FINANCIAL MATHEMATICS

This course aims to introduce students to the fundamental concepts of financial mathematics and to provide them the quantitative tools for the solution of financial problems under certainty.

Having passed the first-year Mathematics course and remember what you learned in that course. Know how to use basic Excel.

Knowledge and understanding: the student will learn the theoretical elements for a correct methodological approach to quantitative finance problems in order to understand their relevant terms and characteristics; he will be able to use problem-solving techniques. Applying knowledge and understanding: the student will be able to solve issues related to financial assessments in the economic and business environment, so that he or she can make a rational choice between several alternatives and decide the best of several options. The exercises carried out during the course aim to use theoretical tools to arrive at clear numerical evaluations. Criticism of judgment: the student will be aware of the results obtained through the knowledge of the theoretical/technical procedures followed to achieve them; he/she will be able to formulate autonomous and objective judgements and will be able to recognize wrong or inefficient solutions in an economic-firm logic. Communication skills: the student will learn to communicate in a simple, unambiguous and clear way the results achieved, even and especially if they are the result of complex procedures and also to people with different cultural backgrounds, in order to facilitate the exchange of information in an efficient way. Learning skills: the student will be able to carry out the activities of financial evaluator in the business and economic field, making use of the lessons of theory and applications carried out in the computer lab, enriched by interactions with the teacher.

Financial operations. Actuarial methods for calculating interests and discounts. Effective rates. Nominal rates. Capital markets. Term structure of prices and interest rates in capital markets. Yield to maturity. Annuities. Present value and accumulated value of an annuity. Annuities classification. Problems concerning constant annuities: determining present value, amounts to pay, number of payments, interest rate. Debt securities: bonds. Bootstrapping. Time and variability indexes. Evaluating and selecting economic-financial projects. Selection criteria: N.P.V., Final Value, T.R.M. and I.R.R. Amortizing a loan. Elementary approach vs. financial approach. Usufruct and bare ownership. Amortization methods. Setting-up a capital.

C. Crenca, P. Fersini, G. Melisi, G. Olivieri, M. Pelle, Elementi di Matematica Finanziaria - Pearson Italia, I ed – Marzo 2018 Additional material on the website learn.luiss.it

Theoretical frontal lesson. Theoretical and practical frontal lesson (learning by doing). Online lesson. Periodic online test. Exercise, with division of students into groups, for the application of theory to the solution of practical problems with the use of Excel.

The methods for verifying learning for 2nd year students will consist of: a) ongoing assessment of the students' ability to set up and solve the exercises. All students, divided into groups, will have to solve the exercises assigned to them every week and, in turn, explain their progress by interacting with the TA. Each group will be evaluated both in the theoretical bases and in the numerical application and the evaluation will weigh for 30% of the final grade. b) written test (compulsory) to be taken in person (or online according to the university guidelines) in the official exam sessions: specifically 3/4 Excel exercises in 90 minutes, aimed at assessing the understanding and the ability to solve the fundamental problems of financial mathematics; the results of the written test will weigh 35% on the final evaluation. c) oral exam (mandatory) to be taken in person (or online according to university guidelines) in the official exam sessions: questions on the theory topics covered during the course. The evaluation of the oral exam will account for 35% of the final grade. The final evaluation of the oral exam will contribute, to the extent of 10% (out of the total 35%), the ongoing evaluations that each student will obtain by answering the questions administered weekly on Moodle, concerning the topics covered. It should be noted that, with reference to the conduct of the ongoing theory tests on Moodle, they consist of multiple choice questions and the following rules apply: A) it is not possible to go back (navigate) during the test B) wrong answer: -0.2 answer not given: 0 correct answer: +1 The ongoing activities (exercises with Excel and tests on Moodle) must be carried out by students for at least 80% of both. Those who do not respect this constraint, or who refuse the evaluation attributed by the teacher to the ongoing activity on excel and / or on moodle, will carry out the final written and oral tests respectively with a greater number of exercises for the same time and a greater number of questions, respectively. The evaluation of each test will weigh for 50% of the final mark. For all students of previous years, the rules in force in the year in which the course was followed apply.

The final paper will be awarded on the basis of the evaluation of the interest and skills shown by the candidate in relation to the topics of Financial Mathematics and in particular of their applications in the economic and business fields.