas and concepts covered in the course.
2. That he knows how to apply the knowledge in the resolution of exercises/cases put in context.
The exam questions will directly or indirectly test the student's understanding of the tools and the reasoning of the student through the choices he or she will make. The exam will cover the entire subject matter, so there will be at least one question per chapter of the course.
The content and method of evaluation will remain the same in the second session.
Benninga, S. (2008), Financial Modeling, 3rd edition, MIT Press.
Couppey-Soubeyran, J. (2010) Economie : les taux d'intérêt ou le prix du temps. Alternatives économiques, 11 (N°296).
DeFusco, R. , W. McLeavey, D. , Pinto, J.E. , and Runkle, D.E. (2007) Quantitative Methods for Investment Analysis, Second Edition, CFA Institute .
Devolder, P., M. Fox., F. Vaguener. (2016) Mathématiques financières, Pearson france.