The course aims to provide the knowledge about some basic elements of financial mathematics, by introducing tools for the evaluation and estimation of financial operations in a risky environment. The theoretical tool to deal with the problem of building an optimal portfolio of risky assets will be provided. Definitions and evaluation methods of the most used derivatives (Futures and Options) must be known by the student and the end of the lessons. Finally, the course will provide some elements to look at the behavior of operators in financial markets through the lens of psychology and behavioral studies (behavioral finance).   

Part A (Evaluation in a risky environment)
Evaluation methos in a risky environment. The Mean Value theorem and the St.Petersbourg Paradox. The expected utility theory. Risk attitudes. Examples of utility functions. The Mean-Variance method. Risk-return analysis. Indifference curves. Isoutility curves in the M-V plane. 
The portfoflio theory. Optimal portfolio with two risky assets and with n risky assets. Optimal portfolio with n risky assets and a risk free asset (CAPM; Capital Asset Pricing Model). 

Part B (Financial Derivatives)
Forward contracts and markets. Futures contracts and their price. Options. American call and put options. Evaluation of Options (The Binomial model and the Black and Scholes model). 

Part C (Hints about Behavioral Finance) The Efficient markets hypothesis. Behavioral Finance. Examples of inefficient markets. Investors' biases. Fundamental and technical analysis. Models of behavioral finance. 

Learning outcomes and competences to be acquired

At the end of the course the student must have gained a good command of the financial mathematics topics discussed in the course. He/she will have to be able to properly carry out the studied methods to build an optimal portfolio and be able to understand the main features and the moest known financial derivatives.  

Knowledge and understanding

On the topics covered in the course, the financial sector, the student must acquire the knowledge for understanding the key financial variables and their use in the computation models. Examples and working mode are shown in the classroom during lessons and exercises.

Applying knowledge and understanding

At the end of the course the student must have acquired a good ability to use financial variables studied in situations similar to those presented in the course. He/she should be able to properly apply the studied formulation and be able to solve financial mathematical problems similar to those studied. In particular, he/she must be able to apply acquired knowledge even in contexts slightly different from those studied and have the ability to use the acquired knowledge to solve problems that may appear new. Examples of such applications are shown in the classroom during lessons and exercises.

Making judgements

At the end of the course, the student must have acquired a good ability to analyze subjects and problems of financial mathematics, the ability to critically evaluate solutions proposed for different problems, and to correctly interpret the related topics.

Communication skills

At the end of the course, the student must have acquired a good ability to clearly communicate considerations concerning problems of financial mathematics. The working mode is shown in the classroom during lessons and during the exercises.

Learning skills

At the end of the course the student must have acquired a good degree of autonomy in the study of discipline, reading and interpretation of financial data, in the search for useful information to deepen the knowledge of the discussed topics.

The teaching material prepared by the lecturer in addition to recommended textbooks (such as for instance slides, lecture notes, exercises, bibliography) and communications from the lecturer specific to the course can be found inside the Moodle platform › blended.uniurb.it

Teaching

Frontal lessons.

Innovative teaching methods

Debate - Flipped classroom

Course books

Part A:  Material shared by the teacher through the blended platform.

Part B: Chapters 1-7 of the book:

 Castellani G., De Felice M. and Moriconi F., Manuale di finanza III. Modelli stocastici e contratti derivati. Il Mulino. Last Edition.

Part C: Material on Behavioral Finance shared by the teacher through the blened platform.

Assessment

The exam consists in a written test. Students have 1h and 30 minutes to complete the test. The test is made by two theoretical open questions and an exercise on part A and two open theoretical questions and an exercise on parts B-C. The final rating is determined by summing up the marks (from 0 to 5 points) achieved in each question/exercise. The assessment of each answer is based on the different levels of knowledge of the subject matter: the knowledge of the meaning and the computation procedure and its correct application in the subject matter, the knowledge of theoretical arguments and proofs leading to the results.

Disability and Specific Learning Disorders (SLD)

Students who have registered their disability certification or SLD certification with the Inclusion and Right to Study Office can request to use conceptual maps (for keywords) during exams.

To this end, it is necessary to send the maps, two weeks before the exam date, to the course instructor, who will verify their compliance with the university guidelines and may request modifications.

Teaching

The same of Attending students.

Course books

The same of Attending students.

Assessment

The same of Attending students.

Disability and Specific Learning Disorders (SLD)

Students who have registered their disability certification or SLD certification with the Inclusion and Right to Study Office can request to use conceptual maps (for keywords) during exams.

To this end, it is necessary to send the maps, two weeks before the exam date, to the course instructor, who will verify their compliance with the university guidelines and may request modifications.

English material is available upon request.